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Modeling the Transition to a New Economy:Lessons from Two Technological Revolutions

By ANDREW ATKESON AND PATRICK J. KEHOE*

Many view the period after the Second Industrial Revolution as a paradigm of atransition to a new economy following a technological revolution, including theInformation Technology Revolution. We build a quantitative model of diffusion andgrowth during transitions to evaluate that view. With a learning process quantifiedby data on the life cycle of US manufacturing plants, the model accounts for the keyfeatures of the transition after the Second Industrial Revolution. But we find thatfeatures like those will occur in other transitions only if a large amount ofknowledge about old technologies exists before the transition begins. (JEL L60,N61, N62, N71, N72, O33)

The 1860–1900 period is often called theSecond Industrial Revolution because of thelarge number of technologies invented duringthat time. Historians tell us that the SecondIndustrial Revolution launched a century ofrapid development of new manufacturing tech-nologies based on electricity (Sam H. Schurr etal. 1960; Nathan Rosenberg 1976; Warren D.Devine, Jr., 1983; Paul A. David 1990, 1991).This increase in the pace of technical change ledeventually to a new economy, characterized byfaster growth in manufacturing productivity, asmeasured by output per hour.

That particular transition to a new economy isviewed by many as paradigmatic of what hap-pens after any major and sustained increase inthe pace of technical change. The transition hasthree main features: a productivity paradox (asurprisingly long delay between the increase inthe pace of technical change and the increase inthe growth rate of measured productivity); slow

diffusion of new technologies; and continuedinvestment in old technologies. David (1990)and Boyan Jovanovic and Peter L. Rousseau(2005) have argued that all three of these fea-tures of the transition after the Second IndustrialRevolution have parallels in the transition afterthe more recent Information Technology (IT)Revolution.

Why did the transition after the Second In-dustrial Revolution have these features? Andare they likely to be seen in other such transi-tions? Here we attempt to answer those ques-tions by building and using a model oftechnology diffusion and growth. The model isintended to capture the main elements of histo-rians’ hypotheses about the technological con-straints facing manufacturing plants, which arethought to have shaped the transition to a neweconomy after the Second Industrial Revolu-tion. (See, for example, Schurr et al. 1960;Rosenberg 1976; Devine 1983; David 1990,1991.) These elements are as follows: new tech-nologies are embodied in plants, so that plantsmust be redesigned in order to use the newtechnologies; improvements in the technologiesfor new plants are ongoing; and new plantsrequire a period of learning in order to use thenew technologies. We employ this model toinvestigate what aspects of the technologicalconstraints are critical quantitatively for gen-erating this particular transition’s three mainfeatures. We then use the model to ask what

* Atkeson: Department of Economics, UCLA, Box951477, Los Angeles, CA 90095-1477 (e-mail: [email protected]); Kehoe: Research Department, Federal Re-serve Bank of Minneapolis, 90 Hennepin Avenue, Min-neapolis, MN 55401-1804 (e-mail: [email protected]). We thank Kathy Rolfe and Joan Gieseke for excel-lent editorial assistance and the National Science Founda-tion for research support. The views expressed herein arethose of the authors and not necessarily those of the FederalReserve Bank of Minneapolis or the Federal ReserveSystem.

64

lessons from the transition after the SecondIndustrial Revolution can be learned to usefullyguide research on other technological revolu-tions, especially the recent IT Revolution.

We discover that, quantitatively, learning isthe critical technological constraint in ourmodel. Indeed, to reproduce the three main fea-tures of the transition, the model needs learningabout embodied technologies to be both sub-stantial and protracted.

When the learning process in the old econ-omy is substantial and protracted, our modelgenerates the first of the transition features—aproductivity paradox. It does so because, withsuch a learning process, the model implies thatat the start of the transition, agents have built upa large stock of knowledge about old embodiedtechnologies. Agents who have done that natu-rally don’t quickly abandon the existing tech-nology in favor of a new one. Instead, theyspend a long time continuing to learn about theirexisting technology before abandoning it in fa-vor of a new one. This procedure creates a longdelay between the increase in the pace of tech-nical change and the increase in the growth rateof measured productivity.

By the same logic, learning and built-upknowledge are critical for generating the secondof the three transition features—a slow diffu-sion of new technologies. Our model generatesS-shaped diffusion curves from heterogeneityacross plants in built-up knowledge about oldtechnologies: plants with little built-up knowl-edge adopt the new technology sooner, whileplants with a lot of built-up knowledge adopt itlater.

Finally, when learning is substantial and pro-tracted, our model also generates the third tran-sition feature—ongoing investment in oldtechnologies even after new technologies areintroduced. This ongoing investment occurs be-cause existing plants embodying old technolo-gies continue to learn and thus grow by addingphysical capital and labor for quite some timeafter new technologies are introduced.

We use micro data on US manufacturingplants to measure the learning process at theplant level and find that it is, in fact, substantialand protracted. Indeed, one of our main contri-butions in making the model quantitative is touse micro data on the life-cycle patterns ofplants in the US economy—their birth, growth,

and death—to infer the parameters of the learn-ing process at the plant level. Our method herebuilds on the work of Hugo Hopenhayn andRichard Rogerson (1993) and our own earlierwork (Atkeson and Kehoe 2005). With ourmethod, we find that learning continues for atleast 20 years.

When the parameters of our model are setusing our method for inferring learning, themodel’s predictions match the three main fea-tures of the transition after the Second IndustrialRevolution surprisingly well. We find it intrigu-ing that the model matches the data so well,even though we did not attempt to replicate anyfeatures of the transition after the Second Indus-trial Revolution when we chose the parametersof our model.

