Path Dependence

Stephen E. Margolis

S. J. Liebowitz


S. J. Liebowitz: Management School, University of Texas at Dallas, Richardson, Texas 75083

Stephen E. Margolis: Department of Economics, North Carolina State University, Raleigh, North Carolina 27695


Path dependence is a term that has come into common use in both economics and law. In all instances that path dependence is asserted, the assertion amounts to some version of "history matters." Path dependence can mean just that: Where we are today is a result of what has happened in the past. For example, the statement "we saved and invested last year and therefore we have assets today" might be more fashionably expressed as, "the capital stock is path dependent."

Path dependence is an idea that spilled over to economics from intellectual movements that arose elsewhere. In physics and mathematics the related ideas come from chaos theory. One potential of the non-linear models of chaos theory is sensitive dependence on initial conditions: Determination, and perhaps lock-in, by small, insignificant events. In biology, the related idea is called contingency -- the irreversible character of natural selection. Scientific popularizations (Gleick [1987], Gould [1991]) have moved these ideas into the public view.

We must caution, however, that the analogies are incomplete. If turtles become extinct, they will not reappear suddenly when circumstance change to make it advantageous to have a shell. But if people stop using large gas guzzling engines because gasoline has become expensive, or extend patent protection to the "look and feel" of software, they can always revert to their old ways if they came to regret the switch.

Similarly, path dependence and chaos have an apparent unity that may be misleading. In chaos theory, small events or perturbations tend to cause a system to evolve in very different ways but the system never settles down in any repeatable path or fixed equilibrium. The essence of "chaos theory" is that this seemingly endless pattern, which never finds an equilibrium, is not random but rather has a determinate structure. Path dependence in economics has imported the view that minor initial perturbations are important, but has grafted this on to a theory where there are a finite number of perfectly stable alternative states, one of which will arise based on the particular initial conditions. The never ending "disequilibrium" that seems the essence of chaos theory is thus missing from the economic analysis of path dependence.

In mathematics, path independence is a condition for the existence of exact solutions for differential equations. In probability theory, a stochastic process is path dependent if the probability distribution for period t+1 is conditioned on more than the value of the system in period t. In both cases, path independence means that it doesn’t matter how you get got to a particular point, only that you geot there. What is interesting is that in both of these mathematical uses of path independence, history does matter in the ordinary sense. History matters in that it is what gets us to the present state. In a game of coin tossing, for example, the history of coin tosses does determine the winnings of each player. But the particular sequence of winnings does not influence the probabilities on the next toss. In contrast, if a process is path dependent, the sequence does influence the next step. So in mathematics, path dependence is a stronger claim than simply that history matters. Unfortunately, as path dependence has been borrowed into the social sciences, it has taken on several different and often conflicting meanings. Sometimes it means only that history matters in the very narrowest sense, and other times it means something more.

I. The issue

Economics has always recognized that history matters. The wealth of nations has much to do with the accumulation of capital of every sort; our saving, investing, studying and inventing. All this is history.

Some writers have lately raised concerns that current economic circumstances may depend in important ways on the quirks and accidents of history. Further, they raise a concern that our circumstances may depend on these quirks and accidents in particularly perverse ways. The present that we inherit or the future that we build may come about not as a result of endowments and preferences--the important givens or the inevitable forces of economic history--but rather from little things that we might easily change if we only realized how they affected us. A shelter is built at a particular clearing for no very important reason, which leads to the development of a village. In turn, the village may develop into a city. Similarly, a chance experiment with one technology leads to additional experimentation with that technology, which increases its advantages over untried alternatives. In each instance, we build on what we have, making the best of it. In this context, individuals may have limited incentives to examine whether what we have is what we ought to have and limited opportunity to effect a change. Are we optimizing in some global sense, or are we just finding some minor, local and insignificant optimum? This is the concern raised by path dependence as it has been applied to economic allocations.

