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Douglas Puffert, University of Warwick
Path dependence is the dependence of economic outcomes on the path of previous outcomes, rather than simply on current conditions. In a path dependent process, "history matters" -- it has an enduring influence. Choices made on the basis of transitory conditions can persist long after those conditions change. Thus, explanations of the outcomes of path-dependent processes require looking at history, rather than simply at current conditions of technology, preferences, and other factors that determine outcomes.
Path-dependent features of the economy range from small-scale technical standards to large-scale institutions and patterns of economic development. Several of the most prominent path-dependent features of the economy are technical standards, such as the "QWERTY" standard typewriter (and computer) keyboard and the "standard gauge" of railway track -- i.e., the width between the rails. The case of QWERTY has been particularly controversial, and it is discussed at some length below. The case of track gauge is useful for introducing several typical features of path-dependent processes and their outcomes.
Standard Railway Gauges and the Questions They Suggest
Four feet 8-1/2 inches (1.435 meters) is the standard gauge for railways throughout North America, in much of Europe, and altogether on over half of the world's railway routes. Indeed, it has been the most common gauge throughout the history of modern railways, since the late 1820s. Should we conclude, as economists often do for popular products or practices, that this standard gauge has proven itself technically and economically optimal? Has it been chosen because of its superior performance or lower costs? If so, has it proven superior for every new generation of railway technology and for all changes in traffic conditions? What of the other gauges, broader or narrower, that are used as local standards in some parts of the world -- are these gauges generally used because different technology or different traffic conditions in those regions favor these gauges?
The answer to all these questions is no. The consensus of engineering opinion has usually favored gauges broader than 4'8.5", and in the late nineteenth century an important minority of engineers favored narrower gauges. Nevertheless, the gauge of 4'8.5" has always had greater use in practice because of the history of its use. Indeed, even the earliest modern railways adopted the gauge as a result of history. The "father of railways," British engineer George Stephenson, had experience using the gauge on an older system of primitive coal tramways serving a small group of mines near Newcastle, England. Rather than determining optimal gauge anew for a new generation of railways, he simply continued his prior practice. Thus the gauge first adopted more than two hundred years ago for horse-drawn coal carts is the gauge now used for powerful locomotives, massive tonnages of freight shipments, and passenger trains traveling at speeds as great as 300 kilometers per hour (186 mph).
We will examine the case of railway track gauge in more detail below, along with other instances of path dependence. We first take an analytical look at what conditions may give rise to path dependence -- or prevent it from arising, as some critics of the importance of path dependence have argued.
What Conditions Give Rise to Path Dependence?
Durability of Capital Equipment
The most trivial -- and uninteresting -- form of path dependence is based simply on the durability of capital equipment. Obsolete, inferior equipment may remain in use because its fixed cost is already "sunk" or paid for, while its variable costs are lower than the total costs of replacing it with a new generation of equipment. The duration of this sort of path dependence is limited by the service life of the obsolete equipment.
In railways, none of the original gauge-specific capital equipment from the early nineteenth century remains in use today. Why, then, has Stephenson's standard gauge persisted? Part of the reason is the technical interrelatedness of railway track and the wheel sets of rolling stock. When either track or rolling stock wears out, it must be replaced with equipment of the same gauge, so that the wheels will still fit the track and the track will still fit the wheels. Railways almost never replace all their track and rolling stock at the same time. Thus a gauge readily persists beyond the life of any piece of equipment that uses it.
A further reason for the persistence, and indeed spread, of the Stephenson gauge is increasing returns to the extent of use. Different railway companies or administrations benefit from using a common gauge, because this saves costs and improves both service quality and profits on through-shipments or passenger trips that pass over each other's track. New railways have therefore nearly always adopted the gauge of established connecting lines, even when engineers have favored different gauges. Once built, railway lines are reluctant to change their gauge unless neighboring lines do so as well. This adds coordination costs to the physical costs of any conversion.
In early articles on path dependence, Paul David (1985, 1987) listed these same three conditions for path dependence: first, the technical interrelatedness of system components; second, increasing returns to scale in the use of a common technique; and, third, "quasi-irreversibility of investment," for example in the durability of capital equipment (or of human capital). The third condition gives rise to switching costs, while the first two conditions make gradual change impractical and rapid change costly, due to the transactions costs required to coordinate the actions of different agents. Thus together, these three conditions may lend persistence or stability to a particular path of outcomes, "locking in" a particular feature of the economy, such as a standard railway track gauge.
David's early work on path dependence represents, in part, the culmination of an earlier economic literature on technical interrelatedness (Veblen 1915; Frankel 1955; Kindleberger 1964; David 1975). By contrast, the other co-developer of the concept of path dependence, W. Brian Arthur, based his ideas on an analogy between increasing returns in the economy, particularly when expressed in the form of positive externalities, and conditions that give rise to positive feedbacks in the natural sciences.