What lessons can be drawn from our modelfor transitions after other technological revolu-tions, particularly after the more recent IT Rev-olution? We investigate this question byfollowing the lead of David (1990), Timothy F.Bresnahan, Erik Brynjolfsson, and Lorin M.Hitt (2002), and others who argue that informa-tion technologies are similar to electricity in thatthey open up new possibilities for organizingbusiness practices within all types of organiza-tions, and these organizations need to be rede-signed to make productive use of the newinformation technologies. Motivated by thiswork, we reinterpret our model as having busi-ness organizations rather than manufacturingplants as the basic units of production. Weassume that each new business organization em-bodies a new set of business practices that rep-resent the current frontier of such practices, andthen learns to become more productive withthese practices over time.

The general lesson we draw from our modelis that its implications for the transition after atechnological revolution depend on the histori-cal context in which the revolution occurs. Inparticular, our model predicts a slow transition,such as that seen after the Second IndustrialRevolution, only if agents have accumulated alarge stock of built-up knowledge of old tech-nologies before the transition begins. For theSecond Industrial Revolution, we argue thatagents did have a large stock of built-up knowl-edge about factories based on steam and water-power. For the IT Revolution, our model willpredict a slow transition only if, at the start of

65VOL. 97 NO. 1 ATKESON AND KEHOE: MODELING THE TRANSITION TO A NEW ECONOMY

that revolution, agents had a large stock ofbuilt-up knowledge about business practicesbased on old information technologies.

We use the model to examine which factorsdetermine the extent of built-up knowledge inequilibrium. We find that the relative pace oftechnical change in the old economy is one ofthose factors: the faster the pace of the change,the smaller is the extent of built-up knowledgeand, hence, the faster is the transition to a neweconomy after a technological revolution. Wealso find that the more protracted and substan-tial the learning process, the larger the extent ofbuilt-up knowledge and the slower the transi-tion after a technological revolution.

Currently, we know little about the extent ofbuilt-up knowledge about business practices inorganizations at the start of the IT Revolution.Our model suggests, however, that the extent ofthat knowledge can be inferred from data on thediffusion and life cycle of business practices. Togenerate quantitatively a slow transition afterthe IT Revolution in our model, we must as-sume that the diffusion of business practicesbefore that revolution was very slow and thatthe life cycle of these business practices wasvery prolonged. For example, for our modelto generate a transition after the IT Revolu-tion that is as slow as that after the SecondIndustrial Revolution, at the start of the ITRevolution over 50 percent of the work forcemust have been employed in organizationswith business practices that were more thansix decades old.

Our method of measuring learning at theplant level contrasts sharply with the standardapproach in the learning literature, exemplifiedby the work of Byong-Hyong Bahk and MichaelGort (1993). These researchers associate learn-ing in a plant with changes in the average pro-ductivity of labor and capital at that plant as theplant ages. This method leads to the conclusionthat there is very little learning at the plant level.Hence, if the method were used with our model,it would predict a fast transition, a fast diffusionof new technologies, and little or no ongoinginvestment in old technologies.

We argue in favor of our method of measur-ing learning because, in the context of ourmodel, the method proposed by Bahk and Gort(1993) is conceptually flawed. Indeed, if it wereapplied to our model, it would find no learning

at all, regardless of how much learning wasactually going on. Our method for measuringlearning is one of the features that distinguishour work from related models of transitionbased on embodiment and learning, includingthose of Andreas Hornstein and Per Krusell(1996) and Jeremy Greenwood and MehmetYorukoglu (1997).

At the general level, the technology diffusionin our model is related to the theoretical litera-ture on S-shaped diffusion curves, including thework of Jovanovic and Saul Lach (1989) andV. V. Chari and Hopenhayn (1991). In contrastto that work, we have neither spillovers oflearning nor complementarities. Our model alsodiffers from most of the literature on diffusionin that it generates substantial ongoing invest-ment in old technologies. (An important excep-tion is the work of Chari and Hopenhayn 1991.)

More recent theoretical work on diffusionafter a major technical change includes that ofPhilippe Aghion and Peter Howitt (1998), El-hanan Helpman and Manuel Trajtenberg(1998), and John Laitner and Dmitriy L. Stol-yarov (2003). In this literature, often referred toas work on general purpose technologies, thediffusion of a major new technology is con-strained by the need to develop complementaryinputs for that technology. These explanationsfor the slow diffusion of new technologies donot account for substantial investment in oldtechnologies after major technical change.

I. Documenting the Transition after the SecondIndustrial Revolution

We document the three main features of thetransition to a new economy that occurred afterthe Second Industrial Revolution: a productivityparadox, a slow diffusion of new technologies,and ongoing investment in old technologies.

Many of the technologies that had a profoundimpact on living standards in the twentieth cen-tury were invented between 1860 and 1900.These technologies include electricity, the inter-nal combustion engine, the production of petro-leum and other chemicals, telephones andradios, and indoor plumbing. (For a descriptionof technological inventions during this time, seethe work of Robert J. Gordon 2000a.) Althoughall of these inventions undoubtedly had a sub-stantial economic impact, we follow Schurr et

66 THE AMERICAN ECONOMIC REVIEW MARCH 2007

al. (1960, 1990), Rosenberg (1976), Devine(1983), and David (1990, 1991) and focus onthe new technologies based on electricity. Thesehistorians have argued that this revolutionlaunched a century-long period of rapid devel-

opment of new technologies for manufacturingbased on electricity (Devine 1990).