2. A taxonomy of path dependence.

Several very different types of claims appear in the literature as path dependence. Unfortunately, although these different claims may have vastly different implications, discussions of path dependence have not always distinguished among them. An earlier paper [Liebowitz and Margolis 1995] elaborates on these different sorts of claims and explains the potential for error in treating these claims as if they were equivalent. A summary of that taxonomy follows.

A minimal form of path dependence is present whenever there is an element of persistence or durability in a decision. For example, an individual does not alter his consumption of housing services every day in response to changes income or relative prices. Since one’s exact consumption of housing is largely determined by a rental or purchase decision made some time in the past, an observer could not expect to determine the values of a consumer's housing consumption today even with full knowledge of the current values that enter that consumer's optimization problem. So here we have something that could be called path dependence. What we have today depends critically on conditions that prevailed and decisions taken at some time in the past. The observation that the consumer’s bundle is narrowly wrong, given today’s income and prices, would not, however, prompt anyone to claim that the consumer is irrational, nor would it prompt us to discard consumer rationality as a basis for analysis. In any practical approach to modeling the consumer’s choice problem, we would recognize the presence of some fixed or quasi-fixed factors and the presence of transaction costs, and examine the consumer’s action as a rational pursuit of his interests. Here we have persistence and perhaps nothing else. The consumer may well have properly predicted all future prices, incomes, family size developments, and so on. If so, there is no error or inefficiency. This is what we have termed "first degree" path dependence. Path dependence here does no harm, it is simply the fact of durability.

Since information is always imperfect, a second circumstance is always possible. When individuals fail to predict the future perfectly, it is likely that ex ante efficient decisions may not turn out to be efficient in retrospect. You may build a house without knowing that five years hence a sewage treatment plant will be built nearby, lowering property values and the neighbourhood amenities available. Here the inferiority of a chosen path is unknowable at the time a choice is made, but we later recognize that some alternative path would have yielded greater wealth. In such a situation, which we have termed second-degree path dependence, there is a dependence on past conditions that leads to outcomes that are regrettable and costly to change. We would not have built the house had we known what was going to transpire. This dependence is not, however, inefficient in any meaningful sense, given the assumed limitations on knowledge.

The strongest form of path dependence claim, which we have termed third degree path dependence, is a claim that alleges the existence of remediable inefficiencies. You know a sewage plant is going to be built but build a house nearby anyway since all of your friends are buying houses there and you value being part of that neighbourhood. You would rather buy a house away from the sewage plant, and so would your friends, but you and your friends are somehow unable to coordinate your actions.

The three types of path dependence make progressively stronger claims. First-degree path dependence is a simple assertion of an intertemporal relationship, with no implied error of prediction or claim of inefficiency. Second-degree path dependence stipulates that intertemporal effects together with imperfect prediction result in actions that are regrettable, though not inefficient. Third-degree path dependence requires not only that the intertemporal effects propagate error, but also that the error was avoidable.

Williamson (1993b: 140) introduces the term "remediability" to refer to the circumstance in which known feasible and preferable alternatives exist. He argues that it is necessary to establish remediability in this sense, in making any claim that an allocation is inefficient. Demsetz 1973, Coase 1964, Calabresi 1968, and Dahlman 1979 have made similar points.

Clearly, the phenomena that we are calling first and second degree path dependence are extremely common. They are a reflection of ordinary durability and they have always been a part of economic thought. Ordinary theories of capital and decision making under uncertainty acknowledge the considerations that give us the first and second degree forms of path dependence.

All this is not to claim that there is nothing new to be said with regard to first- and second-degree forms. It can be both novel and important to observe persistence in circumstances where it might not be immediately apparent. For example, people will adapt their behavior and make fixed investments in response to laws and other economic institutions. These adaptations can make it costly to change these laws and institutions later on. Nevertheless the main focus and novelty of the current economic literature of path dependence is on the third- degree form, and prominent examples in this literature feature specific claims of inefficiency. For example, listen to Paul David: "The accretion of technological innovations inherited from the past therefore cannot legitimately be presumed to constitute socially optimal solutions provided for us -- either by heroic enterprises or herds of rational managers operating in efficient markets." [1992: 137].

