geroski - 2000 - models of technology diffusion

.Research Policy 29 2000 603625www.elsevier.nlrlocatereconbase

Models of technology diffusionP.A. Geroski )

London Business School, Sussex Place, Regents Park, London NW 4SA, UK

Abstract

The literature on new technology diffusion is vast, and it spills over many conventional disciplinary boundaries. Thispaper surveys the literature by focusing on alternative explanations of the dominant stylized fact: that the usage of newtechnologies over time typically follows an S-curve. The most commonly found model which is used to account for thismodel is the so-called epidemic model, which builds on the premise that what limits the speed of usage is the lack ofinformation available about the new technology, how to use it and what it does. The leading alternate model is often calledthe probit model, which follows from the premise that different firms, with different goals and abilities, are likely to want toadopt the new technology at different times. In this model, diffusion occurs as firms of different types gradually adopt it.There are actually many ways to generate an S-curve, and the third class of models which we examine are models of densitydependence popularized by population ecologists. In these models, the twin forces of legitimation and competition help toestablish new technologies and then ultimately limit their take-up. Finally, we look at models in which the initial choicebetween different variants of the new technology affect the subsequent diffusion speed of the chosen technology. Suchmodels often rely on information cascades, which drive herd like adoption behaviour when a particular variant is finallyselected. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Technology diffusion; Epidemics; Probit models; Density dependence; Information cascades

1. Introduction

It is not easy to understand why things sometimestake a long time to happen, particularly when oneviews events with the benefit of 20:20 hindsight. Inpart, this lack of understanding is a reflection of howwe think about social phenomena. For economists

and others who use comparative statics or equilib-.rium analysis to answer questions about what will

) Tel.: q44-171-262-5050; fax: q44-171-402-0718; e-mail:[email protected]

happen in given circumstances and why, the questionof when that thing will occur is often not evenregarded as an interesting question to ask. The prob-lem of understanding how long things take to happenalso reflects the inherent difficulty of the question:social phenomena involve many people makingchoices, often in an interdependent manner, and

there are no basic reference points like the speed of.light which can be used as a metric to measure the

passage of time in such processes. Unlike moleculeswhich act and react mechanically, people try to thinkbefore they act and this can be a very slow andunpredictable business for some of them.

0048-7333r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. .PII: S0048-7333 99 00092-X

( )P.A. GeroskirResearch Policy 29 2000 603625604

The diffusion of new technology is a good exam-ple of this problem. Sometimes it seems to take anamazingly long period of time for new technologiesto be adopted by those who seem most likely tobenefit from their use. The literature which tries toexplain why this happens is enormous, and it sprawlsover several disciplinary boundaries. For many, thequestion of why things diffuse slowly has becomevery focused on a single stylized fact about thatslowness, namely that the time path of usage usuallyfollows an S-curve: diffusion rates first rise and thenfall over time, leading to a period of relatively rapidadoption sandwiched between an early period ofslow take up and a late period of slow approach tosatiation. My goal in this paper is examine how wetypically think about what gives rise to S-curvediffusion patterns. 1 Mental models often have anamazingly powerful effect on how people think aboutparticular phenomena, an effect that is sometimesstimulating and sometimes limiting. The premisebehind this particular survey is the thought that if weare going to think creatively about public policiestoward diffusion, we may need to think reflectivelyabout how we think about technology diffusion.

The plan is as follows. Probably the most popularexplanation of S-curve is an epidemic model ofinformation diffusion, while the leading alternative isa probit model which argues that differences inadoption time reflect differences in the goals, needsand abilities of firms. I will explore these two waysof thinking about diffusion in Sections 2 and 3below. I will also explore two other ways of thinkingabout diffusion. The first is drawn from the literatureon organizational ecology, and argues that the pri-mary drivers of S-curves are the processes of legiti-mation and competition. The second is as much amodel of technology choice as it is one of technol-ogy diffusion, and it is based on the phenomena ofinformation cascades, aided and abetted by networkexternalities. These last two models will be exploredin Sections 4 and 5. I will close with some final

1 For recent surveys of this literature, see Metcalfe 1981;. . .1988 , Stoneman 1983; 1987 , Thirtle and Ruttan 1987 ,

. .Karshenas and Stoneman 1995 , Vickery and Northcott 1995 , .Baptista 1999 and others.

reflections on what all of this might mean for tech-nology policy in Section 6.

2. Epidemic models

The central feature of most discussions of tech-nology diffusion is the apparently slow speed atwhich firms adopt new technologies. 2 If a newtechnology really is a significant improvement overexisting technologies, it is important to ask whysome firms shift over to it more slowly than otherfirms. Possibly the most obvious explanation is thatthey just find out about the new technology laterthan other firms do. If this is truly the case, one islikely to learn a lot about the time path of technologydiffusion by studying the spread of information aboutit.

Suppose that there are N potential users of a newtechnology, and that each adopts the technology

3 .when hershe hears about it. At time t, y t firms .4have adopted and Nyy t have not. Suppose fur-

ther that information is transmitted from some cen-tral source, reaching a% of the population eachperiod. If as1, then the source contacts all Npotential users in the first period, and diffusion isinstantaneous. If, on the other hand, a-1, theninformation spreads gradually and so, therefore, doesusage of the new technology. A transmitter that

2 .Mansfield 1989 for example, observed the following timesfor half the population of potential users to adopt new technolo-gies: by-product coke ovens, 15 years; centralized traffic control,14 years; car retarders and continuous annealing, 13 years; indus-trial robots, 12 years; and diesel locomotives, 9 years. At the otherend of the spectrum are: tin containers, 1 year; continuous miningmachines, 3 years; and numerically controlled machine tools,shuttle cars and pallet loading machines, 5 years.

3 I have in mind that the unit of adoption is the firm, so that .y t measures the number of firms using the new technology.

However, firms rarely fully adopt a new technology meaning thatinter-firm diffusion often happens simultaneously with intra-firm

.diffusion . In the literature, some models focus on the outputproduced by firms using the new technology, or the market sharethat output represents. I am also going to talk as if it were a singleartefact that was diffusing. In fact, subsequent developments ofthe original artefact often generate a sequence of artefacts whichdiffuse over time.

( )P.A. GeroskirResearch Policy 29 2000 603625 605

contacts a% of the current population of non-users, .4Nyy t , at time t over the time interval D t

. .increases awareness or usage by an amount D y t .4sa Nyy t D t, and, taking the limit as D t0

and solving for the time path of usage,

w xy t sN 1yexp ya t . 1 4 . .

.Eq. 1 is a modified exponential function and Fig. 1 .plots its time path see the curve labelled A . Clearly,

smaller a means slower diffusion and smaller num- .ber of users at any time given that there are y 0

.initial users . What is equally clear is that this partic-ular information diffusion process does not producethe S-curve we expected to observe: it lacks an

initial convex segment curve B in Fig. 1 is S-.shaped .

This kind of model of information diffusion is notan implausible story of how people become aware ofa new yoghurt product or news about the fall of theBerlin Wall. However, technology adoption oftentakes an order of magnitude longer than it takes for

information to spread. To understand what lies be-hind this difference, it is useful to draw a distinctionbetween the hardware and the software as-

.pects of new technology Rogers, 1995, p. 12 . Thehardware is the tool, machine or physical object thatembodies the technology, while the software is theinformation base needed to use it effectively. Al-though some of the software can be transmittedimpersonally through a users manual, much of thesoftware of a particular technology is built up fromthe experience of using it, and at least some of thatvaluable knowledge will be tacit. As a consequence,it must be transmitted from person to person, andcannot effectively be broadcast from a commonsource. Thus, while the common source model em-

.bodied in Eq. 1 may usefully describe the transmis-sion of information about the existence of a newhardware, it may not accurately trace flows of infor-mation about the associated software. And, withoutgood software knowledge, many potential users willnot adopt the new technology, however aware theyare of its existence.

. .Fig. 1. Plots of the modified exponential A and logistic B diffusion functions.


To pass on software knowledge, potential usersneed to be able to communicate directly with currentusers who have accumulated experience with thenew technology. This suggests that software knowl-edge may often follow a word of mouth informationdiffusion process in which the main source of infor-mation is previous users. Suppose that each existinguser independently contacts a non-user with proba-

.bility b. If there are y t current users, then theprobability that contact will be made with one of the .4 .Nyy t current non-users is b y t , meaning thatusage will increase over the interval D t by an amount

. . .4D y t sb y t Nyy t D t. Assuming that there are .y 0 )0 initial users, taking the limit as D t0 and

solving for the time path of usage yields

y1w xy t sN 1qf exp yk t , 2 4 . .

