Acerca del autor

William A. Sundstrom is Professor of Economics at Santa Clara University. Timothy W. Guinnane is Professor of Economics at Yale University. Warren C. Whatley is Professor of Economics at the University of Michigan.

De la contraportada

De la solapa interior

Fragmento. © Reproducción autorizada. Todos los derechos reservados.

HISTORY MATTERS

STANFORD UNIVERSITY PRESS

Contents

List of Contributors.........................................................................................................................................................................................................................xiPreface......................................................................................................................................................................................................................................xiiiEditors' Introduction Timothy W. Guinnane, William A. Sundstrom, and Warren Whatley.........................................................................................................................................................1PART I WHY HISTORY MATTERS: PATH DEPENDENCE AND ECONOMIC THOUGHTChapter 1 Path Dependence and Competitive Equilibrium Kenneth J. Arrow......................................................................................................................................................................23Chapter 2 Path Dependence and Reswitching in a Model of Multi-Technology Adoption Paul Stoneman.............................................................................................................................................36Chapter 3 Path Dependence, Network Form, and Technological Change Douglas J. Puffert........................................................................................................................................................63Chapter 4 The Tension between Strong History and Strong Economics Melvin W. Reder...........................................................................................................................................................96PART II PATH DEPENDENCE IN PRACTICEChapter 5 Financial History and the Long Reach of the Second Thirty-Years' War Charles W. Calomiris.........................................................................................................................................115Chapter 6 Path Dependence in Action: The Adoption and Persistence of the Korean Model of Economic Development Phillip Wonhyuk Lim...........................................................................................................142Chapter 7 Continuing Confusion: Entry Prices in Telecommunications Peter Temin..............................................................................................................................................................163Chapter 8 After the War Boom: Reconversion on the Pacific Coast, 1943-1949 Paul W. Rhode....................................................................................................................................................187Chapter 9 Standardization, Diversity, and Learning in China's Nuclear Power Program Geoffrey Rothwell.......................................................................................................................................221PART III CONTEXT MATTERS: THE INFLUENCE OF CULTURE, GEOGRAPHY, AND POLITICAL INSTITUTIONS ON ECONOMIES AND POLICIESChapter 10 Incentives, Information, and Welfare: England's New Poor Law and the Workhouse Test Timothy Besley, Stephen Coate, and Timothy W. Guinnane.......................................................................................245Chapter 11 Family Matters: The Life-Cycle Transition and the Antebellum American Fertility Decline Susan B. Carter, Roger L. Ransom, and Richard Sutch......................................................................................271Chapter 12 Building "Universal Service" in the Early Bell System: The Coevolution of Regional Urban Systems and Long-Distance Telephone Networks David F. Weiman............................................................................328Chapter 13 International Competition for Technology Investments: Does National Ownership Matter? Trond E. Olsen.............................................................................................................................364PART IV EVIDENCE MATTERS: MEASURING HISTORICAL ECONOMIC GROWTH AND DEMOGRAPHIC CHANGEChapter 14 Conjectural Estimates of Economic Growth in the Lower South, 1720 to 1800 Peter C. Mancall, Joshua L. Rosenbloom, and Thomas Weiss...............................................................................................389Chapter 15 The Value-Added Approach to the Measurement of Economic Growth Mark Thomas and Charles Feinstein.................................................................................................................................425Chapter 16 A User's Guide to the Joys and Pitfalls of Cohort Parity Analysis Warren C. Sanderson............................................................................................................................................459Chapter 17 Stochastic Dynamic Optimization Models with Random Effects in Parameters: An Application to Age at Marriage and Life-Cycle Fertility Control in France Under the Old Regime Thomas A. Mroz and David R. Weir.....................483

Chapter One

Kenneth J. Arrow

1. INTRODUCTION

Paul David has been a pioneer and innovator in so many directions that it is hard to keep track of them all. He has moved with ease from specific historical events and episodes to broad generalizations, both theoretical and empirical in nature. The diffusion of the reaper, with close attention to both social interaction and profitability, the need for purchasing-power comparisons to replace foreign-exchange rates in international welfare comparisons, the bias toward labor-saving innovation in explaining the evolution of the distribution of income, the interpretation of Habbakuk's thesis on American economic growth relative to England's, and more recently the comparative roles of science and technology in technical change are merely a few of the many contributions that David has made to the progress of economics and in particular to the analysis of technical change and its economic implications.

