2002 Japan Conference: A Summary of the Papers

Introduction

How long does a typical "market leader" in an industry maintain its position? This question has attracted continuing attention in the (IO) industrial organization literature over the past generation. Two rival views have emerged. The first, associated with Alfred Chandler inter alia, asserts that leadership tends to prsist for a "long" time. The rival view, sometimes labeled "Schumpeterian", emphasizes the transience of leadership positions; an explicit version of this view is spelled out in Franklin Fisher's model of "lepfrogging competition." The central problem with this debate is that no benchmark is proposed relative to which the duration of leadership might be judged "long" or "short." Thus, if it is observed that the typical market leader stays in place for 20 years, this can be interpreted as "long"' by writers in the first group, and as "short" by those in the second.

This paper introduces a formal model of market share dynamics, and uses it to provide a benchmark case, coresponding to a "neutral" situation in which neither positive ("Chandlerian") effects nor negative (Schumpeterian") effects are present. This model provides a natural benchmark against which empirically bserved patterns of persistence can be gauged.

What degree of persistence should we expect on the basis of theory? Game-theoretic models offer little guidance on this question. The issue turns on the following consideration: suppose the market share gapbetween the leader and its (nearest) rival narrows, will this then induce an increase or a decrease in efort by the leader relative to the rival? It is easy to construct game-theoretic models which can go either way; whether they go one way or the other depends crucially on factors (such as the belief of agents) that are notoriously difficult to measure, proxy, or control for in empirical investigations.

The central theme of this paper lies in the classic observation of William Feller to the effect that passage times in Markovian processes tend to be extremely long relative to what we might expect inuitively. Feller identifies this as the most surprising feature to emerge from the study of stochastic processes. In the light of this, it seems natural to inquire into the degree of persistence that we would get in a simple Markovian model. For much of the discussion, the literature pre-supposes that a "long" duration of leadership must imply that some "economically interesting" mechanism is at work to account for this persistence. What Feller's insight suggests is that looking for such explanations may be inappropriate. Even if leader and laggard are equally lucky or equally capable, we will still see leadership persist for what appears intuitively to be a "long" time, and for reasons that are more a matter of arithmetic than economics.

Technicalities

From a statistical viewpoint, the duration of the leadership question translates into a question of the "first crossing times" of stochastic processes. In principle, the problem involves crossing times between a st of interdependent random walks. My analysis takes advantage of two striking empirical features of the data to arrive at a much-simplified representation of the problem. The first is that, for all but the four most highly concentrated of the 45 industries in the dataset, changes in market share for the first and second largest firm display a very low degree of correlation. The second feature relates to the relationship between a firm's market share and the variance of changes in market share; this turns out to obey a simple scaling (power-law) relationship. Combining these two features, we can obtain a transformation of the data that allows the analysis to be carried out by reference to the (well-known) properties of crossing times for a simple random walk.

The Data

This analysis is based on a dataset consisting of annual observations of market shares for leading firms in 45 narrowly defined industries in Japanese manufacturing over the 25-year period 1974-99. These data were comiled using the annual volumes published by the Yano Company. This source covers a large number of inustries, although occasional changes in coverage and presentation do occur. Thus it was possible to construct fairly complete and consistent series over the full 25-year period only for these 45 industries. series of interviews with selected companies was used to check issues of interpretation and reliability of data.

Data of this kind would be very difficult to compile for a broad cross-section of industries in other countries; the availability of the Yano data was a primary reason for focusing on Japan. The second, qually important, reason for this focus lies in the rarity of mergers and acquisitions. For U.S. or U.K. data, for example, it would be difficult to study the distribution of first passage times over an extended period without having to confront the confounding influence of mergers and acquisitions. In the present dataset, only one merger involving "leading" firms occurs over the 25-year period in these 45 industries.

Results

A series of tests on the data indicates that we cannot reject the null hypothesis of simple Markovian beavior (that is, no bias in either the Chandlerian or Schumpeterian direction). Why are market share dynamics "well represented" by a simple stochastic model? The central argument of this paper is that such a model in principle could be improved as a representation of any one industry by incorporating industry-specific features including a strategic representation of firms' competitive responses to market share changes. Once we aim at constructing a "richer" model of this kind, though, we find that "strategic effects" turn on various features, some of which are intrinsically "unobservable" as far as the outside economist is concerned. Most importantly in the present context, they include the beliefs of agents as to their rivals' private information, and their strategic responses to this information.

One implication of this is that, when we look across a broad spectrum of industries without access to this kind of industry-specific information, it may be useful to begin by seeing how far we can progress using the low-level description afforded by a simple "stochastic process" model of the kind used here: shocks to the variables underlying market shares are represented as exogenous. A more sophisticated model would retain exogenous shocks to underlying "technology and tastes" parameters, but would extend each firm's reactions beyond the price-quantity adjustments allowed for in our benchmark model to deal with changes in marketing and/or R and D outlays. In respect to these latter adjustments, subtle differences appear across different industries, seemingly driven by various factors, some of which are very difficult to measure, proxy, or control for in empirical studies. In the final part of the paper, this theme is developed by reference to six industries that exhibit widely different patterns of market-share dynamics.