.. . .where kbN and f Nyy 0 ry 0 . Eq. 2 isa logistic function and Fig. 1 plots its time path see

.curve B . Smaller values of b mean smaller values .of k for a given population, N and, therefore,

slower diffusion. It is clear that, unlike the commonsource model discussed above, this model traces outan S-curve over time: the rate of infection gradually

rises as the population of users gradually rises,increasing the aggregate stock of software informa-

.tion that can be passed on until it hits a maximum atNr2, and then it declines as non-users get increas-

.ingly hard to find and, therefore, to infect . As Fig. 1shows, this means that while usage increases year byyear over time, it does so more rapidly in the earlyyears after the introduction of a new technology thanit does after the technology has become fairly wellestablished.

Although the word of mouth model generates thekind of S-shaped diffusion curve that we are lookingfor, it has a serious weakness: it cannot explain thediffusion of an innovation from the date it is in-vented, but only from the date when some number, .y 0 )0, of early users have begun using it. Word of

mouth diffusion processes can only begin to happenafter an initial base of users has been built up, and,needless to say, the larger is this initial base of users,the faster is diffusion. Since early adopting individu-

.als or firms have evidently chosen to use thetechnology despite not having had access to theexperience of a previous user, it seems clear that

they are somehow different from subsequent users. 4This suggests that a more satisfactory model should

.distinguish between at least two different types ofagents, a suggestion that we will explore shortly.Alternatively, one might say that these initial usersare much more susceptible to common source infor-mation than subsequent users, who insist on receiv-ing word of mouth information before they adopt.This second suggestion means that the right model ofinformation diffusion might actually be a mix of Eqs. . .1 and 2 .

. .Putting Eqs. 1 and 2 together is pretty straight-forward, although the resulting mathematics are notpretty. Over the time interval D t, existing non-usersare subject to two sources of information, and the

probability that one of them will be informed or. .4infected is aqb y t . The first term in the brack-

ets is the common source information which reachesusers at a rate which is constant over time for at

.least as long as the common source is transmitting .The second term reflects word of mouth diffusion inwhich the contact rate is dependent on the currentsize of the population of existing users. Performingthe usual manipulations, the time path of adoption inthis mixed information source model isy t sN 1yexp y ars t 4 . .

=y11qc exp y brs t , 3 4 . .

.where sar aqk measures the relative strengthof the common source: if ks0, then no word ofmouth transmission occurs and ss1, while if as0then the common source does not broadcast and

.ss0. Note that when ss0, y t s0 for all t sinceno common source of information exists to create theinitial user base that is needed to start a word ofmouth process. When s is small then the time

.path of y t will resemble the logistic curve shownas B in Fig. 1, but with an inflection point at . . .4Nr2 1y2s r 1ys -Nr2. As s rises, theinflection point falls and the logistic curve becomes

4 There is no doubt that the psychological and sociologicalcharacteristics, educational achievements, outlook and attitudes torisk of early users are likely to differ from later users in a numberof ways. This is a subject which has loomed much larger in themarketing and sociology literature than in the economics litera-

.ture; see Rogers 1995 for a survey of some of it.


increasingly asymmetric, meaning that the upper,concave segment of the curve stretches out we

.shall return to this point below , and the lower,convex segment shrinks. In the limit as s1, the

.time path of y t resembles the modified exponential . 5function curve A on Fig. 1 .

In principle, it is not difficult to develop hypothe-ses about the potential determinants of b. Diffusionis likely to be faster for simpler technologies wheresoftware knowledge is easily learned and transmit-ted, for populations which are densely packed andwhere mixing is easily, where early users spread the

word with enthusiasm and do not die or forget what.they have learned , and in situations where the new

technology is clearly superior to the old one and nomajor switching costs arise when moving from oneto the other. For many economists, these diversefactors often boil down to expected profits, learningand risk. The problem in empirical work is not withtheory but with practice: most of these factors aredifficult to observe and measure. 6 As a conse-quence, it is very difficult to see much in the way ofreally persuasive formal tests of the hypothesis that

. expected profits or risk drive diffusion rates muchless an assessment of just how much they really

.matter in this literature, which is probably not aserious problem since no one really doubts the im-

5 The exposition in the text follows Lekvall and Wahlbin .1973 who call these two models external and internalinfluence models respectively. The mixed model is frequently

.used in the marketing literature; see Mahajan et al. 1990 for asurvey. For some attempts to empirically discriminate between

. . .Eqs. 2 and 3 , see Karshenas and Ireland 1992 , and Zettelmeyer .and Stoneman 1993 , who observe that although the epidemic

model implicitly presumes that all users participate in the processof informing others, epidemic models seem to work better empiri-cally when one allows for the possibility that less than the fullstock of users actively contribute to learning.

6 .Eq. 2 is the workhorse of much of the diffusion literature in .economics Eq. 3 seems to play much the same role in the

.marketing literature . The pioneering studies of diffusion speed .effectively imposed Eq. 2 on the data, modelling b as a

.function of various observables of interest; see Griliches 1957 , . .Mansfield 1961; 1963 , Romeo 1975; 1977 , Link and Kapur

. 1994 and others for informal applications of epidemic models.in case study work, see Nabseth and Ray, 1974 . However, recent

. .work by Oster 1982 , Hannan and McDowell 1984 , Levin et al. . . .1987 , Rose and Joskow 1990 , Karshenas and Stoneman 1993 ,and others has focused on modelling hazard rates or the timetaken for particular firms to adopt a particular technology.

portance of expected profits and risk in principle.More to the point, most studies use a measure oflearning which reflects the passage of time since theinnovation was first introduced, and, at least in theearly years of diffusion, this almost always has thekind of positive effect on diffusion rates or adoptiondecisions which one expects from epidemic models.

In many ways, it seems more natural to apply Eq. . . .1 , Eq. 2 or Eq. 3 to the diffusion of informationflows rather than to the diffusion of artefacts. Foreconomists interested in the diffusion of new tech-nology, the information flows of most interest havetypically been technology spillovers; i.e., involuntaryflows of information between rivals in the samemarket. A large empirical literature has pursued thequestion of whether such spillovers exist, and, if so,how large they are. In general, few doubt thatspillovers occur, although it is not clear how fast theprocess takes and what path the information flowstake through the economy. A more recent literaturewhich has tried to track flows of information bylooking at patent citations is a little more illuminat-ing. The focus in this work has typically been ontrying to build up a map which identifies the maininformation superhighways in the economy, andit suggests that such knowledge flows are oftenlocalized. This is consistent with a word of mouthprocess, and suggests that the speed of diffusionmight depend on how fast knowledge flows betweendifferent geographical regions. Further, most patentsreceive the majority of their citations shortly after

they are issued, but some particularly those in Drugs.and Medicine are sometimes cited for long periods

.of time i.e., 1520 and more years . This suggeststhat the total number of citations of any particularpatent is likely to follow an asymmetric S-curve over

time: a very rapid initial rise in citations for those.which are cited at all is followed by a slowing rate

of citation over time which may only tail off after 25or 30 years. 7 One way or the other, none of this isinconsistent with an epidemic model of informationdiffusion.

7 The maximum citation frequency is 5 years in the study by . .Jaffee and Trajtenberg 1996 ; see also Jaffee et al. 1993 ,

. .Trajtenberg et al. 1997 and others. See Griliches 1992 , or . .Geroski 1995a; b for two amongst many recent surveys of the

empirical literature on spillovers.


The basic hypothesis that we have been exploringis that it takes time for information about new tech-nology to reach all potential users, and we haveobserved that different mechanisms of knowledgetransfer common source and word of mouth affect the pattern of diffusion over time. However,these two models are rather simple, and the relativelyeven flow of information between individuals whichthey are built on is plausible only when applied tohomophilic populations. 8 When populations are het-erophilic, differences between individuals can im-pede the process of communication or, more likely,the process of persuasion. To understand diffusion inthis context, one needs to understand which individu-als are particularly influential and how they meetother individuals over whom their influence is deci-sive. It is hard to see much in the way of a general

.model or class of models emerging from the analy-sis of network structures, 9 but one can get a senseof what might happen by considering a simple exten-sion of the word of mouth model to two populations.