I want here to discuss one particular thesis that David has been strongly associated with, the idea of path dependence. This is a concept whose general meaning is fairly clear, though a precise definition is not so easy. Roughly speaking, it means that the long-term historical evolution of an economy (or any other system) depends on where it started, or perhaps on some of the disturbances to the system during its history. The critical point is that the effect of these initial conditions or disturbances is essentially permanent; it does not gradually vanish with time.

Many economic theories do not show path dependence, for example, the Solow growth model, which predicts that all economies will converge to the same limiting capital-labor ratio even though they may start with very different ratios. It is a thesis of Paul David and others that real economies display path dependence.

I do not think there is the slightest question that path dependence is a real phenomenon in economic history and development, as it is in biological evolution and in the history of political and social institutions. My purpose in this chapter is to examine one claimed aspect of path dependence, namely, that it arises as a result of increasing returns to scale in some relevant part of the economy. I will argue, by means of an example, that this is not so. Even with constant returns to scale and perfectly competitive equilibrium, path dependence is possible.

My suggestion is that it is the irreversibility of investment, not increasing returns, that is at the root of path dependence. Even though Paul David has emphasized the role of increasing returns in path dependence, my thesis is rooted in one of his papers, that on the failure of Great Britain to adopt the reaper (David 1971). A study of his paper convinced me that the argument there did not depend in any way on increasing returns, and the model of this chapter is loosely suggested by David's analysis.

2. THE FORMAL NOTION OF PATH DEPENDENCE

A. Dynamic Systems in General

In this chapter, I confine myself to deterministic dynamic systems. The evolution of the system is governed by the dynamic relations and the initial conditions. Suppose the system converges for all or some set of initial conditions. There is path dependence if the limit depends on the initial conditions-that is, if for different initial conditions the system converges to different limits. The classic case is that of a drop of rain falling on a hill. Once landed, the water's flow is determined by the law of gravity and the particular topography. The rain will eventually go into a valley, but which valley depends on the point of initial contact with the ground.

B. Intertemporal Competitive Equilibrium

The specific dynamic system we want to look at is intertemporal competitive equilibrium with an infinite horizon. The finite-horizon intertemporal equilibrium model was first formulated by Lindahl (1929) and subsequently by Hicks (1939); the infinite-horizon version of a complete general equilibrium was first studied by Bewley (1972). It is now known that such models are capable of extremely complex behavior, even chaotic solutions (Boldrin and Montrucchio 1991). It is perhaps therefore not surprising that path dependence is possible in intertemporal equilibria.

Note that in competitive models, including intertemporal competitive models, we are assuming concavity of the production functions and therefore rejecting increasing returns.

3. SOME EXAMPLES OF PATH DEPENDENCE

A. Path Dependence in General History

Historians, unlike economists, have always been very prone to assume path dependence. Large consequences flow from the idiosyncrasies of kings and other leaders (for example, Henry VIII's love life and the separation of England from the Catholic Church). Blaise Pascal's remark that the history of the world would have been different if Cleopatra's nose were somewhat longer would be compatible with much historical analysis, though Pascal himself was no historian. I ran across the work of the great Dutch historian Pieter Geyl (1961-64) on the separation of the Netherlands from Belgium. He argued that, to begin with, there was little difference between the northern and southern Netherlands, as they then were. Politically, they were a set of fiefs jointly under the effective sovereignty of the Spanish ruler. The resentment of Spanish rule was common. The religious division between Protestants and Catholics was about the same. However, as the Spanish sought to reestablish their control against the revolt, the convoluted seacoasts in the north provided greater refuge for the rebels. As the Spanish regained control in the south, Protestant refugees fled north, changing the religious balance. It was therefore because of geography that the north became the successful point of resistance and also the center of Protestantism, to the point that when independence was ceded to the north, the two areas increasingly diverged in religion and other social attitudes. Two hundred years later, the unity of the Netherlands was reestablished by the decision of the victors over Napoleon but could not be maintained with such divergence of religion and of national sentiment.