Dynamic Increasing Returns to Adoption
In a series of theoretical papers starting in the early 1980s, Arthur (1989, 1990, 1994) emphasized the role of "increasing returns to adoption," especially dynamic increasing returns that develop over time. These increasing returns might arise on the supply side of a market, as a result of learning effects that lower the cost or improve the quality of a product as its cumulative production increases. Alternatively, increasing returns might arise on the demand side of a market, as a result of positive "network" externalities, which raise the value of a product or technique for each user as the total number of users increases (Katz and Shapiro 1985, 1994). In the context of railways, for example, a railway finds a particular track gauge more valuable if a greater number of connecting railways use that gauge. (Note that a track gauge is not a "product" but rather a "technology," as Arthur puts it, or a "technique," as I prefer to call it.)
In Arthur's (1989) basic analytical framework, "small events," which he treated as random, lead to early fluctuations in the market shares of competing techniques. These fluctuations are magnified by positive feedbacks, because techniques with larger market shares tend to be more valuable to new adopters. As a result, one technique grows in market share until it is "locked in" as a de facto standard. In a simple version of Arthur's model (Table 1), different consumers or firms initially favor different products or techniques. At first, market share for each technique fluctuates randomly, depending on how many early adopters happen to prefer each technique. Eventually, however, one of the techniques will gain enough of a lead in market share that it will offer higher payoffs to everyone -- including to the consumers or firms that have a preference for the minority technique. For example, if the total number of adoptions for technique A reaches 80, while the number of adoptions of B is less than 60, then technique A offers higher payoffs for everyone, and it is locked in as the de facto standard.
Table 1. Adoption Payoffs in Arthur's Basic Model
|Number of previous adoptions||0||10||20||30||40||50||60||70||80||90|
|"R-type agents" (who prefer technique A):|
|"S-type agents" (who prefer technique B):|
Source: Adapted from Arthur (1989).
Which of the competing techniques becomes the de facto standard is unpredictable on the basis of systematic conditions. Rather, later outcomes depend on the specific early history of the process. If early "small" events and choices are governed in part by non-systematic factors -- even "historical accidents" -- then these factors may have large effects on later outcomes. This is in contrast to the predictions of standard economic models, where decreasing returns and negative feedbacks diminish the impact of non-systematic factors. To cite another illustration from the history of railways, George Stephenson's personal background was a non-systematic or "accidental" factor that, due to positive feedbacks, had a large influence on the entire subsequent history of track gauge.
Efficiency, Foresight, Remedies, and the Controversy over Path Dependence
Arthur's (1989) basic model of a path-dependent process considered a case in which the selection of one outcome (or one path of outcomes) rather than another has no consequences for general economic efficiency -- different economic agents favor different techniques, but no technique is best for all. Arthur also, however, used a variation of his modeling approach to argue that an inefficient outcome is possible. He considered a case where one technique offers higher payoffs than another for larger numbers of cumulative adoptions (technique B in Table 2), while for smaller numbers the other technique offers higher payoffs (technique A). Arthur argued that, given his model's assumptions, each new adopter, arriving in turn, will prefer technique A and adopt only it, resulting later in lower total payoffs than would have resulted if each adopter had chosen technique B. Arthur's assumptions were, first, that each agent's payoff depends only on the number of previous adoptions and, second, that the competing techniques are "unsponsored," that is, not owned and promoted by suppliers.
Table 2. Adoption Payoffs in Arthur's Alternative Model
|Number of previous adoptions||0||10||20||30||40||50||60||70||80||90|
Source: Arthur (1989), table 2.
Liebowitz and Margolis's Critique of Arthur's Model
Arthur's discussion of efficiency provided the starting point for a theoretical critique of path dependence offered by Stan Liebowitz and Stephen E. Margolis (1995). Liebowitz and Margolis argued that two conditions, when present, prevent path-dependent processes from resulting in inefficient outcomes: first, foresight into the effects of choices and, second, opportunities to coordinate people's choices, using direct communication, market interactions, and active product promotion. Using Arthur's payoff table (Table 2), Liebowitz and Margolis argued that the purposeful, rational behavior of forward-looking, profit-seeking economic agents can override the effects of events in the past. In particular, if agents can foresee that some potential outcomes will be more efficient than others, then they have incentives to avoid the suboptimal ones. Agents who already own -- or else find ways to appropriate -- products or techniques that offer superior outcomes can often earn substantial profits by steering the process to favor those products or techniques. For the situation in Table 2, for example, the supplier of product or technique B could draw early adopters to that technique by temporarily setting a price below cost, making a profit by raising price above cost later.
Thus, in Liebowitz and Margolis's analysis, the sort of inefficient or inferior outcomes that can arise in Arthur's model are often not true equilibrium outcomes that market processes would lead to in the real world. Rather, they argued, purposeful behavior is likely to remedy any inferior outcome -- except where the costs of a remedy, including transactions costs, are greater than the potential benefits. In that case, they argued, an apparently "inferior" outcome is actually the most efficient one available, once all costs are taken into account. "Remediable" inefficiency, they argued in contrast, is highly unlikely to persist.