Suppose that there are two populations, N and1N , which do not interact with each other. Each has2

. .an initial number of users, y 0 and y 0 , who1 2initiate word of mouth diffusion processes withspeeds b and b , respectively. Following exactly1 2the same argument as earlier, the increase in the total

. . .number of users, y t y t qy t , over the inter-1 2val D t is

D y t s b y t N yy t 4 . . .1 1 1 1qb y t N yy t D t . 4 4 4 . . .2 2 2 2

.It is relatively easy to extend Eq. 4 to the casewhere the two groups interact. Suppose, for example,

8 Rogers defines homophily as: . . . the degree to whichtwo or more individuals who interact are similar in two or moreattributes, such as beliefs, education, social status and the like,

.observing that: . . . homophilous communication . . . is . . . more . likely . . . and . . . also more likely to be effective 1995, p. 19;

.see also his Chapter 8 .9 .See Bartholomew 1973 , for a review of several more com-

plex epidemic models which involve imperfect mixing; Debresson . . .and Amesse 1991 , Midgley et al. 1992 and Rogers 1995

contain stimulating discussions of the effect of network structure .on diffusion and references to the relevant literature . For an

introduction into the work on the geographical diffusion of inno- .vations, see the survey by Baptista 1999 .

that users in population 1 contact non-users in popu-lation 2 at a rate h while users in 2 contact12

.non-users in 1 at a rate h . Then Eq. 4 can be21written as:

D y t s b y t qh y t N yy t 4 . . . . 1 1 12 2 1 1q b y t qh y t . .2 2 21 1

= N yy t D t , 5 4 . .42 2which is very similar to the LotkaVolterra model ofcompetitive exclusion that is often discussed by pop-

.ulation ecologists e.g., see Roughgarden, 1996 . It is .relatively easy to imagine what Eq. 4 might look

like. Suppose that the first population adopts firstand at higher speed. Amongst other things, it thenacts as a source of information for the second popu-lation which begins word of mouth diffusion at sometime tU )0. The aggregate diffusion path is thevertical sum of the S-curves of these two popula-tions, and it is likely to be an asymmetric S-curvewith what looks like a long upper tail: aggregateusage will display a relatively quick initial diffusionmainly driven by what happens within the first

.population , followed by a relatively slow subse-quent approach to satiation caused by the gradual

increase in usage by the slower adopting second.population . The aggregate speed of diffusion will

depend on a weighted average of the two b s and hs,while the overall limit to diffusion is the sum of thetwo populations.

One of the big problems with the epidemic modelis that it takes N and b as fixed, and the twopopulation model that we have just discussed isuseful because it is an easy way to get round thesedrawbacks. In particular, it can be used to mimic aprocess in which b declines over time. There areany number of reasons why this might happen. Oneobvious possibility is that users become increasingly

resistant to word of mouth communication i.e., re-sistance to the disease increases and infection rates

.fall off ; another is that late adopters may simply beless able to understand the new technology thanearly adopters. If, for example, the total populationof potential users is composed of more able andless able firms, and the former start earlier and

.diffuse information faster i.e., have a large b , then


the diffusion of the new technology is likely to . .follow the time path of Eq. 4 or Eq. 5 with b

falling over time as users from the second populationbecome more numerous. The two population modelcan also be used to mimic a situation in which thetotal pool of potential users, N, is not fixed butincreases over time. Suppose, for example, that thereare two groups in the population: those for whom thenew technology is ideally suited, and those for whomit initially does not work as well as existing alterna-tives. Further, imagine that the new technology grad-ually improves in a way which makes it increasinglysuited to the needs of the second group. Then,diffusion is likely to proceed as follows: the processwill start with the new technology diffusion amongstthe first group, and then, when the technology hasbeen modified enough to appeal to the second group,they will join in the process. This can carry onindefinitely: as diffusion spreads and the new tech-nology develops or matures, N will gradually in-crease as usage spreads to other, more remote orperipheral populations.

Finally, it is worth emphasising that one rarelyencounters symmetric S-curves in the actual diffu-sion of new technology. In almost all cases, the laterstages of diffusion occur much more slowly thanwould be predicted by a symmetric S-curve. For

.example, Dixon 1980 extended and reworkedGriliches original data on the diffusion of hybridseed corn and found that an asymmetric model likethe Gompertz fitted the data better than the logistic

.model, Eq. 2 , in 27 of the 31 US states examined. .Similarly, Davies 1979 observed that eight of the

diffusion processes in his sample of 22 displayed apositive skew, while seven were symmetric seven

.could not be easily classified . Asymmetry is a prop-erty of several of the models which we have exam-

ined thus far and it will feature in many of those.that we will be considering below , and it is worth

listing some of its more important causes. Asymme-try arises when: populations are heterogeneous anddiffusion involves the introduction of progressivelyslower diffusion population groups; information pro-cesses involve the addition of common source infor-mation diffusion to word of mouth processes; theinfection rate, b , declines over time as knowl-edge depreciates, early converts lose some of theirevangelical zeal or non-users increase their resis-

tance to the new technology; and when the popula-tion of potential users increases over time, forcingdiffusion to pursue a moving target that graduallydrifts upward. And, finally, an information diffusion

. w .x4process in which D y t sb log Ny log y t gen-erates a Gompertz diffusion curve which also haspositive skew.

So, where does all of this leave us? The basicpremise of the epidemic model is that informationdiffusion drives technology diffusion. In a sense, it ishard to dispute this. However, the word of mouthdiffusion process is clearly inconsistent with the data

.in many sometimes not terribly important ways,and one might, therefore, be tempted to reject it. Atone level, fixing the simple word of mouth model isnot all that difficult. It seems clear that a satisfactoryepidemic model needs a good story of how theprocess of infection starts, and it probably mustallow for imperfect mixing of some sort, endogenousdecreases in b and increases in N. The net result isalmost certain to be an asymmetric S-curve. How-ever, a deeper problem with the model is that it ishard to believe that information diffuses as slowly asnew technologies typically do. Evidently what mat-ters is the type of information which users needbefore they are willing to adopt the new technology.There is an important distinction to be draw betweenunderstanding something and being persuaded, be-tween hearing and acting on what you have heard.We have tried to capture this in drawing a distinctionbetween hardware and software, and there aredoubtless other useful distinctions which can bedrawn. However, the important point is that once onebegins to think seriously about diffusion as a processof persuasion rather than simply as a process ofspreading news, the analogy with epidemics beginsto break down.

Some scholars have followed this line, and havetried to rework this model by focusing on risk oruncertainty rather than on the process by whichpeople become informed about something. This usu-ally results in a model with the property that somemeasure of uncertainty declines at increasing andthen at decreasing rates over time, leading a patternof technology adoption in which risk taking usersrapidly, and then risk averse users more gradually,

.climb on board i.e., leading to an S-curve . In fact,there is a basic equivalence between learning, expec-


tations and uncertainty, one which becomes transpar-ent when one thinks about the costs of knowledge

transfer including both transmission and receiving.costs . If there are no knowledge transfer costs,

learning will be instantaneous and knowledge will becomplete. If, however, knowledge transfer is costly,agents will not acquire complete information aboutthe new technology and they will be uncertain aboutjust what new the technology does and how best touse it. Further, the ability of individuals to learn hasan effect on learning costs, and their degree of riskaversion affects how they react to the uncertaintywhich they experience when their learning is incom-plete. This observation suggests that it might bemore useful to concentrate on the individual adop-tion decisions made by particular firms, examining .inter alia the effects that information transfer costs,risk aversion and other firm specific factors have onthe decisions mades by particular firms. Probit mod-els are a natural way to do this.

3. Probit models

Epidemic models abstract from differences in thegoals, capabilities or actions of individual membersof the population in order to focus on the diffusionof information in a simple, tractable, non-strategicsetting. This is a particularly useful simplificationwhenever social structures affect information trans-mission, or when externalities and competitive ef-fects of one type or another are created by thedensity of usage. However, it is a simplification. It isimportant not to lose track of the fact that thedecision to adopt is a choice made by a particular

.individual or firm , and that agents frequently makedifferent choices for the best of reasons. It followsthat differences between individuals may have apotentially important role to play in explaining pat-terns of diffusion. One natural way to think aboutthis is by using a probit model to analyse individualadoption decisions.

Possibly the simplest way to think about an indi-vidual choice based model of diffusion is to supposethat individuals differ in some characteristic, x ,iwhich affects the profitability of adopting the newtechnology. Further, suppose that they will adopt if

x exceeds some threshold level, xU. Individualsidiffer in their characteristics, and we will supposethat x is distributed across the population accordingi

.to some function f x . Fig. 2 shows two possibili-ties. In the top panel, the distribution of abilitiesacross the population is normal. Those agents with

U levels of x larger than x choose to adopt thei. Ushaded area , while the rest dont. Clearly, if x

.falls i.e., shifts left at a constant rate over time, therate of adoption will gradually rise as we climb up

.the right hand side of the distribution function and .then fall as we go down the left side , generating an

S-shaped diffusion curve. The lower panel of Fig. 2shows a situation where the distribution of abilities

.across the population is rectangular or uniform . Inthis case, an S-shaped diffusion curve will comeabout if xU falls at a rate which first rises and then

falls over time see David, 1969 for a classic discus-.sion of this model .