In Figure 1, we show this historical perioddoes include a productivity paradox, or a sub-stantial lag between the increased pace of tech-

FIGURES 1–2. A Gradual Transition to a New Economy

2.5

3.0

3.5

4.0

4.5

5.0

5.5

1860 1880 1900 1920 1940 1960 1980

Log

Trend growth: 1.6%

Trend growth: 2.6%

Trend growth: 3.3%

1949–19691869–1899 1899–1929

FIGURE 1. A SLOW INCREASE IN PRODUCTIVITY GROWTH ...(Log of output per hour and trend growth in US manufacturing, 1869–1969)

Source: US Department of Commerce (1973).

0

10

20

30

40

50

60

70

80

90

100

1869 1879 1889 1899 1909 1919 1929 1939

%

Steamengines

Waterwheelsand turbines

Electric motors

FIGURE 2. ... AND A SLOW DIFFUSION OF ELECTRIC POWER

(Percentage of total horsepower from three sources of mechanical drive in USmanufacturing, 1869–1939)

Source: Devine (1983, 351, table 3).


nical change and the response of measuredproductivity growth.1 We have computed lineartrends in annual output per hour in US manu-facturing for three periods: 1869–1899, 1899–1929, and 1949–1969. (We chose these periodsto omit the Great Depression and World War II;data are from the US Department of Commerce1973.) The trend growth rate of output per hourin the three periods increases gradually, from1.6 percent to 2.6 percent to 3.3 percent. (Wechose 1869 as the starting point because theearly data are derived from the US Census Bu-reau’s censuses of manufacturing establishments,which have been taken every decade since thatyear. We focus on the subsequent 100-year pe-riod. Gordon (2000b) documents a similar grad-ual acceleration for the growth of output perhour for the US economy as a whole.)

In documenting the slow diffusion of newtechnologies, we focus on the diffusion of elec-tric power in manufacturing over the 1869–1939 period. In Figure 2 we plot the percentagesof mechanical power in US manufacturing es-tablishments that were derived from water,steam, and electricity from 1869 to 1939 (De-vine 1983, table 3). Before 1899, more than 95percent of mechanical power was derived fromwater and steam. Between 1899 and 1929, elec-tricity use gradually replaced water and steam,so that by 1929, over 75 percent of mechanicalpower was electric. If we measure the diffusionof electricity in manufacturing starting in 1869,we see that it took 50 years for electricity toprovide 50 percent of mechanical power. Thismeasure of the speed of diffusion is, of course,sensitive to the choice of starting date. A measure

of the speed of diffusion that is less sensitive tothat choice is the time required for a technology todiffuse from 5 percent to 50 percent. For electric-ity in US manufacturing, such diffusion took placeover about 20 years, from 1899 to 1919.

In documenting the ongoing investment inold technologies, we focus on the ongoinggrowth of steam power over the 1869–1939period. Figure 2 also shows that the percentageof mechanical power derived from steam in-creased from roughly 50 percent in 1869 toroughly 80 percent in 1899. Given that the totalamount of mechanical power in US manufac-turing increased over this time period, thesedata imply that there was substantial net newinvestment in steam power for at least 30 yearsafter the development of electric power. To putthe diffusion paths of these three types of powerin a longer-term perspective, recall that water-power is an extremely old technology, while theuse of steam power started to increase in theUnited States between 1800 and 1810 (JeremyAtack, Fred Bateman, and Thomas Weiss1980). During the 1800–1899 period, water-power slowly gave way to steam power, andonly after that did electric power gradually re-place both of these older technologies.

II. A Model of Technology Diffusion

We now present our quantitative generalequilibrium model of the diffusion of new tech-nologies and the corresponding impact of thesetechnologies on economic growth. We build inthree assumptions meant to capture historians’hypotheses about the technological constraintsfaced by manufacturers during the transitionafter the Second Industrial Revolution. (For amore detailed discussion of the links betweenthe historical analyses and our model, see ourearlier work, Atkeson and Kehoe 2001.) Theassumptions are the following:

● New plants embody new technologies.2 Thisassumption is motivated by the work of

1 Throughout, we take as given the standard view ex-pressed by historians (like David 1990) that a sustainedincrease in the rate of technical change began in the SecondIndustrial Revolution and continued for many decades af-terward. This view, together with the data on manufacturingproductivity, leads many observers to see a productivityparadox after the Second Industrial Revolution. Our objec-tive is to assess quantitatively whether our model of growthand technology diffusion can account for this productivityparadox as well as the associated diffusion patterns of newand old technologies. An alternative approach, which we donot take, is to argue that the historians are mistaken: thepace of technical change did not increase until severaldecades after the Second Industrial Revolution and, hence,there is no productivity paradox. Such an approach wouldhave to confront the issue of how to generate the observedpatterns of diffusion of new and old technologies.

2 Note that we do not assume that all new technologiesare embodied in new plants. In fact, our model is consistentwith the idea that most of the ongoing technical change inthe economy is driven by either disembodied technicalchange or technical change embodied in other factors, suchas capital goods or labor.


Devine (1983, 1990) and David (1990,1991), who argue that manufacturing plantsneeded to be completely redesigned in or-der to make good use of the new technol-ogies stemming from the development ofelectric power.

● Improvements in the technology for newplants are ongoing. Specifically, we modelthe transition to a new economy after the Sec-ond Industrial Revolution as arising from aonce-and-for-all increase in the rate of improve-ment in the frontier technology embodied in thedesign of new plants. This assumption capturesthe arguments of Schurr et al. (1960), Rosen-berg (1976), Devine (1990), and Sidney Sonen-blum (1990) that the process of improvingefficiency through changes in factory designafter the Second Industrial Revolution con-tinued for decades, through at least the 1980s,and lay behind the new economy after thisrevolution.