Liebowitz and Margolis's analysis gave rise to a substantial controversy over the meaning and implications of path dependence. In the view of Liebowitz and Margolis, the major claims of the economists who promote the concept of path dependence have amounted to assertions of remediable inefficiency. Liebowitz and Margolis coined the term "third-degree" path dependence to refer to such cases. They contrasted this category both to "first-degree" path dependence, which has no implications for efficiency, and to "second-degree" path dependence, where transactions costs and/or the impossibility of foresight lead to outcomes that offer lower payoffs than some hypothetical -- but unattainable -- alternative. In Liebowitz and Margolis's view, only "third-degree" path dependence offers scope for optimizing behavior, and thus only this type stands in conflict with what they call "the neoclassical model of relentlessly rational behavior leading to efficient, and therefore predictable, outcomes" (1995). Only this category of path dependence, they argue, would constitute market failure. They cast strong doubt on the likelihood of its occurrence, and they asserted that no empirical examples have been demonstrated.
Responses to Liebowitz and Margolis's Critique
Proponents of the importance of path dependence have responded, in large part, by asserting that the interesting features of path dependence have little to do with the question of remediability. David (1997, 2000) argued that the concept of third-degree path dependence proves incoherent upon close examination and that Liebowitz and Margolis had misconstrued the issues at stake. The present author asserted that one can usefully incorporate several of Liebowitz and Margolis's ideas on foresight and forward-looking behavior into the theory of path dependence while still affirming the claims made by proponents (Puffert 2000, 2002, 2003).
Imperfect Foresight and Inefficiency
One point that I have emphasized is that the cases of path dependence cited by proponents typically involve imperfect foresight, and sometimes other features, that make remediation impossible. Indeed, proponents of the importance of path dependence partly recognized this point prior to the work of Liebowitz and Margolis. Nobel Prize-winner Kenneth Arrow argued in his foreword to Arthur's collected articles that Arthur's modeling approach applies specifically to cases where foresight is imperfect, or "expectations are based on limited information" (Arthur 1994). Thus, economic agents cannot foresee future payoffs, and they cannot know how best to direct the process to the outcomes they would prefer. In terms of the payoffs in Table 2, technique A might become locked-in because adopters as well as suppliers initially think, mistakenly, that technique A will continue to offer the higher payoffs. Similarly, David (1987) had argued still earlier that path dependence is sometimes of interest precisely because lock-in might happen too quickly, before the payoffs of different paths are known. Lock-in, as David and Arthur use the term, applies to a stable equilibrium -- i.e., to an outcome that, if inefficient, is not remediable. (Liebowitz and Margolis introduce a different definition of lock-in.)
Imperfect foresight is, of course, a common condition -- and especially common for new, unproven products (or techniques) in untested markets. Part of the difference between path-dependent and "path-independent" processes is that foresight doesn't matter for path-independent processes. No matter what the path of events, path-independent processes still end up at unique outcomes that are predictable on the basis of fundamental conditions. Generally, these predictable outcomes are those that are most efficient and that offer the highest payoffs. By contrast, path-dependent processes have multiple potential outcomes, and the outcome selected is not necessarily the one offering the highest payoffs. This contrast to the results of standard economic analysis is part of what makes path dependence interesting.
Winners, Losers and Path Dependence
Path dependence is also interesting, however, when the issue at stake is not the overall efficiency (i.e., Pareto efficiency) of the outcome, but rather the distribution of rewards between "winners" and "losers" -- for example, between firms competing to establish their products or techniques as a de facto standard, resulting in profits or economic rents to the winner only. This is something that finds no place in Liebowitz and Margolis's taxonomy of "degrees." In keeping with Liebowitz and Margolis's analysis, competing firms certainly exercise forward-looking behavior in efforts to determine the outcome, but imperfect information and imperfect control over circumstances still make the outcome path dependent, as some of the case studies below illustrate.
Lack of Agreement on What the Debate Is About
Finally, market failure per se has never been the primary concern of proponents of the importance of path dependence. Even when proponents have highlighted inefficiency as one possible consequence of path dependence, this inefficiency is often the result of imperfect foresight rather than of market failure. Market failure is, however, the primary concern of Liebowitz and Margolis. This difference in perspective is one reason that the arguments of proponents and opponents have often failed to meet head on, as we shall consider in several case studies.
These contrasting analytical arguments can best be assessed through empirical cases. The case of the QWERTY keyboard is considered first, because it has generated the most controversy and it illustrates opposing arguments. Three further cases are particularly useful for the lessons they offer. Britain's "coal wagon problem" offers a strong example of inefficiency. The worldwide history of railway track gauge, now considered at greater length, illustrates the roles of foresight (or lack thereof) and transitory circumstances, as well as the role of purposeful behavior to remedy outcomes. The case of competition in videocassette recorders illustrates how path dependence is compatible with purposeful behavior, and it shows how proponents and critics of the importance of path dependence can offer different interpretations of the same events.
The Debate over QWERTY
The most influential empirical case has been that of the "QWERTY" standard typewriter and computer keyboard, named for the first letters appearing on the top row of keys. The concept of path dependence first gained widespread attention through David's (1985, 1986) interpretation of the emergence and persistence of the QWERTY standard. The critique of path dependence began with the alternative interpretation offered by Liebowitz and Margolis (1990).