It is the third- degree path dependence claim that constitutes a new challenge to invisible-hand theorems that private optimization leads individuals to wealth maximizing allocations. Consider this example. It could happen that we each prefer the Beta format for video tape recording, but if we each think everyone else is buying VHS recorders, and we care about compatibility, we might all buy VHS. We each maximize privately given this expectation, and it turns out that our forecasts are correct, yet we each end up worse off that we might have. Of course, that such a thing could happen does not mean that it does. Because there is wealth loss in third degree path dependence, various agents will have interests in avoiding this loss. It is an empirical issue, therefore, whether we do get the wrong video recorder, or more generally whether we enter or remain on inefficient paths where known, feasible, and superior alternatives exist.

While some writers do use path dependence simply to mean that history matters, many are explicitly concerned with efficiency claims. A prominent example is Mark Roe [1996], who offers a taxonomy of path dependence that upon first reading appears very similar to that offered in Liebowitz and Margolis [1995]. Roe seeks to establish a contrast between the economists’ alleged presumption of evolution towards efficiency and what he refers to as a "richer understanding."

In his "weak path dependence" two alternatives are equally efficient, but one is chosen and it survives. Although these alternatives may differ from one another in important ways, the choice has no efficiency consequences. Roe’s "weak path dependence" is not noticeably different from his "false path dependence" which appears to be his terminology for first-degree path dependence. The only difference between Roe’s "false" and "weak" path dependencies appears to be that the former are efficient and the latter are not inefficient. This appears to be a distinction without a difference.

Roe’s "semi-strong form" path dependence is a choice that "has become inefficient but is not worth changing." Roe tells us on page 648 that this form arises from errors in forecasting the future. At that point, Roe’s semi-strong form appears to be parallel in most respects to our second-degree path dependence, though we have emphasized that is it misleading to call this circumstance "inefficient." An additional problem is that while the definition (648) seems clear enough, Roe’s discussion of the durability of certain U.S. financial institutions (650) demonstrates the pitfalls of his taxonomy. Roe ponders whether this durability constitutes path dependence of the weak form or the semi-strong form. In so pondering, he ignores entirely the possibility that the persistence of American financial arrangements might just be efficient, that is, an instance of his "false path dependence." Since it would only be by remarkable serendipity that the alternative arrangements would be exactly as efficient as the ones that now exist (his "weak-form" path dependence), Roe argues that current American financial institutions seem overwhelmingly likely to exhibit the semi-strong form of path dependence, at best. All this with no actual evidence that these American institutions are locked in to any inefficiencies at all.

Finally, Roe offers strong-form path dependence as "highly inefficient structures that society cannot eliminate." If we understand that "cannot eliminate" means that the costs of eliminating these structures are prohibitive, an immediate problem with this definition is that the circumstance in which something is inefficient but not worth changing is not distinct from to the circumstance that Roe calls the semi-strong form.

The distinction Roe would like to sustain here is that the costs that prevent change in the strong form are "information and public choice costs." But these costs are not fundamentally different from other sorts of cost. Roe does acknowledge this, but not its full import. He writes: "We can reinterpret [the strong form] as a variant of the second [semi-strong] form: public choice and information are real costs of action." [651] Again we have a distinction that doesn’t seem to make a difference. Nevertheless, in observing this possibility, Roe does join most other observers in his observation that with rational agents, inefficiencies from path dependence can only occur where there is some coordination problem among agents. His definitional novelty would seem to be in his focus on path-created coordination (information) costs, although how and why path-created costs differ from other coordination costs is unclear.

For all his emphasis on efficiency, however, Roe’s framework does not allow us to consider the possibility of remediable losses. In both the strong and semi-strong forms that Roe defines, there is no possibility of improvement and therefore no socially relevant inefficiency or remediable loss, to be considered.