To get a feel for how probit models work, it isworth dwelling on one particular model in some

.depth. Davies 1979 argues that a firm will chooseto adopt at time t if its expected return p exceeds aithreshold p U ; if, on the other hand, p -p U , theniadoption will not occur. 10 Expected returns andthresholds are not observable, but Davies supposesthat both are simple functions of firm size, S; i.e.,that p rp U suSy. It follows that there is a criticali

U .1ry Usize of firm S 1ru at which p sp .iHence, if S )SU , then firm i will adopt the newi ttechnology at time t, while if S -SU , it will waiti tuntil either it gets larger or SU gets smaller before itadopts. This is the story told in Fig. 2 when x Si i

U U and x S . The model has a very simple but quite.strong prediction: when y)0, then firms will adopt

over time in order from largest to smallest, andconversely when y-0.

As we saw earlier, the precise shape of the diffu-sion curve depends on how x is distributed acrossithe population, and on how xU changes over time. In

10 The Davies model is actually expressed in terms of pay-backperiod: firm i adopts if the length of the period it can pay-backthe money invested in the new technology is less than somethreshold time. I have also simplified the model somewhat byeliminating a discussion of the separate determinants of p andip U.


.Fig. 2. Two distribution of f x with thresholds separating adopters from non-adopters.

the Davies model, firm size is assumed to be dis-tributed lognormally an assertion which is roughly

.consistent with the facts and u to follow a timetrend. If usct c for a particular type of innovation .he calls these group A innoations , then itsdiffusion curve will be cumulatively lognormal; if,

c t on the other hand, u s ce group B.innoations , then it will be cumulatively normal.

Both are S-curves, but, as we saw on Fig. 1, theyhave slightly different shapes. Group A innovationsare taken to be relatively transparent and their soft-ware can diffuse easily. As a consequence, u fallsquite rapidly. Group B innovations, on the other

hand, require more search and may also experienceregular post-innovation improvements which delayadoption, causing the fall in u to occur much laterafter the innovation is first introduced than would bethe case with a more transparent technology. Thebottom line, then, is that group A innovations diffuse

much more rapidly the cumulative log normal diffu-sion curve is asymmetric, showing a rapid early rise

.and a point of inflection well below Nr2 than groupB innovations, which take-off more slowly but reachtheir plateau more quickly when they are establishedthe cumulative normal is a symmetric, S-shaped

.diffusion curve .


The trick with probit models is to identify inter-esting and relevant characteristics x . Firm sizeiturns out to be a very commonly explored variable inthe empirical literature on diffusion. This is partlybecause it is relatively easy to observe, and partlybecause it is typically taken as a proxy for all kindsof things: large firms are sometimes thought to be

more capable they may have higher quality or more.technically able people on their staff , and, for this

reason, they may be less likely to need word ofmouth persuasion to adopt; they may use process

.innovations more intensively e.g., on a larger scaleand so earn more profits from adopting than smaller

11 firms would; they might be less or, for that.matter, more risk averse; they may be freer from

financial constraints; they might have market poweror be more inclined to strategically pre-empt smallerrivals; the new innovation might be complementarywith other activities they undertake or be capable ofbeing applied to a wider range of activities thanwould be the case if the adopting firm were spe-cialised; and so on. Needless to say, these differentinterpretations of what firm size might mean are notalways mutually consistent, and consequently it ishard to unambiguously interpret the empirical resultswhich have been reported in the empirical literature.What is clear, however, is that the preponderance ofthe evidence suggests that, for one reason or another,large firms are, by and large, quicker imitators thansmall firms. 12

11 .David 1975 provides a nice illustration of this kind ofargument: the adoption of mechanical reapers only makes sense ifthe savings in wage costs exceeds the cost of the machine, andthis, of course, depends on how many workers are on the payrolland on the number of acres over which the fixed costs of the

.machine will be spread . As the price of reapers drops, smallerand smaller farms will find adoption to be economic.

12 . . . .David 1969 , Metcalfe 1970 , Romeo 1975 , Davies 1979 , . .Hannan and McDowell 1984 , Levin et al. 1987 , Rose and

. .Joskow 1990 , Pennings and Harianto 1992 , Ingham and . .Thompson 1993 , Karshenas and Stoneman 1993 and many of

.the studies reported in Nasbeth and Ray 1974 all report positivecorrelations between firm size and the speed of adoption. How-

.ever, Mansfield 1963 found insignificant effects, and there havebeen several negative correlations reported. Possibly the most

.famous of these was reported by Oster 1982 in her study of thediffusion of the basic oxygen furnace in the US steel industry.

Firm size is not the only interesting characteristicof firms which might be thought to drive decisions toadopt new technology. Anything which induces xU

.to shift to the left, either at the same time as f xshifts right or in the absence of such a shift, willmake adoption more attractive for a firm. Here itmight be useful to think of x as the net benefit ofiadoption, and xU as the cost of acquiring the newequipment in which it is embodied. One set ofimportant agents who will affect these costbenefitcalculations are suppliers. They are frequently re-sponsible for facilitating the flow of informationabout the new technology, and, more generally, formarketing it. Their pricing and servicing policieshave a direct bearing on the cost of new technologyacquisition, and their success at designing a newtechnology which exactly meets the needs of theusing population can often be the deciding factorbetween successful, rapid diffusion and outright fail-ure. Finally, whatever technology they have designedand however they have chosen to market it, thelearning process which suppliers undergo is likely tolead to a downward trajectory in prices which willpush xU to the left at an initially high but subse-

.quently declining rate. For a fixed distribution f x ,this is likely to induce an asymmetric S-curve de-scribing downstream adoption. One way or the other,the important point is that conditions of competitionupstream will affect diffusion downstream. 13

Suppliers are also interesting because they areoften key players in the competition between thenew technology and the older, existing technologywhich it displaces: in some cases, they control bothtechnologies, while in others different groups ofsuppliers champion the different technologies. Oneway or the other, it is rarely the case that the existingtechnology which is being threatened remains static,and any sort of incremental innovations of the exist-ing technology will clearly slow the diffusion of the

13 For some theoretical work that explores the effects that the .market structure and other features of supplying industries may

.have on diffusion rates in using industries, see Bass 1980 , . .Metcalfe 1981 , Ireland and Stoneman 1982 , David and Olsen

. .1984 David and Olsen 1986; 1992 and others.


new technology. 14 Similarly, the new technology isunlikely to arrive on the market in its final form,and, in both cases, technological expectations arelikely to have a major impact on diffusion: current orexpect near future improvements in either the old orthe new technology are likely to inhibit the diffusionof the new technology. Again, if x is the net benefitand xU the cost of acquiring the new technology,then any technological progress which makes the oldtechnology more attractive, or lowers the benefits of

adopting the new technology now as opposed to.adopting it in the near future effectively raises the

opportunity cost of adopting now; i.e., it shifts xU tothe right.

One final class of exogeneous drivers of diffusionworth considering are costs. Those who come toprobit models from the literature on epidemics willnaturally focus in the first instance on learning andsearch costs. When they are first introduced, thebenefits of adopting new technologies are often areoften difficult to gauge with certainty, and they mayseem too risky to be worth it. However, as time

.passes and usage increases , more information be-comes available which enables firms to reassess theexpected returns and risk involved. How fast this

occurs depends, inter alia, on how firms learn i.e.,.on how they update their prior information . Many

models of this phenomena use statistical updating .rules such as Bayesian learning which have the

property that early bits of acquired information havea much bigger impact in changing prior views thaninformation bits acquired when the firm has alreadyundergone substantial learning. If x is a measure ofithe amount of risk a firm is willing to tolerate andx

U is the current estimate of risk, then learningmodels typically describe a process in which xUshifts to the left at initially high but subsequently

14 Diffusion of a new technology is also slowed whenever itstimulates technical progress in the older, established technology:

. . for some examples, see Harley 1973 , Mokyr 1990 pp. 90 and. .129 , Macleod 1992 and others. On the other hand, the early

introduction of relatively inexpensive complementary goods oughtto speed diffusion: for some work on the effects of CD software

.on the diffusion of CD players, see Gandal et al. 1999 .

declining speeds. 15 Alternately, one might interpretx as the expected value of acquiring software infor-imation on a new technology and xU as the searchcosts of doing so. Firms who initially have high

expectations about the new technology those in the.shaded area of Fig. 2 are willing to make the

investment, while others are unwilling to invest insearch. However, as more firms become familiarwith the new technology, search costs fall and xUshifts to the left.