B. Veblen on German Economic Development

Thorstein Veblen's (1915) study of the rise of Germany as an industrial power is a prime example of path dependence in economic history. Veblen's rich analysis covers many aspects of German development and still repays study, but the particular point I want to emphasize is his explanation why Germany, a latecomer to industrial development in comparison with Great Britain, managed to surpass it. If we assume the two countries had access to the same technologies in, say, 1870, but Great Britain had accumulated more capital, we would expect according to simple models that Germany would gradually catch up with Great Britain but would always lag behind it. As generally perceived, though, the latecomer actually surpasses its rival.

Veblen's view was that this was not an accident but the natural result of being a follower. His argument was illustrated by the railroad systems and the corresponding freight-handling equipment at the ports. The British started with narrow-gauge railroads and built equipment to transfer freight from railroads to ships that matched. Later technological developments showed that standard-gauge railroads were more efficient. The Germans, building later, followed the later technology. The technological knowledge was equally available to the British, but since they would have had to replace both railways and freight-handling equipment, it was never worthwhile. Hence, though both countries had access to the same technology and both were responding rationally, the Germans would develop higher productivity than the British.

In Veblen's account, there is path dependence because the future course of economic development is determined, even in the long run, by the initial capital configurations around 1870.

C. Urban Agglomeration

It is fairly common to observe that industrial and commercial activity is concentrated in cities rather than spread out uniformly. Further, while some cities clearly have some special locational advantage, such as a fine port, many do not. Many are located on plains where there seems to be no special advantage over many other sites. It is has long been a common argument, already found in Marshall (1920), that there are external economies that explain the structure of cities. This point of view was elaborated in the work on the economics of location; see Christaller (1966); Lsch (1954).

This insight can be given a dynamic interpretation. Given an initial unequal distribution of activity, the locations with denser activities have an advantage that causes new activities to accumulate there, reinforcing the original inequality. This process has been elaborated on by Arthur (1988).

D. Lock-in in Product Development

It has several times been claimed that the specific characteristics of products can be historically determined. An outstanding example is Paul David's argument that the configuration of the typewriter keyboard was determined by historical accident (David 1985). In early typewriters, there were many different assignments of letters to keys. The one now used had as its chief advantage not speed but avoidance of jamming the keys. As the technology improved, this property became irrelevant. But in the meantime there was an accumulation of human capital invested in learning the keyboard, an investment that made it uneconomic to switch to a new keyboard designed for speed, even though such existed.

Arthur (1989) gave a general model in which development of a product in one direction lowered the costs of continuing in that direction, even though an alternative path would ultimately have yielded a greater product. He argued that the development of the videocassette recorder, in choosing between two rival formats, illustrated his model.

E. British Nonuse of the Mechanical Reaper

As I have indicated, interpreting David (1971) has led to this paper. Paul David sought to explain why the mechanical reaper, whose use was so widespread in the United States, was not used by British farmers. He argued that it was due to the plowing practices that were well adapted to an economy with hand-reaping. The furrows were very deep, made more so by centuries of repeated plowing. As a result, the reaper would cut only the grain growing at the tops of the furrows, leaving the rest to be discarded or reaped by hand. Hence, there might be no gain to the farmers from switching to the reaper. Of course, the fields could be replowed to adapt to the mechanical reaper; but this would require a large capital cost that, it might be inferred, would not pay in subsequent labor-saving. The American farmers, starting with virgin soil, had no such capital cost.