David (1986) noted that the QWERTY keyboard was designed, in part, to reduce mechanical jamming on an early typewriter design that quickly went out of use, while other early keyboards were designed more with the intention of facilitating fast, efficient typing. In David's account, QWERTY's triumph over its initial revivals resulted largely from the happenstance that typing schools and manuals offered instruction in eight-finger "touch" typing first for QWERTY. The availability of trained typists encouraged office managers to buy QWERTY machines, which in turn gave further encouragement to budding typists to learn QWERTY. These positive feedbacks increased QWERTY's market share until it was established as the de facto standard keyboard.
Furthermore, according to David, similar positive feedbacks have kept typewriter users "locked in" to QWERTY, so that new, superior keyboards could gain no more than a small foothold in the market. In particular the Dvorak Simplified Keyboard, introduced during the 1930s, has been locked out of the market despite experiments showing its superior ergonomic efficiency. David concluded that our choice of a keyboard even today is governed by history, not by what would be ergonomically and economically optimal apart from history.
Liebowitz and Margolis (1990) directed much of their counterargument to the alleged superiority of the Dvorak keyboard. They showed, indeed, that claims David cited for the dramatic superiority of the Dvorak keyboard were based on dubious experiments. The experiments that Liebowitz and Margolis prefer support the conclusion that it could never be profitable to retrain typists from QWERTY to the Dvorak keyboard. Moreover, Liebowitz and Margolis cited ergonomic studies that conclude that the Dvorak keyboard offers at most only a two to six percent efficiency advantage over QWERTY.
Liebowitz and Margolis did not address David's proposed mechanism for the original triumph of QWERTY. Instead, they argued against the claims of some popular accounts that QWERTY owes its success largely to the demonstration effect of winning a single early typing contest. Liebowitz and Margolis showed that other, well-known typing contests were won by non-QWERTY typists, and so they cast doubt on the impact of a single historical accident. This, however, did not address the argument that David made about that one typing contest. David's argument was that the contest's modest impact consisted largely in vindicating the effectiveness of eight-finger touch-typing, which was being taught at the time only for QWERTY.
Although Liebowitz and Margolis never addressed David's claims about the role of third-party typing instruction, they did argue that suppliers had opportunities to offer training in conjunction with selling typewriters to new offices, so that non-QWERTY keyboards would not have been disadvantaged. They did not, however, present evidence that suppliers actually offered such training during the early years of touch-typing, the time when QWERTY became dominant. Whether the early history of QWERTY was path dependent thus seems to depend largely on the unaddressed question of how much typing instruction was offered directly by suppliers, as Liebowitz and Margolis suggest could have happened, and how much was offered by third parties using QWERTY, as David showed did happen.
Liebowitz and Margolis showed that early typewriter manufacturers competed vigorously in the features of their machines. They inferred, therefore, that the reason that typewriter suppliers increasingly supported and promoted QWERTY must have been that it offered a competitive advantage as the most effective system available. This reasoning is plausible, but it was not supported by direct evidence. The alternative, path-dependent explanation would be that QWERTY's competitive advantage in winning new customers consisted largely in its lead in trained typists and market share. That is, positive feedbacks would have affected the decisions of customers and, thus, also suppliers. David presented some evidence for this, although, in light of the issues raised by Liebowitz and Margolis, this evidence might now appear less than conclusive.
Liebowitz and Margolis highlighted the following lines from David's article: "… competition in the absence of perfect futures markets drove the industry prematurely into de facto standardization on the wrong system -- and that is where decentralized decision-making subsequently has sufficed to hold it" (emphasis original in David's article). In Liebowitz and Margolis's view, the focus here on decentralized decision-making constitutes a claim for market failure and third-degree path dependence, and they treat this as the central claim of David's article. In the view of the present author, this interpretation is mistaken. David's claim here plays only a minor role in his argument -- indeed it is less than one sentence. Moreover, it is not clear that David's comment about decentralized decision-making amounts to anything more than a reference to the high transactions costs that would be entailed in organizing a coordinated movement to an alternative outcome -- a point that Liebowitz and Margolis themselves have argued in other (non-QWERTY) contexts. (A coordinated change would be necessary because few typists would wish to learn a non-QWERTY system unless they could be sure of conveniently finding a compatible keyboard wherever they go.) David may have wished to suggest that centralized decision-making (by government?) would have greatly reduced these transactions costs, but David made no explicit claim that such a remedy would be feasible. If David had wished to make market failure or remediable inefficiency the central focus of his claims for path dependence, then he surely could and would have done so in a more explicit and forceful manner.
Part of what remains of the case of QWERTY is modest support for David's central claim that history has mattered, leaving us with a standard keyboard that is less efficient than alternatives available today -- not as inefficient as the claims David cited, but still somewhat so. Donald Norman, one of the world's leading authorities on ergonomics, estimates on the basis of several recent studies that QWERTY is about 10 percent less efficient than the Dvorak keyboard and other alternatives (Norman, 1990, and recent personal correspondence).