A variety of factors lock firms into existing tech-nologies, raising switching costs and slowing thediffusion of new technologies. In terms of Fig. 2,think of x as a measure of the net benefits ofiadopting the new technology: firms with higher

switching costs will have lower values of x ceterisi.paribus and are, therefore, less likely to pass the

threshold xU and adopt. These costs include thedirect cost of software acquisition, something which

ought to depend on a firms ability to learn some-. 16times called its absorptie capacity . They

also depend on the often very long learning processwhich a firm must go through in order to use thenew technology to its fullest. Since new processtechnologies often create new products or servicesor, at least provide the means to differentiate exist-

.ing goods and services more fully and new productsmean developing new markets, the costs of comingto terms with a new technology often include mar-keting and other costs incurred downstream. Finally,the more fundamental the break with previous activi-

15 . .See Stoneman 1981 , Jensen 1982; 1983 , Balcer and Lipp- . .man 1984 , Tonks 1986 and others for a variety of learning

.models. Rosenberg 1976 is a stimulating discussion of the rolethat expectations can play more generally in affecting diffusion.

16 .See Cohen and Levinthal 1989 for a discussion and some .evidence. Wozniak 1987 provides some evidence on the effect

of education and human capital formation has on diffusion. Casestudy and statistical evidence are united in suggesting that firms

.with higher absorptive capacity however it is measured adoptnew technologies sooner than others. For example, higher educa-tional attainment seems to have been associated with more rapid

adoption of computer technology by California farmers McWil-.liams and Zilberman, 1996 while the adoption of video banking

by US commercial firms was fastest among those who has previ-ous experience with IT and with the number of inter-firm arrange-

.ments it had Pennings and Harianto, 1992 .


ties caused by a new technology, the greater areswitching costs. Firms that find it easier to spot coststhan new sources of revenues may well may well bemore reluctant to adopt a new technology than oth-ers. 17 Similarly, some new technologies will aug-ment the competencies of a firm, strengthening themand making it more competitive, while others willdisrupt existing competencies. In this later case, thecosts of adopting a new technology include thoseassociated with developing the new competenciesneeded to make the most of the new technology. 18Switching costs can also be affected by governmentregulations. 19

Opportunity costs are also important, and can becreated by previous investments in machinery whichhave not fully depreciated. In particular, firms withnew vintages of capital stock are less likely to switchto a new technology than firms with older, lessvaluable vintages, since the net benefits will belower and the capital costs of change will be greater.This is particularly true for capital equipment that isso specialised that the costs incurred on installing ithave been sunk, since, in this case, there are nosecond hand markets which the old equipment mightbe sold on to. Let x measure the age of a firmsicapital goods, and suppose that when its equipment

17 One particular example of this which has attracted recentattention are firms who resist new technologies for fear of causingtoo much disruption for their customers, or fail to adopt thembecause they are not well suited to their current customers currentneeds. Such firms are said to be too close to their customers,and are generally thought likely to adopt sustaining new

.technologies but not disruptie ones; see Christensen 1997for some vivid case studies of this phenomena.

18 There is a literature which argues that firms who possessdynamic competencies will be more able to adopt new tech-nologies, and it seems plausible to believe that new technologieswill diffuse more rapidly in industries where these skills abound;

.see Teece and Pisano 1994 and the suggestive case studies by . .Iansiti and Clark 1994 , Henderson 1994 and others.

19 Much of the recent econometric work suggests that govern-ments rarely speed things up, and government owned enterprisesrarely move faster than private owned ones; see Oster and Quigley . . .1977 , Hannan and McDowell 1984 , Rose and Joskow 1990and others. On the other hand, countries that were quick to grantlicenses to mobile phone operators seem to have stimulated much

higher rates of diffusion than others particularly when the alsohave introduced competition and facilitated the switch from ana-

. .logue to digital technology ; see Gruber and Verboven 1999 .

is older than xU , the firm switches to the newtechnology. The distribution of equipment age in the

.industry shown as f x in Fig. 2 will gradu-ally shift to the right, and the speed at which it doesso will determine the speed of diffusion. 20

Where does all of this leave us? One clear gainfrom thinking about diffusion using the probit modelis that it enables one to generate a long and fairlyimpressive list of firm specific potential determinantsof diffusion speeds. What is more, the link to deci-sion making puts a certain precision on these argu-

.ments, and makes it possible in principle to identifya who and a why for each point on thediffusion curve. Finally, the fact that it identifiesobservable factors which, in certain circumstances,will trigger an adoption decision makes it possible .in principle at least to identify a number of levers

which policy makers can use to speed up or slow.down the diffusion of particular technologies.

To put these gains into some perspective, it isworth distinguishing the probit model of diffusionfrom what one might call population models of

diffusion of which the epidemic model is a classic.example . This latter type of model focuses on ex-

plaining the percentage of the population of firmswho have adopted the new technology at any pointin time. Population models have a natural appeal ifone is primarily interested in the gradually unfoldingimpact that a new innovation has on markets, since

the size of this impact depends at least in the first.instance on aggregate usage, and not on which firms

in particular are using it. Further, while probit mod-els seem more natural and more attractive to

economists because they focus on individual deci-.sion making , they are less transparent than popula-

tion models in describing phenomena which occurbetween individuals. The gradual increase of infor-

mation available to potential users or the decline in.the risk which they perceive appears to be exoge-

20 There is no reason to think that equipment ages at the samerate over time, and many scholars believe that scrapping rates rise

in recessions this is sometimes called the pit stop theory of .recession; see Cabellaro and Hammour 1994 , and for some

. .evidence, Oulton 1989 , Geroski and Gregg 1998 and others. Ifthis is true, then one expects to see variations in diffusion rateswhich can be associated with macroeconomic fluctuations.


nously driven in probit models; epidemic models atleast have the virtue of making the true endogeneityof this phenomena absolutely plain to see. The realquestion here is whether diffusion is a social processthat is something other than the sum of its parts.Anyone who thinks that this might be the case will

find the focus on apparently exogenously deter-.mined differences in firm characteristics in the pro-

bit model a little unsatisfactory.All of this said, there is not much choice between

population and probit models. There are no driversof diffusion which feature in population modelswhich cannot be expressed one way or the other inprobit form. And, as we have seen, population mod-els can be extended to allow for heterogeneous popu-lations defined by differences in some characteristicx . 21 The really interesting choice, I think, is be-itween different types of population models, and ournext task is to explore some of these.

4. Legitimation and competition

The analogy between word of mouth epidemicprocesses and the S-curve typically observed in thediffusion of new technologies is so well establishedin the literature that it is probably worth pointing outwhat should in any case be rather obvious: there aremany different models which have nothing to dowith information diffusion that can be used to gener-ate an S-curve. Probably the leading alternative is theprobit model which we have just discussed; othersinclude the so-called stock adjustment modelwhich has featured in several studies, and evolution-

21 The equivalence between population models which count thenumber of users and probit models which describe the choice by afirm of whether or not to use a new technology is exact. However,

firms can use a new technology more or less intensively in.practice, they rarely switch over wholesale to a new technology ,

and this can drive a wedge between population models whichtrack usage and probit models which describe the adoption deci-sion. Note that intra-firm diffusion rates can sometimes be veryslow. For example, it took both Ford and GM more than 20 years

to reach 50% of their 1989 usage of robots Nissan took 13 years. .to accomplish the same thing ; see Mansfield 1989 and refer-

ences cited therein.

ary models of diffusion. 22 There is, however, afourth alternative derivation of the S-curve whichderives from the population ecology literature.

Population ecologists use density dependentgrowth models to account for the systematic in-creases and decreases in net birth rates which they

.observe in natural settings. Suppose that y t is acount of the members of some particular populationwhich inhabits a particular environmental niche, and

.that it increases at constant rate g. Then: d y t rd t .sgy t , and, in principle, the population will even-

tually explode. This will never happen of course.Constraints imposed by the limitations of the nicheas population density rises will depress birth rates,r , and raise death rates, r . If, for example, r sbb d b

. .yk y t and r sdyk y t , then the net rate ofb d dincrease in the population is gr yr sryb d

. .rKy t , where rbyd, and Krr k qk . As ab dconsequence, population growth is given by:

. . . 4d y t rd tsry t 1y y t rK , which yields a lo- .gistic time path for y t of

y1w xy t sK 1qhexp yrt , 6 4 . .w .x 4where h Kry 0 y1 . This is, of course, exactly

.the form of Eq. 2 , but in this case the characteristicrise and fall of growth rates is caused by the effectsof density on birth andror death rates. The twoparameters r and K in this model have naturalinterpretations: r is sometimes called the natural

rate of increase of the population i.e., that whichwould occur if there were no constraints on birth or

.death processes , while K is the carrying capacityof the niche and gives an upper bound on the

.population size which can be supported by the niche .

