Competing technologies, increasing returns and the role of historical events

Transcription

1 Competing technologies, increasing returns and the role of historical events Federico Frattini Economia Applicata Avanzata Advanced Applied Economics

2 W. Brian Arthur (1989) Competing technologies, increasing returns, and lock-in by historical events, The Economic Journal, 99(394):

3 Topic «dynamics of allocation under increasing returns in a context where increasing returns arise naturally: agents choosing between technologies competing for adoption. [...] the more they are adopted, the more experience is gained with them, and the more they are improved [learning by using: Rosenberg N. (1982), Inside the black box: technology and economics, Cambridge: Cambridge University Press]. When two or more increasing-returns technologies compete, insignificant events may by chance give one of them an initial advantage in adoption. This technology may then improve more than the others, so it may appeal to a wider proportion of potential adopters. It may therefore become further adopted and further improved. Thus a technology that by chance gains an early lead in adoption may eventually corner the market of potential adopters, with the other technologies becoming locked-out» (p. 116)

4 Multiple equilibria «Competition between technologies may have multiple potential outcomes. [...] By allowing the possibility of random events occurring during adoption, it might examine how these influence selection of the outcome how the sets of random historical events might cumulate to drive the process towards one market-share outcome, others drive it towards another» (p. 116)

5 Increasing-returns properties /1 non-predictability «how increasing returns act to magnify chance events as adoptions take place, so that ex ante knowledge of adopters preferences and the technologies possibilities may not suffice to predict the market outcome» (p. 116) potential inefficiency «how increasing returns might drive the adoption process into developing a technology that has inferior longrun potential» (p. 117)

6 Increasing-returns properties /2 inflexibility «once an outcome (a dominant technology) begins to emerge, it becomes progressively more lockein» (pag. 117) non-ergodicity «historical small events are not averaged away and forgotten by the dynamics they may decide the outcome» (p. 117)

7 Model dynamics of technologies market shares under condition of increasing, diminishing and constant returns how returns affect predictability, efficiency, flexibility, and ergodicity the circumstances under which the economy might become locked-in by historical events to the monopoly of an inferior technology» (p. 117)

8 Two unsponsored technologies two new technologies, A and B, compete for adoption by a large number of economic agents the technologies are not sponsored or strategically manipulated by any firm and they are open to all agents are simple consumers of the technologies who act directly or indirectly as developers of them (p. 117)

9 Agents agent i comes into the market at time t i : at this time he chooses the latest version of either technology A or technology B; and he uses this version thereafter agents are of two types, R and S, with equal numbers in each the two types are independent of the times of choice but differing in their preferences, perhaps because of the use to which they will put their choice the version of A or B each agent chooses is fixed or frozen in design at his time of choice, so that his payoff is affected only by past adoptions of his chosen technology (p. 117)

10 Conditions for increasing returns returns [or net present value] to choosing A or B realised by any agent [...] depend upon the number of previous adopters, n A and n B, at the time of his choice with increasing, diminishing, or constant returns to adoption given by r and s simultaneously positive, negative, or zero a R > b R and a S < b S, so that R-agents have a natural preference for A, and S-agents have a natural preference for B (p. 118) Table: Returns to choosing A or B given previuos adoption (p. 118) Technology A Technology B R-agent a R + rn A b R + rn B S-agent a S + sn A b S + sn B

11 The observer an observer who has full knowledge of all the conditions and returns functions, except the set of events that determines the times of entry and choice { t i } of the agents the observer thus sees the choice order as a binary sequence of R and S types with the property that an R or an S comes nth in the adoption line with equal likelihood, that is, with probability one half

12 historical events «those events or conditions that are outside the ex ante knowledge of the observer - beyond the resolving power of his model or abstraction of the situation» «The supply (or returns) functions are known, as is the demand (each agent demands one unit inelastically). Only one [...] element is left open, and that is the set of historical events that determine the sequence in which the agents make their choice. Of interest is the adoption-share outcome in the different cases of constant, diminishing, and increasing returns, and whether the fluctuations in the order of choices these small events introduce make a difference to adoption shares» (p. 118)

13 Process properties /1 «[the process is] predictable if the small degree of uncertainty built in averages away so that the observer has enough information to predetermine market shares accurately in the long run» (p. 118) if the observer can ex ante create a forecasting sequence { x n * } with the property that x n x n * 0 with probability 1 as n (p. 128) «[the process is] flexible if a subsidy or tax adjustment to one of the technologies returns can always influence future market choices» (p. 118) if a given marginal adjustment g to the technologies returns can alter the future choices (p. 128)

14 Process properties /2 «[the process is] ergodic (not pathdependent) if different sequences of historical events lead to the same market outcome with probability one» (p. 118) if, given 2 samples from the observer s set of possible historical events { t i } and { t i } with corresponding time paths { x n } and { x n }, then x n x n * 0 with probability 1 as n (p. 128) «[the process is] path-efficient if at all times equal development (equal adoption) of the technology that is behind in adoption would not have paid off better» (p. 119) if, whenever an agent chooses the more-adopted technology z, versions of the lagging technology w would not have delivered more had they been [...] available for adoption [...] returns remain such that z ( m ) max j { w ( j ) } for k j m, where there have been m previuos choices of the leading technology and k of the lagging one (p. 128)

15 Dynamics of adoption n A ( n ) and n B ( n ) are the number of choices of A and B respectively, when n choices in total have been made the process is described by x n, the market share of A at stage n, when n choices in total have been made d n = n A ( n ) n B ( n ) is the difference in adoption x n = d n / 2n through the variables d n and n is possible to fully describe the dynamics of adoption of A versus B (pp )