For Liebowitz and Margolis, it was most important to show that the costs of switching to an alternative keyboard would outweigh any benefits, so that there is no market failure in remaining with the QWERTY standard. This claim appears to stand. David had made no explicit claim for market failure, but Liebowitz and Margolis -- as well, indeed, as some supporters of David's account -- took that as the main issue at stake in David's argument.
Britain's "Silly Little Bobtailed" Coal Wagons
A strong example of inefficiency in path dependence is offered by the small coal wagons that persisted in British railway traffic until the mid-twentieth century. Already in 1915, economist Thorstein Veblen cited these "silly little bobtailed carriages" as an example of how industrial modernization may be inhibited by "the restraining dead hand of … past achievement," that is, the historical legacy of interrelated physical infrastructure: "the terminal facilities, tracks, shunting facilities, and all the ways and means of handling freight on this oldest and most complete of railway systems" (Veblen, 1915, pp. 125-8). Veblen's analysis was the starting point for the literature on technical and institutional interrelatedness that formed the background to David's early views on path dependence.
In recent years Van Vleck (1997, 1999) has defended the efficiency of Britain's small coal wagons, arguing that they offered "a crude just-in-time approach to inventory" for coal users while economizing on the substantial costs of road haulage that would have been necessary for small deliveries if railway coal wagons were larger. More recently, however, Scott (1999, 2001) presented evidence that few coal users benefited from small deliveries. Rather, he showed, the wagons' small size, widely dispersed ownership and control, antiquated braking and lubrication systems, and generally poor physical condition made them quite inefficient indeed. Replacing these cars and associated infrastructure with modern, larger wagons owned and controlled by the railways would have offered savings in railway operating costs of about 56 percent and a social rate of return of about 24 percent. Nevertheless, the small wagons were not replaced until both railways and collieries were nationalized after World War II. The reason, according to Scott, lay partly in the regulatory system that allocated certain rights to collieries and other car owners at the expense of the railways, and partly in the massive coordination problem that arose because railways would not have realized much savings in costs until a large proportion of antiquated cars were replaced. Together, these factors lowered the railways' realizable private rate of return below profitable levels. (Van Vleck's smaller estimates for potential efficiency gains from scrapping the small wagons were largely the result of assuming that there would be no change in the regulatory system or in the ownership and control of wagons. Scott argued that such changes added greatly to the potential cost savings.)
Scott noted that the persistence of small wagons was path dependent, because both the technology embodied in the small wagons and the institutions that supported fragmented ownership long outlasted the earlier, transitory conditions to which they were a rational response. Ownership of wagons by the collieries had been advantageous to railways as well as collieries in the mid-nineteenth century, and government regulation had assigned rights in a way designed to protect the interests of wagon owners from opportunistic behavior by the railways. By the early twentieth century, these regulatory institutions imposed a heavy burden on the railways, because they required either conveyance even of antiquated wagons for set rates or else payment of high levels of compensation to the wagon owners. The requirement for compensation helped to raise the railways' private costs of scrapping the small wagons above the social costs of doing so.
The case shows the relevance of Paul David's approach to path dependence, with its discussion of technical (and institutional) interrelatedness and quasi-irreversible investment, above and beyond Brian Arthur's more narrow focus on increasing returns.
The case also supports Liebowitz and Margolis's insight that an inferior path-dependent outcome can only persist where transactions costs (and other costs) prevent remediation, but it undercuts those authors' skepticism toward the possibility of market failure. The high transactions costs that would have been entailed in scrapping Britain's small wagons indeed outweighed the potential gains, but these costs were high only due to the institutions of property rights that supported fragmented ownership. When these institutions were later changed, a remedy to Britain's coal-wagon problem followed quickly. Thus, the failure to scrap the small wagons earlier can be ascribed to institutional and market failure.
The case thus appears to satisfy Liebowitz and Margolis's criterion for "third-degree" path dependence. This is not completely clear, however. Whether Britain's coal-wagon problem qualifies for that status depends on whether the benefits of solving the problem would have been worth the cost of implementing the necessary institutional changes, a question that Scott did not address. Liebowitz and Margolis argue that an inferior outcome cannot be considered a result of market failure, or even meaningfully inefficient, unless this criterion of remediability is satisfied.
In this present author's view, Liebowitz and Margolis's criterion has some usefulness in the context of considering government policy toward inferior outcomes, which is Liebowitz and Margolis's chief concern, but the criterion is much less useful for a more general analysis of these outcomes. If Britain's coal-wagon problem does not qualify for "third-degree" status, then it suggests that Liebowitz and Margolis's dismissive approach toward cases that they relegate to "second-degree" status is misplaced. The case seems to show that path dependence can have substantial effects on the economy, that the outcomes of path-dependent processes can vary substantially from the predictions of standard economic models, that these outcomes can exhibit substantial inefficiency of a sort discussed by proponents of path dependence, and that all this can happen despite the exercise of foresight and forward-looking behavior.