22 .For work using the stock adjustment model, see Chow 1967 .and Stoneman 1976 . These models typically just posit an adjust-

U 4 Ument rule, such as: dSrd ts aS S yS , where S is thet tequilibrium stock of usage, S, towards which the system graduallyadjusts. In certain circumstances, this yields a logistic curve

tracking usage over time e.g., if adjustment were thought to beproportional to the difference between logsU and log S , then thet

.diffusion curve would be Gompertz . Evolutionary models sharewith probit models the presumption that users are heterogeneous,and then examine the effect that selection mechanisms have on

.technology adoption choices: see Silverberg et al. 1988 , Met- .calfe 1995 and others.


Both are directly analogous to the parameters b and ..N in the epidemic model i.e., Eq. 2 .

An interesting extension of the density dependentpopulation growth model has recently been advanced

.by sociologists studying the growth and decline inthe populations of different types of organizationsHannan and Freeman, 1989; Hannan and Carroll,

.1992 and others . This model posits the existence oftwo forces affecting the birth and death rate oforganizations over time: competition andlegitimation. Competition arises whenever re-source constraints limit the number of organizations

which can survive in a particular market or social.setting , and depends mainly on population density

in these models. In the context of organizations,legitimation is the process by which a new type oforganization becomes accepted, institutionalized orsimply just taken for granted, and it clearly depends .amongst other things on the number of such orga-nizations already in existence. Plausible assumptionsabout the effects of competition and legitimation onbirth and death rates produces a non-linear relation-ship between the net birth rate of the population and

population density rather than the linear dependence ..which underlies Eq. 6 , but, with some additional

assumptions, the model can be made to generate anS-shaped or logistic curve tracing the number offirms alive in the market. Intuitively, the argumentgoes as follows. Legitimation gradually erodes barri-ers facing a new type organization, raising its birthrate and increasing its survival prospects. This drives

.a gradual increase in the net birth rate of the neworganization. However, as the population of the newtype of organization increases, a competition forresources sets in. This crowding is likely to have theeffect of lowering birth rates and raising death rates,and, as a consequence, it lowers the rate of organiza-

.tional expansion. This rise and fall in the net birthrate is, of course, just what underlies the S-curve.

This sort of story translates very naturally into thecontext of new technology diffusion. Consider theS-shaped curve labelled B on Fig. 1 once again, and,for simplicity, divide the elapsed time of diffusioninto two periods: the early period up until timetst , and the late period which takes place after

tst there is, of course, no reason to focus only onthe time it takes to reach the inflection point as the

.dividing point . In the early period, what matters to

everyone involved with the new technology iswhether it will work, whether it is superior to anyother new technologies which might possibly arrivein the near future, whether there is a supply infra-structure available to support adopters, whether buy-ers will resist products made from the new technol-ogy, and so on. This legitimation process is clearlyanalogous to a standards setting processes, and thatmeans that its length is likely to depend on switchingcosts between the old standard and the new standard,the size of the installed base of new users andexpectations about market growth and the future

23 evolution of technology. By time tst or some.such time , this legitimation process will be com-

plete; i.e., the new technology will have becomeestablished. As it continues to be adopted, however,a second set of forces begins to limit its diffusion inthe market. As more and more firms begin to use thenew technology, competition in the market for thegoods or services which use this technology beginsto lower the returns earned by early adopters, andthis, of course, reduces the returns that non-users canexpect if they adopt. This slows diffusion rates andultimately brings the whole process to an end.

In simple ecology models, density dependence isthe main driver of population dynamics. These mod-els have the great virtue of providing a simple andtractable account of market dynamics, and the twoforces which we have examined legitimation andcompetition help to account for the distinctivefeature of S-curves: their initial convexity and subse-quent concavity. However, density dependence isjust too simple a story. Economic agents are not ants:their incentive structures are more complicated, andthey often behave strategically in response to envi-ronmental pressures. This, unfortunately, means thatthe effects of legitimation and competition on tech-nology diffusion can cut both ways.

The simplest stories about competition which aretold by economists are density dependent in nature.In simple Cournot models of competition for exam-ple, profits per firm almost always declines as the

number of firms using a particular technology and

23 .See, for example, Katz and Shapiro 1985 , Farrell and Sa- . .loner 1985; 1986 and others; David and Greenstein 1990

surveys much of the early literature on standards.


.selling similar goods operating in the market rises.This kind of argument suggests that competition willslow diffusion rates in just the same manner asdiscussed above. There is, however, more to thestory than this. If agents are at all foresighted, theywill realise that the market will eventually getcrowded, and they will wish to adopt the new tech-nology before the returns from using it are competedaway, pre-empting as many rivals as possible. Thistype of strategic behaviour may actually speed updiffusion, at least initially. Further, early users willtry to create barriers to the entry of later adopters,and this may gradually slow the rate of adoption. 24In fact economists have identified two other competi-tive forces that are likely to affect the timing deci-sions of firms: the pre-emption effect and rentdisplacement. The first arises when the new tech-nology complements the existing activities of somefirms more than it does others, giving rise to anincentive for these more favoured firms to move firstand adopt it before their rivals do. Rent displacementarises when the new technology cannibalizes someof a firms existing activities, making adoption morecostly than it would be in the absence of suchactivities. This argument is often used to explainwhy incumbents can be slower to adopt new tech-

nologies than new entrants who have nothing to.cannibalize , and it is likely to be part of any story

about why market leaders who are champions of oldtechnologies are often slower than others to adoptnew competence displacing technologies. 25

One might deduce from all of this that the neteffect of competition on the rate of diffusion is

24 . .See, Reinganum 1981a; b , Quirmbach 1986 and others formodels of sequential adoption which look at the effect of market

. .power on diffusion; Reinganum 1989 and Beath et al. 1995 .survey the game theoretic literature, while Chatterjee et al. 1998

survey marketing models of competitive diffusion.25 .See Tirole 1988 , Chapter 10, for an exposition of these

forces; Stoneman and Kwon, 1994 document significant crosstechnology effects between different types of machine toolswhich seem similar to those which underlie the pre-emption

.effect; the oxygen steel case discussed by Oster 1982 , is a good .illustration of rent displacement there are many others . The

distinction between competence enhancing and competencedestroying technologies points to very similar effects on be-haviour; see also the very similar distinction between sustaining

.and disruptie technologies made by Christensen 1997 .

ambiguous, and this is certainly a feature of theempirical literature which has looked at the effects ofcompetition on diffusion rates. Not all of the statisti-cal results point in the same direction, and mostsuggest that measures of competition like concentra-tion ratios of counts of the number of firms in anindustry experiencing diffusion are not all that im-portant as a driver of diffusion. 26 It would, how-ever, be imprudent to conclude from this work thatcompetition has no effect on diffusion: the real issueis competition from who, or what?. There is anextensive case study literature which suggests thatincumbent firms are often very slow to adopt newtechnologies when entry barriers are high, and thissuggests that it may be that it is competition from

.entrants or threats of entry which matters most instimulating diffusion. This, of course, only makesplain what common sense suggests, namely that thedegree of competition is likely to be endogenous tothe process of diffusion. What is more, competitionchanges both its character and its intensity as diffu-sion proceeds. Initially competition is between theold technology and different variants of the newtechnology; when the new technology has beenlegitimized, competition is between the various firmswho use the new technology to serve the market. Inshort, competition probably does speed diffusionrates, but the degree of competition felt by adoptersand non-adopters at any time probably depends onthe rate and extent of diffusion which has occurredup to that time.

26 .For what it is worth, Hannan and McDowell 1984 found apositive association between adoption speeds and market concen-

.tration, while Levin et al. 1987 found a negative effect; Romeo .1975 found that diffusion speeds increased with the number offirms in the market and fell with increases in the variance of the

. .firm sizes another measure of concentration , while Davies 1979found that diffusion fell with increases in firm numbers and also

.with increases in the variance of firm sizes . Rather more satisfy- .ing is the approach of Karshenas and Stoneman 1993 . They

distinguish rank effects which reflect differences in the char-. acteristics of adopters , order effects which reflect returns to

adoption associated with pre-emption of late movers by early. movers and stock effects which reflect the decline in benefits

which arise over time as more and more firms adopt the new.technology . The latter two capture different types of competitive

effects which might affect diffusion, but neither seemed to playmuch role in explaining the diffusion of computer numericallycontrolled machine tools in the UK.