● New plants improve their technology througha period of learning. This assumption is con-sistent with a broad body of work on learningas well as the discussions of David (1990,1991) and Alfred D. Chandler (1992).

In describing our model formally below,we build in these assumptions in abstractterms so that, with a simple reinterpretation,the model can be applied to a variety oftransition experiences. At first, we interpretthe elements of the model with an eye towardapplying it to the transition after the SecondIndustrial Revolution. Later we discuss howto reinterpret these elements in order to applythe model to the transition after the IT Rev-olution (see Section IVA).

A. The Basic Structure

In the model, time is discrete and is denotedby periods t � 0, 1, ... . The economy has acontinuum of size 1 of households. Householdshave preferences over consumption ct given by¥t�0

� �tlog(ct), where � is the discount factor.Each household consists of a worker and amanager, each of whom supplies one unit oflabor inelastically. Households are also en-dowed with the initial stock of physical capitaland ownership of the plants that exist in period0. Given sequences of wages for workers, wages

for managers, intertemporal prices {wt, wmt,pt}t�0

� , initial capital holdings k0, and an initialvalue a0 of the plants that exist in period 0, house-holds choose sequences of consumption {ct}t�0

� tomaximize utility subject to the budget constraint

(1) �t � 0

�

pt ct � �t � 0

�

pt �wt � wmt � � k0 � a0 .

Production in this economy is carried out inplants. In any period, a plant is characterized byits specific productivity A and its age s. Tooperate, a plant uses one unit of a manager’stime, physical capital, and (workers’) labor asvariable inputs. If a plant with specific produc-tivity A operates with one manager, physicalcapital k, and labor l, the plant produces output

(2) q � zA�1 � ��/�F�k, l��,

where the function F is linearly homogeneousof degree 1 and the parameter � � (0, 1). Thetechnology parameter z is common to all plantsand grows at an exogenous rate. We call zeconomy-wide productivity. Following RobertE. Lucas, Jr. (1978, 511), we call � the span ofcontrol parameter of the plant’s manager. Here,the parameter � may be interpreted as determin-ing the degree of diminishing returns at theplant level. We refer to the pair (A, s) as theplant’s organization-specific capital, or simplyits organization capital. This pair summarizesthe built-up expertise, or knowledge, that dis-tinguishes one organization from another. In(2), the exponent (1 � ��)/� on A is a conve-nient scaling of specific productivity.

Each plant produces a differentiated product,which a competitive firm aggregates to producea homogeneous final good. Each plant choosesits price and inputs to maximize profits, given thedownward-sloping demand from the firm that pro-duces final goods. The competitive final goodsfirm produces aggregate output according to

yt � � �s�

A

qt(A)��t(A, s)� 1/�

,

where �t(A, s) denotes the measure of plantswith organization capital (A, s) that operate in t.The final goods firm has a static demand func-


tion qt(A) � pt(A)�1/(1�� )yt. Note that we use asymmetry property of the equilibrium: indepen-dently of age, all operating plants with the samespecific productivity A choose the same outputand set the same price. We also normalize theprice of the final good to be 1.

The timing of events in period t is as follows.An owner’s decision whether to operate a plant ismade at the beginning of the period. Plants that donot operate produce nothing; the organization cap-ital in these plants is lost permanently. Plants withorganization capital (A, s) that do operate, in con-trast, hire a manager, capital kt, and labor lt andproduce output q according to (2). At the end ofthe period, operating plants draw independent in-novations (or shocks) � to their specific produc-tivity, with probabilities given by age-dependentdistributions {s}. Thus, a plant with organizationcapital (A, s) that operates in period t has stochas-tic organization capital (A�, s � 1) at the begin-ning of period t � 1.

Consider the process by which a new plantenters the economy. Before a new plant canenter in period t, a manager must spend periodt � 1 preparing and adopting a blueprint forconstructing the plant that determines theplant’s initial specific productivity t. Blueprintsadopted in period t � 1 embody the frontier ofknowledge (or frontier blueprint) regarding thedesign of plants at that point in time. Thisfrontier evolves exogenously, according to thesequence {t}t�0

� . Thus, a plant built in t � 1starts period t with initial specific productivity tand organization capital (A, s) � (t, 0). Be-cause this level of productivity is built into theplant at its start, we refer to growth in t asembodied technical change.

We assume that capital and labor are freelymobile across plants in each period. Thus, forany plant that operates in period t, the decisionof how much capital and labor to hire is static.Given a rental rate for capital rt, a wage rate forlabor wt, and a managerial wage wmt, the oper-ating plant chooses employment of capital andlabor to maximize variable profits

(3) dt �A� � maxp,q,k,l

pq � rtk � wtl

subject to (2) and the static demand function.Let pt(A), qt(A), kt(A), and lt(A) denote thesolutions to this problem.

The decision whether to operate a plant isdynamic. This decision problem is described bythe Bellman equation

(4) Vt �A, s� � max�0, dt(A) � wmt

�pt � 1

pt�

�

Vt � 1(A�, s � 1)s � 1(d�)�,

where the sequences {t, wt, rt, wmt, pt}t � 0�

are given. The value Vt( A, s) is the expecteddiscounted stream of returns to the owner of aplant with organization capital ( A, s). Thisvalue is the maximum of the returns fromclosing the plant and those from operating it.The second term in the brackets on the rightside of (4) is the expected discounted value ofoperating a plant of type ( A, s). It consists ofcurrent returns dt( A) � wmt and the dis-counted value of expected future returnsVt � 1( A, s). The plant operates only if theexpected returns from operating it are non-negative.