16 [case] constant returns R-agents always choose A and S-agents always choose B, regardless of the number of adopters of either technology the way in which adoption of A and B cumulates is determined simply by the sequence in which R- and S-agents line up to make their choice n A ( n ) increasing by 1 unit if the next agent in line is an R n B ( n ) increasing by 1 unit if the next agent in line is an S the difference in adoption d n moving upward by +1 unit or downward 1 unit accordingly to the observer the choice-order is random, with agent types equally likely and the state d n appears to perform a simple coin-toss gambler s random walk with each move having equal probability 0.5 (p. 120)

17 [case] increasing returns /1 new R-agents, who have a natural preference for A, will switch allegiance if by chance adoption pushes B far enough ahead of A in numbers and in payoff. That is, new R-agents will switch if d n = n A ( n ) n B ( n ) < R = ( b R a R ) / r new S-agents will switch preference to A if numbers adopting A become sufficiently ahead of the numbers adopting B, that is if d n = n A ( n ) n B ( n ) > S = ( b S a S ) / s regions of choice now appear in the d n, n plane with boundaries between them given by the two switching conditions R and S : once one of the outer regions is entered, both agent types choose the same technology, with the result that this technology further increases its lead (p. 120)

18 [case] increasing returns /2 the two switching conditions in the d n, n plane describe barriers that absorb the process: once either is reached by random movement of d n, the process ceases to involve both technologies it is locked-in to one technology only and the adoption process becomes a random walk with absorbing barriers (p. 121)

19 [case] diminishing returns the process appears to the observer as a random walk with reflecting barriers

20 [discussion] long-term adoption shares constant returns the adoption market is shared: standard deviation of d n increases with n 1/2 (property of free random walk processes) and, as a consequence, d n / 2n 0 and x n 0.5 as n diminishing returns the adoption market is shared: d n is trapped between finite constants ( S < d n < R ) and, as a consequence, d n / 2n 0 and x n 0.5 as n increasing returns the adoption share of A ( or B ) must eventually become 0 or 1, because eventually d n > S ( or < R ) with probability 1: the two technologies cannot coexist indefinetly and one must exclude the other (p. 121)

21 [discussion] predictability constant returns predictability is guaranteed, because the prediction x n * = 0.5 will be correct with probability 1 diminishing returns predictability is guaranteed, because the prediction x n * = 0.5 will be correct with probability 1 increasing returns predictability is lost, because either observer s choice x n * = 1 or x n * = 0 will be wrong with probability 0.5 (p. 121)

22 [discussion] flexibility constant returns flexibility is partial: policy adjustment to the return can affect choices at all times, but only if they are large enough to bridge the gap in preferences between technologies diminishing returns flexibility is guaranteed: an adjustment g can always affect future choices (in absolute numbers, if not in market shares), because reflecting barriers continue to influence the process with probability 1 at times in future increasing returns flexibility is lost: once the process is absorbed into A or B, the subsidy or tax adjustment necessary to shift the barriers enough to influence choices increases without bound (p. 122)

23 [discussion] ergodicity constant returns ergodicity holds, because only extraordinary line-ups with associated probability 0 can cause deviations from x n = 0.5 and the process forgets its small events history diminishing returns ergodicity holds, because any line-up of the agents must still cause the process to remain between the reflecting barriers, drive the market to x n = 0.5 and forget its small events history increasing returns process is path-dependent: some proportion of agent sequence causes the market outcome to tip towards A, the remaining proportion causes it to tip towards B and the small events that determine { t i } decide the path of the market shares (p. 122)

24 [discussion] path-efficiency constant returns path-efficiency holds, because previous adoptions do not affect pay-off, each agent-type chooses its preferred technology and there is no gain foregone by the failure of the lagging technology to receive further development (further adoption) diminishing returns path-efficiency holds: if an agent chooses the technology that is ahead, he must prefer it to the avalaible version of the lagging one, but further adoptions of the lagging technology by definition lowers its payoff and, therefore, there is no possibility of choices leading the adoption process down to and inferior development path increasing returns path-efficiency is not guaranteed: suppose the market locks into technology A, so that R-agents do not lose, but S-agents would each gain ( b S a S ) if their favoured technology B had been equally developed and available for choice there is a regret, at least for one agent type (p. 122)

25 Proporties of the three regimes Table: Properties of the three regimes (p. 121) Predictability Flexibility Ergodicity Necessary path-efficiency Constant YES NO YES YES Diminishing YES YES YES YES Increasing NO NO NO NO

26 Remarks /1 «cases where an early-established technology becomes dominant, so that later, superior alternatives cannot gain a footing» (p. 126)

27 Remarks /2 «the interpretation of economic history should be different in different returns regimes. Under constant and diminishing returns, the evolution of the market reflects only a priori endowments, preferences, and transformation possibilities; small events cannot sway the outcome. But while this is comforting, it reduces history to the status of mere carrier the deliverer of the inevitable. Under increasing returns, by contrast many outcomes are possible. Insignificant circumstances become magnified by positive feedbacks to tip the system into the actual outcome selected. The small events of history become important. Where we observe the predominance of one technology or one economic outcome over its competitors we should thus be cautious of any exercise that seeks the means by which the winner's innate superiority came to be translated into adoption» (p. 127)

28 Remarks /3 «The usual policy of letting the superior technology reveal itself in the outcome that dominates is appropriate in the constant and diminishing-returns cases. But in the increasing returns case laissez-faire gives no guarantee that the superior technology (in the long-run sense) will be the one that survives. Effective policy in the (unsponsored) increasing-returns case would be predicated on the nature of the market breakdown: [...] early adopters impose externalities on later ones by rationally choosing technologies to suit only themselves; missing is an inter-agent market to induce them to explore promising but costly infant technologies that might pay off handsomely to later adopters» (p. 127)