2. The Theory of Path Dependence

Brian Arthur’s writings on path dependence, as well as many other writings in this field (most prominently by Katz and Shapiro 1986, Farrell and Saloner 1986) share certain elements. First, most of them incorporate some version of increasing returns, which in this context may result from the usual economies of scale in the firm or from network effects. These increasing-returns economies often give rise to a second common element in this literature, models of multiple equilibria.

The role of increasing returns may be readily understood using Arthur’s own numerical example (1989). In this example, society is faced with an opportunity to develop one of two technologies. For each technology, the greater the number of adopters of the technology, the greater the payoffs to those adopters.

Individuals make decisions based on their private interests and receive payoffs as shown in the table. A first adopter of any technology would expect a payoff of 10 if he adopts technology A or 4 if he adopts technology B. Under these circumstances, Arthur notes, the adopter would certainly choose A. A second adopter would reach the same conclusion, and so on, as the advantage of technology A over technology B would only increase with additional adoptions of A. But notice that if the number of adopters does eventually become large, technology B offers greater payoffs. Thus for Arthur, the table tells us a story of lock-in, and lock-in to an undesirable outcome.

But there are problems with this table and the lessons that are drawn from it. First, note that the increasing payoffs in the table must be stronger for B than for A if this story is to unfold as presented (see the entry in network externalities and market failure for an explanation of why this is unlikely where increasing returns are due to network effects).

[put Table 1 here]

Table 1. Payoffs to adopters of two technologies













Technology A












Technology B












Also, the table does not allow adopters to anticipate or influence the outcome. But people clearly do both. If the first person who was faced with the opportunity to purchase a fax machine had assumed that he was going to be the only user, we might still be waiting for this technology to catch on. If a technology is owned, the owner of the technology may assure adopters that they will receive highest available payoffs by leasing applications with a cancellation option, and can publicize current and planned adoptions. Additionally, technology owners could simply bribe early adopters through low prices or other compensation. Of course, the owners of both of these technologies can do this, but the owner of the technology that creates more wealth can profitably invest more to win such a contest. Concluding that lock-in is inevitable here requires that we assume a very passive role for both consumers and entrepreneurs. It requires that we assume away consumer and trade magazines, trade associations, guarantees, advertising, brand names and so on.

If agents in the economy have the kind of information that is revealed to us in the table, they will have the motive, and some of them may have the means, of bringing about the preferred outcome. Of course, if no one has this kind of information, any alleged inefficiencies are entirely hypothetical. The alternative technology does not really present us with a known feasible alternative that is an improvement, but rather just an alternative roll of the dice. (See Liebowitz and Margolis 1995 for further discussion of this table.)

Models of multiple equilibria generally begin by assuming increasing returns in some form, and then adding either differences among consumers or a stochastic choice process. Figure 1 illustrates a typical modeling (see Liebowitz and Margolis 1996). Assume, for example, that consumers much chose between two technologies, A and B. This could be the choice between Beta and VHS or between DOS and Macintosh. An equilibrium condition is shown on the upward sloping forty-five degree line. For an equilibrium, the fraction choosing a particular alternative must equal the fraction that has chosen that alternative. (For example, if 75% are using VHS, new purchases must be at 75% VHS for that share to persist.)

[Put Figure 1 here]

The S shaped curve reflects consumer behaviour and is consistent with increasing returns. The curve is upward sloping because as more consumers are A users, option A is more attractive, so the probability that a consumer will chose A is larger. The S shape reflects a kind of critical mass influence. There are three equilibria. The one at M is unstable. At small displacements to the left of this intersection, the fraction choosing A is less than the fraction that have chosen A. This will lead to a smaller share for A, which leads fewer consumers to chose A, and so on. The share of A will decline to zero. To the right of M, A’s share will increase until all consumers are choosing A.

These models are often invoked to illustrate that the outcome depends crucially, though perhaps perversely, on history. If we get started just slightly to the left of M, technology A will fail, regardless of the intrinsic merits of A. If we get started slightly to the right of M, A succeeds, again regardless of its merits. If A were inherently better than the alternative, a differently shaped S-shaped curve would have point M somewhere to the left of centre, but the possibility of a non-A equilibrium would not be removed. History, perhaps some whimsical or coincidental start to things, will dictate the outcome.