An owner’s decision whether to hire a man-ager to prepare a blueprint for a new plant isalso dynamic. In period t, this decision is deter-mined by Vt

0 � �wmt � pt�1Vt�1�t�1,0�/pt. Thevalue Vt

0 is the expected stream of returns to theowner of a new plant, net of the initial fixed costwmt of paying a manager to prepare the blueprintfor the plant. Managers are hired to prepare blue-prints for new plants only if Vt

0 � 0. Since thereis free entry into the activity of starting newplants, in equilibrium we require that Vt

0 t � 0,where t is the measure of managers startingnew plants.

Let kt denote the aggregate physical capitalstock. Then the resource constraints for physicalcapital and labor are ¥s �A kt(A)�t(dA, s) � ktand ¥s �A lt(A)�t(dA, s) � 1. The resourceconstraint for aggregate output is ct � kt�1 �yt � (1 � �)kt, where � is the depreciation rateof capital. The resource constraint for managersis t � ¥s �A �t(dA, s) � 1.

An equilibrium is defined in the obviousway. In this equilibrium, in each period t, thedecision to operate a plant is summarized byan age-dependent cutoff rule A*t(s). In period


t, plants of age s with specific productivityA � A*t(s) continue operating, and those withA � A*t(s) close.

To get a sense of the process for the birth,growth, and death—or the life cycle—of plantsthat our model generates, consider Figure 3. Herewe show the evolution of the specific produc-tivity of two plants that both enter in period t �1860. Both of these plants start with productiv-ity equal to that of the frontier blueprint in 1860,namely, 1860. This frontier blueprint grows ex-ogenously over time at a constant rate, as shownby the solid straight line labeled log t. The twoplants each experience random shocks to theirplant-specific productivity drawn from age-de-pendent distributions s. Plant 1 is relativelylucky in that it draws especially favorableshocks to its specific productivity, and plant 2 isrelatively unlucky.

In every period, each plant makes a decisionwhether to continue or to close, or exit. Thisdecision is based on a comparison of the plant’scurrent specific productivity At and its futureprospects for learning, determined by the age-dependent distributions s relative to the al-ternative of exiting and starting a new plantwith the current frontier blueprint. The age-dependent cutoff rule A*t(s) summarizes the de-cision. Plant 1 has relatively high specific

productivity; hence, it exits only after operating30 years. Plant 2 has relatively low specificproductivity and exits much sooner. After theseplants exit, the manager of each plant starts anew plant with the current frontier blueprint andbegins the process of building up specific pro-ductivity in the new plant.3

In our model, technologies embodied inplants diffuse throughout the economy as newplants embodying these technologies are bornand grow. Figure 3 also illustrates the me-chanics of this diffusion. In 1863, the man-ager of plant 2 decides to exit and start a new

3 Since our model has a fixed number of managers andeach manager can either start a new plant or operate anexisting plant, our assumptions imply that on a balancedgrowth path, the number of plants is fixed. An alternativeassumption, pursued by Hopenhayn and Rogerson (1993), isthat, instead, what is fixed is the cost in terms of consump-tion goods of starting a new plant. In that alternative model,the number of plants grows over time.

We have chosen our specification because it seems to bea good approximation to the data. Saul S. Sands (1961)reports that over the 1904–1947 period, the number ofmanufacturing plants in the United States grew only 0.5percent per year, while output per manufacturing establish-ment grew nearly 3.0 percent per year. Clearly, most of thegrowth of output in this period came from more output fromeach plant and only a small part from an increase in thenumber of plants.

Exit

Log of specific productivity

1863 1890

New plant

New plant

Exit

Time

Plant 1

Plant 2

Frontierblueprintlog t

1860 1864 1891

log 1860

FIGURE 3. THE LIFE CYCLE OF PLANTS IN THE MODEL

(Productivity of two plants versus that of frontier blueprint over time)


plant that embodies the frontier blueprint of1864 and then begins to learn with that newtechnology. Likewise, in 1890 the manager ofplant 1 decides to exit and start a new plantthat embodies the frontier blueprint of 1891and then begins to learn with that new tech-nology. In this manner, new plants embody-ing new technologies gradually replace oldones. Since our model has many such plants,each with different shocks to specific produc-tivity, this diffusion of new embodied tech-nologies occurs smoothly over time.

Formally, we measure the diffusion of em-bodied technologies as follows. Let lt,s � �A(lt(A)/lt)�t(dA, s) denote the fraction of laboremployed in plants of age s, and let

(5) Dt,t � k � �s � 0

k

lt,s

be the fraction of labor employed in plants ofage k and younger. We measure the diffusion inperiod t � k of embodied technologies devel-oped in period t or later by Dt,t�k, which, in themodel, is the fraction of labor employed inplants using technologies developed in period tor later.

B. Measuring the Learning Process

In our model, the process governing learningis a key determinant of the rate at which a newtechnology diffuses. In the model, learning atthe plant level is represented by shocks to theplant’s specific productivity. We argue here thatdata on plant size can be used to measure theseshocks.4 We then contrast our approach to mea-suring learning with the standard approachtaken in the literature on learning.

The Link between Plant Size and Plant-Specific Productivity.—Our model implies atight link between plant size and plant-specificproductivity. Given this link, we can use data onthe relative size of plants to infer the actualpattern of productivity changes, or learning, atthe plant level.