Railway Track Gauges
The case of railway track gauge illustrates how "accidental" or "contingent" events and transitory circumstances can affect choice of technique and economic efficiency over a period now approaching two centuries (Puffert 2000, 2002). The gauge now used on over half the world's railways, 4 feet 8.5 inches (4'8.5", 1435 mm), comes from the primitive mining tramway where George Stephenson gained his early experience. Stephenson transferred this gauge to the Liverpool and Manchester Railway, opened in 1830, which served as the model of best practice for many of the earliest modern railways in Britain, continental Europe, and North America. Many railway engineers today view this gauge as narrower than optimal. Yet, although they would choose a broader gauge today if the choice were open, they do not view potential gains in operating efficiency as worth the costs of conversion.
A much greater source of inefficiency has been the emergence of diversity in gauge. Six gauges came into widespread use in North America by the 1870s, and Britain's extensive Great Western Railway system maintained a variant gauge for over half a century until 1892. Even today, Australia and Argentina each have three different regional-standard gauges, while India, Chile, and several other countries each make extensive use of two gauges. Breaks of gauge also persist at the border of France and Spain and most external borders of the former Russian and Soviet empires. This diversity adds costs and impairs service in interregional and international traffic. Where diversity has been resolved, conversion costs have sometimes been substantial.
This diversity arose as a result of several contributing factors: limited foresight, the search for an improved railway technology, transitory circumstances, and contingent events or "historical accidents." Many early railway builders sought simply to serve local or regional transportation needs, and they did not foresee the later importance of railways in interregional traffic. Beginning in the late 1830s, locomotive builders found their ability to construct more powerful, easily maintained engines constrained by the Stephenson gauge, while some civil engineers thought that a broader gauge would offer improved capacity, speed, and passenger comfort. This led to a wave of adoption of broad gauges for new regions in Europe, the Americas, South Asia, and Australia. Changes in locomotive design soon eliminated much of the advantage of broad gauges, and by the 1860s it became possible to take advantage of the ability of narrow gauges to make sharper curves, following the contours of rugged landscape and reducing the need for costly bridges, embankments, cuttings, and tunnels. This, together with the beliefs of some engineers and promoters that narrow gauges would offer savings in operating costs, led to a wave of introductions of narrow gauges to new regions.
At every point of time there was some variation in engineering opinion and practice, so that which gauge was introduced to each new region often depended on the contingent circumstances of who decided the gauge. To cite only the most fateful example, Stephenson's rivals for the contract to build the Liverpool and Manchester Railway proposed to adopt the gauge of 5'6" (1676 mm). If that team had been employed, or if Stephenson had gained his earlier experience on almost any other mining tramway, then the ensuing worldwide history of railway gauge would have been different -- perhaps far different.
After the introduction of particular gauges to new regions, later railways nearly always adopted the gauge of established connecting lines, reinforcing early contingent choices with positive feedbacks. As different local common-gauge regions expanded, regions that happened to have the same gauge merged into one another, but breaks of gauge emerged between regions of differing gauge. The extent of diversity that emerged at the national and continental levels, and thus the relative efficiency of the outcome, thus depended on earlier contingent events.
Once these patterns of diversity had been established by a path-dependent process, they were partly rationalized by the sort of forward-looking, profit-seeking behavior proposed by Liebowitz and Margolis. In North America, for example, a continental standard emerged quickly after demand for interregional transport grew, and standardization was facilitated both by the formation of interregional railway systems and by cooperation among independent railways. Elsewhere as well, much of the most inefficient diversity was resolved relatively quickly. Nonetheless, a costly diversity has persisted in places where variant-gauge regions had grown large and costly to convert before the value of conversion became apparent. Spain's variant gauge has become more costly in recent years as the country's economy has been integrated into that of the European Union, but estimated costs of (U.S.) $5 billion have precluded conversion. India and Australia have only recently made substantial progress toward the resolution of their century-old diversity.
Wherever gauge diversity has been resolved, it is one of the earliest gauges that has emerged as the standard. In no significant part of the world has current practice in gauge broken free of its early history. The inefficiency that has resulted, relative to what other sequences of events might have produced, was not the result of market failure. Rather, it resulted primarily from the natural inability of railway builders to foresee how railway networks and traffic patterns would develop and how technology would evolve.
The case also illustrates the usefulness of Arthur's (1989) modeling approach for cases of unsponsored techniques and limited foresight (Puffert 2000, 2002). These were essentially the conditions Arthur assumed in proposing his model.
Videocassette Recording Systems
Markets for technical systems exhibiting network externalities (where users benefit from using the same system as other users) often tend to give rise to de facto standards -- one system used by all. Foreseeing this, suppliers sometimes join to offer a common system standard from the outset, precluding any possibility for path-dependent competition. Examples include first-generation compact discs (CDs and CD-ROMs) and second-generation DVDs.