All this comes to us dressed in the full rigour of mathematical proofs, supported by theorems on stochastic processes. The weak link, however, is in the phrase, "if we get started." That phrase buries a world of assumptions. In particular, it again abstracts from all of the things that companies do to win technological races and all of the things that consumers do to purchase well. Where we get started is a choice, not an entirely random process. The reasoning that leads to the conclusion of sensitive dependence on initial conditions--the accidents of history-- is that some initial decision-maker just happens to choose A, or B, and that decision has enormous influence. But a single agent with only minimal interest in the process, who might be expected to have chosen whimsically or idiosyncratically, is not likely to have the powerful influence that is assumed for this process.

This model is often used to analyze markets in which consumers benefit from their compatibility with other consumers. In such cases, some researchers have suggested that consumers respond to the installed base of a particular technology, that is, the entire stock of commitments to a technology. Liebowitz and Margolis (1996), notes that if consumers are assumed to base their decisions on the entire stock of old commitments, the resulting models will show great deal of inertia. But if consumers are assumed to respond to concurrent sales, the resulting models will suggest that markets are much more agile. Further, Liebowitz and Margolis argue that consumers ought to be interested in predicting future compatibility, and therefor should be interested in recent and current activity rather that the entire history of consumers’ commitments. Markets are more agile under these circumstances because it is much easier to change the flow of new commitments that it is to change all of history. That is to say, it is a fairly manageable matter for the owner of a technology to choose, or change, the position from which we start out on Figure 1. The owner of a viable technology might invoke any of the strategies we discussed above, or might just simply give some product away in order to move the market from the left of M to the right of M.

None of which proves that the best technology necessarily prevails. It only goes to demonstrate that these models are merely models. They demonstrate particular results in the context of particular assumptions. Whether we are considering the increasing returns story of Table 1, or the multiple equilibrium model that is illustrated with Figure 1, we are left with an empirical question: Have the modeling choices that give us these models captured something important about the way that markets work?

4. Evidence for Third- Degree Path Dependence

The literature of path dependence, both theoretical and empirical, contains a number of claims that path dependent processes lead us to inefficiencies, even for products sold in open markets. Brian Arthur cites as examples of this inefficiency the QWERTY typewriter keyboard (1989), the internal combustion engine (1989), and the VHS videorecorder (1990). Paul David (1985) tells the story of the QWERTY keyboard as a clear example of market failure. Paul Krugman’s Peddling Prosperity contains an entire chapter called "The Economics of QWERTY, where he concludes, "In QWERTY worlds, markets cannot be trusted." (1994)

Empirical support for the third degree claim for path dependence rests almost entirely on a handful of cases. Of these, the typewriter keyboard history is the case that is most often invoked both to illustrate and to support third-degree path dependence paradigm. (Liebowitz and Margolis (1990) is a detailed account of this.)

This story is so important to this literature that we provide a brief summary here. Christopher Latham Sholes patented his typewriter in 1868. Sholes and his collaborators then worked on improving the typewriter. Jamming was one of the major problems and it was addressed by the arrangement of the keyboard. (One version of the story has it that Sholes and his colleagues deliberately chose an arrangement that would slow down touch typists. Unlikely, since touch-typing came much later). Sholes sold the rights to Remington in 1873, and Remington made a few minor modifications and began manufacturing and selling their typewriter, using the QWERTY keyboard.

Alternative keyboard arrangements were developed as the market grew. In 1888, Francis McGurrin, who had taught himself touch typing on a Remington, met Louis Taub in a typing Superbowl, held in Cincinnati. Taub was a very fast hunt-and-peck typist who used a Caligraph typewriter that had a different keyboard arrangement. McGurrin won all phases of the contest in what is said to have been an amazing display. His victory demonstrated the potential of touch-typing and some believe it also enshrined the QWERTY keyboard arrangement as the standard.