To see the link between plant size and pro-ductivity, consider the static problem of allocat-ing a given amount of capital and labor acrossplants at a point in time. For a given distribution�t of organization capital, it is convenient todefine

(6) nt �A� �A

A� t

as the size of a plant of type (A, s) in period t,where A� t � ¥s �A A�t(dA, s) is the aggregate ofthe specific productivities across all plants. Thevariable nt(A) measures the relative size of theplant in terms of its capital or labor, in that theequilibrium allocations are kt(A) � nt(A)kt andlt(A) � nt(A)lt.

A similar result holds for cohorts of plants.To see this result, define the aggregate of thespecific productivities of a cohort of plantsof age s as A� t,s � �A A�t(dA, s). Note from (6)that A� t,s/A� t � �A nt(A)�t(dA, s). We then havethe following proposition.

PROPOSITION: The aggregate of specificproductivities of plants of age s relative to thatof all plants is equal to the share of total em-ployment in those plants; that is, A� t,s/A� t � lt,s,where lt,s � �A [lt(A)/lt]�t(dA, s).

Given this proposition, we can use the dataon employment shares by cohorts, lt,s, to inferthe pattern of learning, as measured by A� t,s/A� t. The data show that employment in a co-hort of plants grows substantially as thecohort ages.5 For example, in terms of the4 Our approach differs from that of a large literature

which models specific productivity as endogenous. An ad-vantage of our approach is that it allows us to match theprocess for productivity associated with learning directly todata on the growth process of plants. Moreover, at least ina steady state, we need not take a stand on whether thisproductivity is derived from active or passive learning,matching, or ongoing adoption of new technologies in ex-isting plants. Outside of a steady state, however, we areimplicitly assuming that the learning process does not varywith the growth rate of the economy.

5 Here and throughout this study, our microeconomicdata are taken from the US Census Bureau LRD on manu-facturing plants. This dataset is described in Davis et al.(1996). We use data on employment, job creation, and jobdestruction from the 1988 panel of the LRD, which weobtained from John Haltiwanger’s Web site, http://www.bsos.umd.edu/econ/haltiwanger.


cross section, the 1988 panel of the US Cen-sus Bureau’s Longitudinal Research Database(LRD) on manufacturing plants shows thatthe employment share of plants rises at leastfor the first 20 years of a plant’s life and thatthe employment share of a cohort of plantsof age 20 is more than 7 times that of thecohort of brand-new plants. In terms of thepanel evidence, J. Bradford Jensen, Robert H.McGuckin, and Kevin J. Stiroh (2001) showthat the employment share of a cohort ofplants starts small and grows steadily withage.

From the perspective of our model, theLRD data imply that the aggregate of specificproductivities of a cohort of plants growsfaster than aggregate productivity for at least20 years. Since in the data the employmentshare of a cohort of plants of age 20 is morethan 7 times that of brand-new plants, ourmodel implies that plants that survive 20years have, at that age, learned so much thatthey are not only much more productive thanthey were when they were first built, but alsomuch more productive than plants that arebrand-new in that twentieth year. Thus, for arelatively long period of time, the ongoinginnovations that occur within an operatingplant are, on average, much larger than theinnovations from the frontier technology. Inthis sense, 20-year-old plants are technologi-cally superior to their contemporary brand-new plants. We interpret this evidence asindicating that learning in plants is both sub-stantial and protracted.

Note that the link between the employmentshares lt,s and relative productivities A� t,s/A� t es-tablished in the proposition is derived fromstatic first-order conditions equating the valuemarginal product across plants. These first-or-der conditions hold regardless of any changes ortrends in overall employment lt. Hence, the factthat the data show trends in manufacturing em-ployment—increasing in the first part of thecentury and decreasing in the second part—hasno bearing on our method of inferring learningfrom employment shares.

We use employment shares of plant cohortsto infer the amount of learning that plants ex-perience as they age. We also use them to inferthe speed of diffusion of new technologies asexpressed in (5).

A Contrast with the Literature on Learning.—We have argued that theory implies thatlearning manifests itself in the plant-specific,or organization-specific, component of pro-ductivity and can be uncovered from data onthe relative size of organizations. This ap-proach is quite different from that followed inmuch of the literature on learning at the or-ganizational level. (For a survey, see the 1990work of Linda Argote and Dennis Epple.) Inthat literature, learning is measured by dataon the relationship between labor productivityat the organization level and the age or pro-duction experience of the organization. Thisliterature identifies many instances of a verystrong relationship between the labor produc-tivity of a specific organization and its age orproduction experience.

We take a different approach for two reasons.One is that more comprehensive panel datasetson manufacturing plants do not reveal a strongsystematic relationship between the labor pro-ductivity of these plants and their age. The otherreason is that, in the context of models like ours,such a relationship has no bearing on the extentof learning.

In the data, a large dispersion in averageproductivity occurs across plants. However,average productivity does not seem to varysystematically with plant age. For example,Jensen, McGuckin, and Stiroh (2001) study alarge panel of plants and find that once theyinclude controls for labor quality and capitalintensity, “surviving cohorts regardless of ageor vintage show similar (labor) productivitylevels” (331). Eric J. Bartelsman and PhoebusJ. Dhrymes (1998) find similar results. Bahkand Gort (1993) run regressions of plant pro-ductivity on plant experience. Using grosssales as their measure of plant output, theyfind an economically small positive relation-ship between plant productivity and plant age.In particular, their regressions imply that la-bor productivity grows at 15 percent over thefirst 15 years of a plant’s life. To see that thisgrowth is economically small, note that overthis 15-year period, the average survivingplant has employment and value added grow-ing by roughly 500 percent. Moreover, evenin Bahk and Gort’s data, there may be norelationship between plant productivity andage: when Bahk and Gort use the theoretically


preferred value-added measure rather thangross output as a proxy for output, they findlittle relation between productivity and age.