Density dependence is also too simple to providea really satisfactory account of the process of legiti-mation or standardization in markets, and for thesame reason: economic agents often behave strategi-cally, anticipating the effects of increased densityand, as a consequence, altering the evolution ofmarket structures. Standardization processes alsogenerate externalities which can complicate marketprocesses and either hasten or delay the developmentof a standard; and what is more important, standard-ization processes involve making choices betweenalternatives, meaning that some technologies will failwhile others succeed. More generally, it seems rea-sonable to believe that the process of making choicesbetween alternatives ought to have a profound affecton the time path of adoption of the technology whichis ultimately selected. To make any kind of progresson this issue, however, means pushing well beyondthe model of density dependence and looking atdiffusion models which encompass both the choicebetween alternative new technologies, and the timepath of imitation which follows that choice.

5. Information cascades

The literature on new technology diffusion isreally a literature about S-curves, and in many waysthis is rather limiting. S-curves have the virtue of

being plausible which is more than can be said foralternatives like instantaneous diffusion or linear

.adoption time paths , they can be a nice way toparameterize the diffusion process making it

straightforward to do empirical work on the determi-.nants of diffusion speeds and, last but by no means

least, they are roughly consistent with the facts.However, they are only roughly consistent with thefacts. As we have already seen, diffusion curves tendto be asymmetric in practice. More fundamentally,

the fact is that most innovations fail i.e., they do not.diffuse at all , and it seems reasonable to insist that

any serious model of diffusion ought to includefailure as a possible outcome.

There are several ways forward from this observa-tion, and, in what follows, I would like to focus onone particular type of model. My starting point is theobservation that new technologies come to the mar-

ket in a variety of forms, often leading to a small .explosion in new products or new product variants

based on that technology. 27 These new products areeither sold directly to consumers or to downstream

.firms where they appear as process innovations .Adopting a new technology in these circum-stances involves choosing between these variants in

the first instance this is similar to the legitimation.process discussed earlier , and then tracing the time

path of imitation that results when one particularvariant has been adopted this is the conventional

.diffusion process . An extension of diffusionmodels to include an explanation of the initial choicebetween alternate variants of the new technology isworth considering for three reasons: it may be more

.descriptively accurate than at least the epidemicmodel; it will turn out to encompass several of themodels discussed earlier, providing what might be auseful framework on which to hang a great numberof more specific arguments about the determinants ofdiffusion; and, last but by no means least, it willidentify when, and how, initial choices made in themarket amongst the possible variants of the newtechnology have an effect on the diffusion of what-

ever variant is chosen if, that is, any become estab-.lished on the market .

Suppose that two variants of a new technology, Aand B, simultaneously appear on the market andthreaten to displace an existing technology. No onereally knows for sure whether A is better than B or Bis better than A, much less whether either is betterthan the existing technology. If, for some reason,early users are willing to experiment with the newtechnology and prefer A to B, then early trials withthe new technology are likely to generate moreinformation about A than B. If A turns out to bebetter than the existing technology, then it will grad-ually become more commonly used. These earlyadoption decisions are investment decisions, but asmore and more information becomes available aboutA in particular, later adopters will be less and lesswilling to invest in making a serious choice between

27 There is a large literature associated with this sylized fact,much of it associated with the dominant design hypothesis; for

.a recent exposition, see Utterbeck 1994 .


A and B: after all, if A seems to work better than theexisting technology, why invest in B and take therisk that it will be worse? It follows that somethingof a bandwagon is likely to develop, with lateradopters making the same choices as early adopterswithout having gone through the same investment inlearning by experience. This process is sometimesreferred to as an information cascade. 28

When network externalities are present, they canstrengthen these effects. After some point, A is likelyto become more attractive than B regardless of itsintrinsic merits simply because A has a larger in-stalled base. Moreover, the possibility of creating asimilar sized installed base for B in the future will besmaller than it once was, since there are fewerpotential adopters left and they are even less likely to

choose B than A in the future, As installed basewill be even larger and there will be even fewerpotential adopters available to create a comparably

.sized installed base for B than there are now . Forboth of these reasons, the incentive to try B falls asthe diffusion of A proceeds, and this effect will bestronger the more important are network externalitiesand the more marginal is the technical differencebetween A and B. In fact, network externalities canhave two effects on diffusion: the lock-in effect justdiscussed, and a risk creating effect which can delaydiffusion. When network externalities exist, earlyusers risk making the wrong choice and becom-ing stranded with a technology which has failed togenerate the network externalities it is potentiallycapable of. This may make early users reluctant tomove first, and may delay the adoption bandwagonthis phenomena is sometimes called excess iner-

28 Information cascades are defined as situations in which . . . itis optimal for an individual, having observed the actions of thoseahead of him, to follow the behaviour of the preceding individualwithout regard to his own information, and are often used to

.explain herd behaviour; see Bannerjee 1992 , De Vany and . . .Walls 1996 , Bikhchandani et al. 1992 pp. 994 , Bikhchandani .et al. 1998 and others for models of information cascades. The

model of technology choice outlined in the text is based on Arthur . .1989 ; see also Arthur et al. 1987 , who examine the underlyingpolyna urn process of the model. The argument that early invest-ment choices may give pioneering brands long lasting advantages

.is discussed in Schmalensee 1982 and others.

. 29tia in the standards literature . The consequencewill be an initial convexity in the time path ofdiffusion.

In fact, one might identify three phases in adiffusion process driven by information cascades:the initial choice between A and B, the lock-in toA, and then the bandwagon induced by imitation.As we have just seen, incentives to invest in informa-tion and network externalities help to explain thelock-in to A, but this is obviously not the wholestory. One obvious reason why A might be chosen isthat it appears on the market before B, and theexpectations of early users at that time are that B is

just not worth waiting for indeed, the arrival of B.might be a surprise . A might also be more effec-

tively championed by its suppliers, who may evendesign A jointly with some of their major customerstypically large or symbolically important early

.users . For these or other reasons, As characteristicsmay suit the needs of early users better than Bscharacteristics. Finally, suppliers may also play astrategically important role even when A and Barrive simultaneously on the market. A may bepriced more economically, software informationabout A may be diffused more effectively or the

support infra-structure or other sources of network.externalities may be more effectively organized by

As suppliers. All of this is to say that the initialchoice between A and B may be hard to predict, andit may appear as if A were chosen by accident.As a consequence, the early time path of diffusionmay be largely stochastic. However, once a choice ismade and lock-in occurs, this early uncertainty islikely to die away, and the subsequent dynamics of

.the system driven by an information cascade willlook much more deterministic. If it turns out thatthere are lots of firms waiting for others to make theinitial choice between A and B, then, when it be-comes clear that A has been chosen, a sudden burstof adoption will occur. As time passes and earlyusers are succeeded by the imitative behaviour of the

29 On the other hand, competitive pressures may encouragefirms to adopt new technologies too soon in order to pre-empttheir rivals. For work on the effects of network externalities on

. .diffusion, see Farrell and Saloner 1986 , Cabral 1990 , Choi .1997 and others.


herd, the rate of adoption will begin to rise sharplyand then, after the rush has passed, tail off. This, of

course, can easily look a lot like an S-curve al-. 30though of course it doesnt have to .

The important point is that choices which occurearly on in the process may have an extremelypowerful effect on the time path of diffusion. Whenthe initial choice between A and B is made quicklyand clearly and when A is clearly superior to theexisting technology, then diffusion is likely to be

rapid quick and decisive decision making will.quickly stampede the herd into action . If, however,

these early choices are muddled, then the processeswhich generate and swell an information cascade arelikely to be fragmented and weak. In these circum-stances, one might observe only a very flat diffusion

path because it takes a while for a winner to be. established , incomplete diffusion both A and B

. come to share the market or no diffusion at all Aand B kill each other off amid confusion or general

.indifference by potential users . This point is, ofcourse, not new. In path dependent processes, initialconditions matter. If diffusion is a path dependentprocess, then clearly it is hard to conceptually sepa-rate the process by which new technology spreadsfrom the process by which economic agents makechoices between the different variants of that newtechnology.

These arguments prompt a second general obser-vation. In this model, S-curves are not the startingpoint of analysis, but they are one of several possibleoutcomes. Diffusion stories which are designed toexplain the S-curve usually take the appearance ofthe new technology for granted, and focus on thequestion of why it takes so long for it diffuse,However, it is rarely clear to anyone at the time thatthe new technology has arrived, or which ofseveral variants it is: it is only with the benefit ofhindsight that the new technology stands out.