In 1936 Professor August Dvorak patented his Dvorak Simplified Keyboard (DSK), which he designed according to ergonomic principles. The DSK is alleged to have been easier to learn and to allow typing at rates that were twenty, forty, or perhaps even eighty percent faster (depending on the source) than QWERTY typing. A study done by the US Navy purportedly demonstrated that the full cost of retraining typists on the DSK was repaid ten days after the typists returned to their normal duties. Yet DSK never caught on.

We have, it appears, the perfect illustration of the path-dependent market failure. An early start for the QWERTY arrangement led to its adoption as the standard, and superior rivals have been unable to dislodge this entrenched incumbent.

The story, however, is a myth. In 1956 Earl Strong, a professor of industrial engineering at Pennsylvania State University, conducted a study for the General Services Administration which showed that the investment in retraining on the DSK could never be recovered. More recent ergonomic studies indicate that the advantage for the DSK over QWERTY is either small or non existent. And there is fairly strong evidence that the Navy study, which was never released as an official Navy report, was conducted by, or under the supervision of, one Lieutenant Commander August Dvorak, the Navy’s chief expert in time and motion studies during the war. Additionally, the report is riddled with error and seeming bias.

Other aspects of the fable are also untrue. There were many touch-typists, on both QWERTY and rival keyboards. There were other typing contests right around the time of the Cincinnati contest, some of which were won by non-QWERTY typists. So it was not the single happenstance of McGurrin’s choice that established QWERTY as the keyboard standard. It is unlikely, therefore, that QWERTY could have survived if it were as poor as it is sometimes alleged to be. If, in fact, some typewriter keyboard really did offer advantages such that the retraining investment would be repaid over every ten days, is it reasonable to think that companies would not make such an investment?

Similarly, Liebowitz and Margolis (1995) reviews the history of the competition between the Beta and VHS formats for videocassette recorders. Here again the usual account leaves out important details. Beta, the story goes, was a better videotaping format but everyone bought VHS because it was more established. Consumers were concerned about compatibility, and so were reluctant to take a flyer on an unusual format, no matter what its advantages might be. The record shows, however, that Beta was actually first on the market. When Sony developed the Beta format, it chose to use a compact tape because it thought that portability of cassettes was important to consumers. For their VHS format, which used virtually identical technology (in part because the VHS and Beta creators worked closely together on previous generations of videorecorder technology), JVC-Matsushita chose a larger tape that offered longer playing time.

Contrary to the popular myth, reviewers did not find Beta to have any advantages in terms of picture quality. Since the size of the cassette was primarily what differentiated the two machines, the major difference between the formats that seems to have mattered to consumers was the potential difference in playing time. VHS licensees capitalized on this difference, making it a highlight of their advertising campaign ("Four hours, $1000, SelectaVision") and Matsushita used this feature to recruit corporate partners for their technology. These strategies allowed VHS to stage a come-from-behind win.

Thus the Beta-VHS competition is a fine example, not of path dependence, but of its opposite. In spite of the fact that Sony was a sophisticated competitor with established marketing and production capabilities, and in spite of the fact that the Beta format had a two-year head start, they lost out. Matsushita, the owner of the VHS format, was able to dethrone Sony by giving consumers more of what was important to them.

There are other cases that have been claimepresentedd at one time or another as path dependent inefficiency. For example, Van Vleck (1997) reconsiders the case of Britain’s small coal cars, long considered an example of "technical backwardness." She finds that the small coal car was in fact well suited to Britain’s geography and coal distribution systems. Ribstein and Kobayashi examine the possibility that the adoption of state laws concerning limited liability companies exhibits path dependence and find little persistence of initial statutory forms.

Our reading of the evidence is that there are as yet no proven examples of third degree path dependence in markets. In non-market arenas, where there may be less opportunity for entrepreneurs to profit from removing inefficiencies, third degree path dependence is more likely to occur. Of course, these non-market arenas may exist largely because political entitiesbodies have chosen to pursue objectives other than economic efficiency.


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