Next we show that, consistent with the data,our model implies that there should be no sys-tematic relation between the labor productivityof a plant and its age or production experience.The model has this implication regardless of theamount of learning assumed at the plant level.To show this, we imagine the results we wouldget if we applied Bahk and Gort’s approach tomeasuring learning to data generated from ourmodel. Specifically, Bahk and Gort run a regres-sion of plant output on plant inputs and somemeasure of experience, and interpret the coeffi-cient on the experience variable as measuringthe extent of learning. Unfortunately, this ap-proach is valid only if the movement in plants’inputs is essentially unrelated to their specificproductivity. Theory, however, predicts pre-cisely the opposite, as the following examplemakes clear.

Consider running Bahk and Gort’s regressionin a simplified version of our model. In thissimplified model, let all plants be competitiveand make a homogeneous final good (� � 1).Let the output in plant i in period t be given bythe production function qit � ztAit

1��lit�, so that

relative employment in this plant is given bylit/lt � Ait/At, where lt � ¥i lit is aggregateemployment and At � ¥i Ait is the aggregate ofspecific productivities of all plants. Hence, tak-ing logs of the plant production function andsubstituting for Ait from lit/lt � Ait/At gives that,in equilibrium,

(7) log qit � logzt�At /lt�1 � � � log lit .

We can use (7) to calculate the coefficients inthe following regression, of the form used byBahk and Gort:

log qit � �1t � �2log lit � �3xit ,

where xit is some measure of the age or pastproduction of the plant. This regression neces-sarily yields estimates of �3 � 0 along with�1t � log[ zt(At/lt)

1��] and �2 � 1. Bahk andGort’s interpretation of �3 � 0 would be that nolearning takes place at the plant level regardlessof how much specific productivity Ait rises withage.

Notice also that in the equilibrium of themodel, (7) implies that labor productivity isgiven by qit/lit � zt( At/lt)

1 � � and, hence, isconstant across all plants, regardless of theirspecific productivity Ait. This observationpoints to the key difference between the im-plications for learning by an individual andthat of an organization, which can add vari-able factors. Individuals who learn increasetheir labor productivity. Organizations thatlearn grow by adding variable factors in orderto keep their labor productivity constant (atleast with Cobb-Douglas production). Hence,we argue that the key variable to look at todetermine the amount of learning (that is,built-up knowledge or organization-specificcapital) is not some measure of either labor orcapital productivity, but rather some measureof relative size.

C. Quantification

To derive our model’s quantitative implica-tions for the main features of transition to a neweconomy, we need to set both the macro and themicro parameters. In the model, a period is ayear.

Macro Parameters.—The model’s macroparameters are few and fairly standard toquantify. The growth rate of output per hour gand the depreciation rate � are chosen toreproduce data on the US manufacturing sec-tor since World War II. We set g � 3.3percent to match the growth of manufacturingoutput per hour from 1949 to 1969. We let theplant-level production function be F(k, l ) �k�l1 � �. Because of imperfect competition,the share of GDP paid to physical capital isgiven by ��. We use data for 1959 –1999obtained from the US Department of Com-merce (various dates) national income andproduct accounts to set �� 19.9 percentand � � 5.5 percent, based on methodologydescribed in our earlier work (Atkeson andKehoe 2005). We set the discount factor � �0.993, so that the steady-state interest rate idefined by 1 � i � (1 � g)/� is 4.1 percent.

Now consider the parameter � � ��. On thebasis of the work of Susanto Basu and John G.Fernald (1995), Basu (1996), and Basu and


Miles S. Kimball (1997), we choose � � 0.9,which implies a markup of 11 percent and anelasticity of demand of 10. The span of controlparameter � measures the degree of diminishingreturns in variable factors at the plant level.Hundreds of studies have estimated productionfunctions with micro data. These analyses in-corporate a wide variety of assumptions aboutthe form of the production technology and drawon cross-sectional, panel, and time-series datafrom virtually every industry and developedcountry. Paul H. Douglas (1948) and Alan A.Walters (1963) survey many studies. More re-cent work along these lines has also been doneby Martin Neil Baily, Charles Hulten, andDavid Campbell (1992), Bahk and Gort (1993),G. Steven Olley and Ariel Pakes (1996), andBartelsman and Dhrymes (1998). This workfinds that the returns to scale in production arefairly close to 1.0, with many of the estimatesfalling in the range from 0.9 to 1.0. We choose� � 0.95. This makes � � 0.85. This value of �is consistent with the discussion of Atkeson,Aubhik Khan, and Lee Ohanian (1996). (As wereport later, in Section IIIA, we did some sen-sitivity analysis with respect to � and found thatwith � � 0.9 and � � 1.0, we get similar results.)

Micro Parameters.—We use the method de-scribed in our 2005 work to set the micro pa-rameters governing plant-specific productivity.We rewrite the model so that the problem ofchoosing the learning parameters governingplant-specific productivity is equivalent to di-rectly choosing parameters governing shocks tosize. We assume that the shocks to size have alognormal distribution, so that log �s � N(ms,�s

2). We choose the means and standard devia-tions of these distributions to be smoothly de-clining functions of s. In particular, we set ms ��1 � �2(S � s/S)2 for s � S and ms � �1otherwise, and �s � �3 � �4(S � s/S)2 for s �S and �s � �3 otherwise. With this parameter-ization, the shocks for plants of age S or olderare drawn from a single distribution. Thus,shocks to plant size are parameterized by{�i}i�1

4 and age S.We choose the parameters governing these

shocks so that the model matches data on thefraction of the labor force employed in plants ofdifferent age groups, as well as data on jobcreation and job destruction in plants of differ-

ent age groups. We use these job statistics to setthe means and variances of shocks to produc-tivity. The data are from the 1988 panel of theUS Census Bureau LRD, which has the mostextensive breakdown of plants by age available.