F. Is Path Dependence a Consequence of Increasing Returns?

Some of the examples given above certainly assume increasing returns. It seems to be assumed by Paul David, by Brian Arthur, and, I suppose, by many others, that path dependence is intrinsically linked with increasing returns. Actually, the presence or absence of increasing returns in these examples is more subtle than might be thought. In the typewriter keyboard case, for example, the indivisibility (I take for granted that increasing returns always depends on the presence of an indivisibility) is in the acquisition of human capital (the skill of working at a particular keyboard). A similar analysis can be made of the other cases. But in the last example, the nonuse of the mechanical reaper in Great Britain, no increasing returns are present at all. The argument is just as valid on an arbitrarily small piece of land with an arbitrarily small amount of reaper-time.

One aspect is common to all the examples: the durability of the capital. If plowing were renewed each year or if typists had to relearn their keyboards at short intervals, none of the lock-in, path-dependent character of economic history would be present. I will present a simple model to show that even under all of the conditions that characterize competitive equilibrium, including constant returns to scale, path dependence is possible when there is an irreversible element to capital formation.

4. AN ILLUSTRATIVE MODEL

There are three production processes, 0, 1, and 2, with successively increasing labor productivities. Process 0 requires no capital; processes 1 and 2 require specific kinds of capital (not shiftable across processes). Some capital of type 1 exists, none of type 2; process 2 has just been invented. Neither kind of capital depreciates. Each production process has fixed coefficients for labor and for capital. Both kinds of capital are produced by labor alone. There is one consumer product, produced by the three processes; utility is linear in the product. There is one consumer, who maximizes the integral (over infinite time) of discounted consumption, with force of discount (consumption interest rate) equal to [rho].

Let [N.sub.i] be the total amount of labor used in process i. Let [M.sub.i] be the amount of labor used to produce capital of type i (i = 1, 2). Let [v.sub.i] be the amount of labor needed to produce one unit of the consumer good by process i (i = 0, 1, 2). Let [.sub.i] be the amount of labor needed to produce one unit of capital of type i (i = 1, 2). Finally, let capital be so measured that in both processes 1 and 2, one unit of capital is needed to produce one unit of the consumption good.

Let [K.sub.i](t) be the amount of capital of type i at time t. [K.sub.1](0) is some given positive number, [K.sub.2](0) = 0.

Given these conditions, an optimum path, which is also a competitive equilibrium in this simple one-person case, is determined. It will be shown that, for a large range of values of the parameters, the optimal path requires full utilization of the existing capital in process 1 forever; the remaining labor force is divided between building up capital in process 2 and producing the consumption good from that process with whatever capital has been built up.

Let the total labor force be normalized at 1, so that, at any time t,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)

Total output of the consumption good is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)

The consumer (and the economy) maximizes the time integral of (2) discounted by exp(-[rho]t), subject to (1), the capital accumulation equations,

d[K.sub.i]/dt = [([[mu.sub.[i]).sup.1] [M.sub.i] (i = 1, 2), (3)

and the constraints in processes 1 and 2 that no more labor is applied than can be used in view of the amount of capital available,

[N.sub.i] [less than or equal to] [v.sub.i][K.sub.i]. (4)

Let [p.sub.i](i = 1, 2) be the costate variables corresponding to the accumulation equations (3), w the Lagrange parameter for the constraint (1), and [q.sub.i] (i = 1,2) be the Lagrange variables for the constraints (4). Then the current-value Hamiltonian for the optimization problem is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The evolution of the costate variables is then given by

[dp.sub.i]/dt = [rho][p.sub.i] - [v.sub.i][q.sub.i] (i = 1, 2). (5)

(Continues...)

Excerpted from HISTORY MATTERS Copyright © 2004 by Board of Trustees of the Leland Stanford Junior University. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.