.Further, this clarity or lack of it is bound to have a .profound effect in shaping at least the initial con-

vexity which we observe early on in the diffusion of

30 .For similar work in this spirit, see Vettas 1998a; b , Jo- . .vanovic and Lach 1989 , Jovanovic and MacDonald 1994 ,

.Kapur 1995 and others who identify conditions in which anS-curve will to emerge from a social learning process.

the new technology. In fact, most of the compet-ing variants of the new technology are likely tofail, meaning that they have no S-curve. What thismeans that our observations of S-curves are colouredby sample selection bias: only successful innovationshave an S-curve, and it is, therefore, by no meansclear that the typical new innovation actually gener-ates an S-curve. This, in turn, prompts the question:if our observations of the S-curve are the result ofsample selection bias, should the S-curve be thecentre-piece of our models?

Finally, notice that the model also says somethingabout the extent of diffusion in the long run: if thereare many more potential users of A than B, then theinitial choice of A will also determine the eventualextent of diffusion: had early users opted for B, thenthe new technology would, in these circumstances,have diffused much less widely. Actually, marketsize is likely to endogenous to diffusion in a deepersense than this. New products are typically targeted

.on specific users e.g. those who prefer variant A ,and then gradually adopted to other users e.g. those

.who prefer variant B or C or D as time passes.These adaptations look like post-innovation techno-

.logical progress which they are , but arguably thereal action comes from the demand side and not thesupply side: that is, they are market widening inno-vations. To put the point a slightly different way, theuser population, N, is likely to gradually increaseover time and more and more marginal agents gradu-ally become users of the new technology. This is a

.model of diffusion which like the probit modelsays that diffusion is a phenomena which largelyarises from the heterogeneity of user populations.

.However unlike the probit model , the nature of theexternalities which drive diffusion when informationcascades are present mean that the most interestingand important users are the first users. Without themthere to start the bandwagon, not much happens atall.

The focus on early events as prime determinantsof subsequent diffusion patterns is a virtue of thekind of model which we have been examining in thissection. However, there is a sense in which the initialchoice between technologies A and B is not wellexplained in this model: we can describe the processby which choices are made, but it is very hard topredict which alternative will be selected. This ob-


servation completes a circle which brings us back tothe epidemic model. In that model, the early pool of

.users y 0 who drive the model is exoge-nously given. These pioneering users have also madea choice, and their choice builds up a base of soft-ware information and reduces risks or increases thebenefits perceived by subsequent users. In a sense,they legitimize the innovation, and once thathappens, an epidemic or information cascade drivessubsequent adoption. This observation raises twoquestions: should the arrial of the new inno-ation be dated from its first appearance, or fromthe time it has gained legitimacy? and: is the legiti-mation of a new innoation any less fundamentalthan the act of inention which brings it about?These two questions suggest that the real problemmay not be understanding how the process of diffu-sion unfolds, but understanding how it starts.

6. Some reflections on technology policy

We use models to help illuminate phenomena thatwe find difficult to understand, or to solve problemswhich are too difficult to think through. These bene-fits come because models simplify reality, and makeit tractable enough for our limited powers of under-standing to grasp. These benefits, however, alsobring costs. Models can easily become prisons. Theycan severely limit the way in which we think aboutthings, and so limit the range of actions which wemight choose to take when we have completed ouranalysis. It is arguably the case that this has hap-pened in the area of technology policy. The domi-nance of the epidemic model in particular seems tohave created a set of policy presumptions which aresurprisingly limited. Thinking about diffusion interms of legitimation, competition and informationcascades raises questions and issues which go wellbeyond the standard policy stance. 31

31 What follows is not designed to be a general survey of theliterature on technology policy much less that associated with

. .diffusion ; for broad overviews of the area, see Metcalfe 1995 , . . .Mowery 1995 , Stoneman and Vickers 1988 , Stoneman 1987 ,

. .David 1986 , Stoneman and Diederen 1994 and others.

The epidemic model is built on the presumptionthat diffusion happens too slowly, mainly becauseinformation does not diffuse fast enough amongstpotential users. Anyone who really believes this willbecome interested in the question of whether publicpolicy makers can do anything to improve the mech-anism by which information spreads through theeconomy. Policy makers might become the commonsource, they might promote word of mouth commu-nication or subsidize the externalities involved with

it, and they may try to identify key actors those who.are particularly persuasive and try to motivate them

or at least support their evangelical activities. If thekey actors turn out to be users or suppliers, subsidiesmay rain down on them or policy makers may try toput together forums in which all parties can gettogether and communicate with each other. The bot-tom line seems to be that diffusion is a problemwhich public policy can ameliorate with a judiciousmix of information provision and subsidies. 32

If the probit model broadens the range of per-cieved policy options, it does so because it points to

firms themselves as the source of the problem if.there is a problem . Firms often need to acquire

special skills and they may lack enough incentives tomove quickly. Aside from policies which speed upinformation diffusion or help suppliers to fly downtheir learning curves, this insight suggests that onemight contemplate subsidies which encourage thebuilding up of various types of human capital, and

policies which stimulate competition particularly by.new entrants . In a sense, however, the probit model

shuts down many policy options. If the problemreally lies within firms, then there are real limits towhat public policy makers can do short of runningthe firms themselves. Policies can be devised whichmake firms more aware of their opportunities andmore able to exploit them, but it is hard to think of apolicy which actually forces them to act when theydont wish to. One can subsidize all kinds of things,but that may not be enough.

The list of exogeneous drivers of diffusionwhich often feature in probit models also frequentlyincludes variables which purport to reflect the effect

32 .See Stoneman and David 1986 for a good discussion of thetrade-off between information provision policies and subsidies.


that competition has on diffusion. At a commonsense level, very few people doubt that a little bit ofcompetition stimulates diffusion, but beyond thatthings become very murky. It is altogether possiblethat too much competition slows diffusion, either

because it lowers the returns to adoption the popula-.tion of users becomes too dense or because it

muddles the initial choice between alternatives. Fur-ther, the nature of the firms who are the source ofcompetitive pressures may matter: domestic rivalswho are located close to other users may have muchmore effect than foreign rivals who compete throughimports. 33 Finally, as we noted earlier, the nature ofcompetition changes over the product life cycle,shifting from competition between alternative vari-ants of the new technology to competition from auser population which gradually becomes more andmore heterogeneous over time. All of these puzzles

mean that competition policy or strategic trade pol-.icy are possible policy tools which can be used to

stimulate diffusion, but they are possibly too bluntand indirectly associated with the diffusion processto be of much practical use.

Models of diffusion which focus on legitimationor information cascades open up several new insightsinto what the public policy problem associated withtechnology diffusion might be, and how it might beameliorated. First and foremost, they destroy anyclear presumption that diffusion is too slow. Theprocess of making choices between alternative tech-nologies is a complicated one, and there are plenty ofexamples where market processes made choices tooquickly and set in motion adoption processes whichled agents to adopt second best technologies. Sec-ond, these models suggest that there is only a limitedwindow in which policy can have important effects,and that is during the choice process. What speedsdiffusion is that choices are made cleanly and clearly,and that the process of choice throws up enoughinformation to create a strong bandwagon. However,once a choice has been made and the bandwagon has

33 One classic example of a diffusion process which was killed .by too many initial variants and the behaviour of their sponsors

.is quadrophonic sound see Postell, 1990 ; for some argumentsabout the effects of different types of competitors, see Porter .1990 .

started, there are probably only limited effects whichpolicy makers can have on what happens next. Third,although the policy window is small, the effects ofpolicy are potentially very large. It is in the nature of

information cascades and many other externality.driven processes that small initial effects can have

very large ultimate consequences. Since efficient andeffective policy making should focus on situations

.where increasing returns in this sense exist, thisobservation reinforces the last: namely, that the tim-ing of policy intervention may be at least as impor-tant as its substance. Finally, since the choice pro-cess is inherently market specific, these observationssuggest that technology policy must necessarily beselective if it is to have any substantive effects.Non-selective policies like subsidies or running tech-nology fairs and forums are administratively conve-

nient and they are consistent with the popular but.sometimes grossly misinformed view that civil ser-

vants are indecisive, bureaucratic and totally ignorantof market realities. They are, however, very bluntpolicy tools, and it is hard to believe that one cannotdo better.

Epidemic and probit models point to informationprovision and subsidies as the major tools of policy,and these alternative models add at least three furthertools to the public policy portfolio. All of themconcentrate on the process of choosing between al-ternative variants of new technologies. Standardssetting processes are sometimes a an important wayto resolve the many externalities which surroundchoice, and administrative processes can be veryappealing when it is important not to choose too

quickly i.e., when the basic underlying technology.is still evolving rapidly and unpredictably . Publicly

geroski - 2000 - models of technology diffusion

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