In the case of consumer videocassette recorders (VCRs), however, Sony with its Betamax system and JVC with its VHS system were unable to agree on a common set of technical specifications. This gave rise to a celebrated battle between the systems lasting from the mid-1970s to the mid-1980s. Arthur (1990) used this competition as the basis for a thought experiment to illustrate path dependence. He explained the triumph of VHS as the result of positive feedbacks in the video film rental market, as video rental stores stocked more film titles for the system with the larger user base, while new adopters chose the system for which they could rent more videos. He also suggested tentatively that, if the common perception that Betamax offered a superior picture quality is true, then the "the market's choice" was not the best possible outcome.
In a closer look at the case, Cusumano et al. (1992) showed that Arthur's suggested positive-feedback mechanism was real, and that this mechanism explains why Sony eventually withdrew Betamax from the market rather than continuing to offer it as an alternative system. However, they also showed that the video rental market emerged only at a late stage in the competition, after VHS already had a strong lead in market share. Thus, Arthur's mechanism does not explain how the initial symmetry in competitors' positions was broken.
Cusumano et al. argued, nonetheless, that the earlier competition already had a path-dependent market-share dynamic. They presented evidence that suppliers and distributors of VCRs increasingly chose to support VHS rather than Betamax because they saw other market participants doing so, leading them to believe that VHS would win the competition and emerge as a de facto standard. The authors did not make clear, however, why market participants believed that a single system would become so dominant. (In a private communication, coauthor Richard Rosenbloom said that this was largely because they foresaw the later emergence of a market for prerecorded videos.)
The authors argue that three early differences in promoters' strategies gave VHS its initial lead. First, Sony proceeded without major co-sponsors for its Betamax system, while JVC shared VHS with several major competitors. Second, the VHS consortium quickly installed a large manufacturing capacity. Third, Sony opted for a more compact videocassette, while JVC chose instead a longer playing time for VHS. In the event, a longer playing time proved more important to many consumers and distributors, at least during early years of the competition when Sony cassettes could not accommodate a full (U.S.) football game.
This interpretation shows how purposeful, forward-looking behavior interacted with positive feedbacks in producing the final outcome. The different strategies, made under conditions of limited foresight, were contingent decisions that set competition among the firms on one path rather than another (Puffert 2003). Furthermore, the early inability of Sony cassettes to accommodate a football game was a transitory circumstance that may have affected outcomes long afterward.
Liebowitz and Margolis's (1995) initial interpretation of the case responded only to Arthur's brief discussion. They argued that the playing-time advantage for VHS was the crucial factor in the competition, so that VHS won because its features most closely matched consumer demand -- and not due to path dependence. Although their discussion covers part of the same ground as that of Cusumano et al., Liebowitz and Margolis did not respond to the earlier article's argument that the purposeful behavior of suppliers interacted with positive feedbacks. Rather, they treated this purposeful behavior as the antithesis of the mechanistic, non-purposeful evolution of market share that they see as the ultimate basis of path dependence.
Liebowitz and Margolis also presented substantial evidence that Betamax was not, in fact, a superior system for the consumer market. The primary concern of their argument was to refute a suggested case of path-dependent lock-in to an inferior technique, and in this they succeeded. It is arguable that they overstated their case, however, in asserting that what they refuted amounted to a claim for "third-degree" path dependence. Arthur had not argued that the selection of VHS, if inferior to Betamax, would have been remediable.
Recently, Liebowitz (2002) did respond to Cusumano et al. He argued, in part, that the larger VHS tape size offered a permanent rather than transitory advantage, as this size facilitated higher tape speeds and thus better picture quality for any given total playing time.
A Brief Discussion of Further Cases
Cowan and Gunby (1996) showed that there is path dependence in farmers' choices between systems of chemical pest control and integrated pest management (IPM). IPM relies in part on predatory insects to devour harmful ones, and the drift of chemical pesticides from neighboring fields often makes the use of IPM impossible. Predatory insects also drift among fields, further raising farmers' incentives to use the same techniques as neighbors. To be practical, IPM must be used on the whole set of farms that are in proximity to each other. Where this set is large, the transactions costs of persuading all farmers to forego chemical methods often prevent adoption. In addition to these localized positive feedbacks, local learning effects also make the choice between systems path dependent. The path-dependent local lock-in of each technique has sometimes been upset by such developments as invasions by new pests and the emergence of resistance to pesticides.
Nuclear Power Reactors
Cowan (1990) argued that transitory circumstances led to the establishment of the dominant "light-water" design for civilian nuclear power reactors. This design, adapted from power plants for nuclear submarines, was rushed into use during the Cold War because the political value of demonstrating peaceful uses for nuclear technology overrode the value of finding the most efficient technique. Thereafter, according to Cowan, learning effects arising from engineering experience for the light-water design continued to make it the rational choice for new reactors. He argued that there are fundamental scientific and engineering reasons for believing, however, that an equivalent degree of development of alternative designs may have made them superior.
Although Shapiro and Varian (1998) did not emphasize the term path dependence, they pointed to a broad range of research documenting positive feedbacks that affect competition in contemporary information technology. Like Morris and Ferguson (1993), they showed how competing firms recognize and seek to take advantage of these positive feedbacks. Strictly speaking, not all of these cases are path dependent, because in some cases firms have been able to control the direction and outcome of the allocation processes. In other cases, however, the allocation process has had its own path-dependent dynamic, affected both by the attempts of rival firms to promote their products and by factors that are unforeseen or out of their control.
Among the cases that Shapiro and Varian discuss are some involving Microsoft. In addition, some proponents of the importance of path dependence have argued that positive feedbacks favor Microsoft's competitive position in ways that hinder competitors from developing and introducing innovative products (see, for example, Reback et al., 1995). Liebowitz and Margolis (2000), by contrast, offered evidence of cases where superior computer software products have had no trouble winning markets. Liebowitz and Margolis also argued that the lack of demonstrated empirical examples of "third-degree" path dependence creates a strong presumption against the existence of an inferior outcome that government antitrust measures could remedy.
Path Dependence at Larger Levels
Geography and Trade
The examples thus far all treat path dependence in the selection of alternative products or techniques. Krugman (1991, 1994) and Arthur (1994) have also pointed to a role for contingent events and positive feedbacks in economic geography, including in the establishment of Silicon Valley and other concentrations of economic activity. Some of these locations, they showed, are the result not of systematic advantages but rather of accidental origins reinforced by "agglomeration" economies that lead new firms to locate in the vicinity of similar established firms. Krugman (1994) also discussed how these same effects produce path dependence in patterns of international trade. Geographic patterns of economic activity, some of which arise as a result of contingent historical events, determine the patterns of comparative advantage that in turn determine patterns of trade.
Path dependence also arises in the development of institutions -- a term that economists use to refer to the "rules of the game" for an economy. Eichengreen (1996) showed, for example, that the emergence of international monetary systems, such as the classical gold standard of the late nineteenth century, was path dependent. This path dependence has been based on the benefits to different countries of adopting a common monetary system. Eichengreen noted that these benefits take the form of network externalities. Puffert (2003) has argued that path dependence in institutions is likely to be similar to path dependence in technology, as both are based on the value of adopting a common practice -- some technique or rule -- that becomes costly to change.
Thus path dependence can affect not only individual features of the economy but also larger patterns of economic activity and development. Indeed, some teachers of economic history interpret major regional and national patterns of industrialization and growth as partly the result of contingent events reinforced by positive feedbacks -- that is, as path dependent. Some suggest, as well, that the institutions responsible for economic development in some parts of the world and those responsible for backwardness in others are, at least in part, path dependent. In the coming years we may expect these ideas to be included in a growing literature on path dependence.
Path dependence arises, ultimately, because there are increasing returns to the adoption of some technique or other practice and because there are costs in changing from an established practice to a different one. As a result, many current features of the economy are based on what appeared optimal or profit-maximizing at some point in the past, rather than on what might be preferred on the basis of current general conditions.
The theory of path dependence is not an alternative to neoclassical economics but rather a supplement to it. The theory of path dependence assumes, generally, that people optimize on the basis of their own interests and the information at their disposal, but it highlights ways that earlier choices put constraints on later ones, channeling the sequence of economic outcomes along one possible path rather than another. This theory offers reason to believe that some -- or perhaps many -- economic processes have multiple possible paths of outcomes, rather than a unique equilibrium (or unique path of equilibria). Thus the selection among outcomes may depend on nonsystematic or "contingent" choices or events. Empirical case studies offer examples of how such choices or events have led to the establishment, and "lock in," of particular techniques, institutions, and other features of the economy that we observe today -- although other outcomes would have been possible. Thus, the analysis of path dependence adds to what economists know on the basis of more established forms of neoclassical analysis.
It is not possible at this time to assess the overall importance of path dependence, either in determining individual features of the economy or in determining larger patterns of economic activity. Research has only partly sorted out the concrete conditions of technology, interactions among agents, foresight, and markets and other institutions that make allocation path dependent in some cases but not in others (Puffert 2003; see also David 1997, 1999, 2000 for recent refinements on theoretical conditions for path dependence).
Addendum: Technical Notes on Definitions
Path dependence, as economists use the term, corresponds closely to what mathematicians call non-ergodicity (David 2000). A non-ergodic stochastic process is one that, as it develops, undergoes a change in the limiting distribution of future states, that is, in the probabilities of different outcomes in the distant future. This is somewhat different from what mathematicians call path dependence. In mathematics, a stochastic process is called path dependent, as opposed to state dependent, if the probabilities of transition to alternative states depend not simply on the current state of the system but, additionally, on previous states.
Furthermore, the term path dependence is applied to economic processes in which small variations in early events can lead to large or discrete variations in later outcomes, but generally not to processes in which small variations in events lead only to small and continuous variations in outcomes. That is, the term is used for cases where positive feedbacks magnify the impact of early events, not for cases where negative feedbacks diminish this impact over time.
The term path dependence can also be used for cases in which the impact of early events persists without appreciably increasing or decreasing over time. The most important examples would be instances where transitory conditions have large, persistent impacts.
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