More formally, we use the relevant statisticsdefined by Steven J. Davis, John C. Haltiwan-ger, and Scott Schuh (1996): employment in aplant in year t is (lt � lt�1)/2, where lt is thelabor force in year t; job creation in a plant inyear t is lt � lt�1 if lt � lt�1 and zero otherwise;job destruction in a plant in year t is lt�1 � lt iflt � lt�1 and zero otherwise. In Figure 4, wereport for each age category these three statis-tics for US manufacturing plants in 1988 for allplants in that category relative to the total em-ployment in all plants. This gives us a total of26 statistics from the data that we use to sum-marize the life cycle of plants.

We set the parameter S � 150 and choose thefour parameters {�i}i�1

4 to minimize the sum ofthe squared errors between the corresponding26 statistics computed from the model and thosein the data. The resulting model statistics arealso plotted in Figure 4. The parameters thatgenerate these shocks are S � 150, �1 ��0.1829, �2 � 0.2520, �3 � exp(�1.7289),and �4 � exp(�7.0134).

In Figure 4A, we see that our modelmatches the employment shares fairly well. InFigures 4B and 4C, we see that our modelimplies a bit more job creation and job destruc-tion on average than are observed in the data.To get some perspective on this, note that theimplied statistics for the overall job creation anddestruction rates are 8.3 percent and 8.4 percentfor the data and are both 9.7 percent for themodel. Note also that in annual data during the1972–1993 period, the standard deviations ofthe overall job creation and job destruction ratesare 2.0 and 2.7 percentage points. Together,then, these data reveal that the overall job cre-ation and job destruction rates in our model arereasonably good estimates—within one stan-dard deviation—of the time-series fluctuationsin these rates observed in the data.

III. Reproducing the Transition after theSecond Industrial Revolution

Now we ask whether our quantitative model,built to capture the historians’ hypotheses about


the constraints facing US manufacturers in theSecond Industrial Revolution, can reproduce thethree main features of the transition after thatrevolution we documented in Section I. To an-swer this question, we use the model to simulatea transition to a new economy with a perma-nently faster pace of technical change, driven byfaster growth in the frontier blueprints for newplants. In this simulation, the faster growth as-signed to the frontier blueprints is meant tocapture the faster pace of technical change em-bodied in US plant design after the developmentof electric power.

Our transition experiment is stark: we assumethat the transition to a new economy starts witha sudden, unanticipated, and permanent increase

in the pace of embodied technical change. Wemake this assumption in order to give a starkpicture of the transition dynamics implied by ourmodel. We also view this assumption in thespirit of the work of historians Devine (1983),David (1990), David and Gavin Wright (1999),and others who document a substantial acceler-ation in the pace of technical change during theSecond Industrial Revolution.

In this experiment, we find that the modelreproduces the three main features of the tran-sition after the Second Industrial Revolution verywell. We follow that experiment with two others,designed to investigate whether the details of thelearning process are key quantitatively in generat-ing these results. We find that they are.

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FIGURE 4. THE MODEL’S REPRODUCTION OF US DATA ON EMPLOYMENT, JOB CREATION, AND

JOB DESTRUCTION

(Each statistic as a percentage of total US 1988 employment for manufacturing plants ofvarious ages)

Source: US Census Bureau 1988 Longitudinal Research Database.


A. The Transition Experiment

Again, we model the Second Industrial Rev-olution as a permanent increase in the pace oftechnical change. Specifically, consider aneconomy that is initially on a balanced growthpath with steady growth in the frontier blue-prints causing output per hour to grow 1.6 per-cent per year. This growth rate is the trendgrowth rate of output per hour in US manufac-turing from 1869 to 1899. We denote this initialgrowth rate of the frontier blueprints by g

old. Inour experiment, we suppose that at the begin-ning of the period labeled 1869, agents learnthat the growth rate of the frontier blueprintsincreases once and for all, so that on the newbalanced growth path, output per hour grows3.3 percent per year (as in the US data for1949–1969), an increase of 1.7 percentagepoints. We denote this new growth rate of thefrontier blueprints by g

new. We refer to thesetwo balanced growth paths as the old economyand the new economy, respectively. We thencompute the transition path of our model econ-omy from the old economy to the new economyin response to this exogenous increase in thepace of embodied technical change.

In our experiment, we must set some initialconditions. We set the initial physical capital-output ratio and the distribution of organizationcapital across plants to be those from the bal-anced growth path of the old economy. In set-ting this initial distribution of organizationcapital, we assume that the distributions of theshocks to specific productivity are the same asthose we used to match the US micro data for1988. Thus, in this experiment, the stochasticprocess for specific productivities is heldfixed, whereas the growth rates of the frontierblueprints are varied. This amounts to assum-ing that the process of learning about anyparticular embodied technology does not de-pend on the rate at which new embodied tech-nologies appear.

Now consider our model’s implications forthe three main features of the transition wedocumented in Section I: a productivity para-dox, a slow diffusion of new technologies, andongoing investment in old technologies.

Begin with the model’s implications for thepath of productivity, measured as output perhour. Figure 5 shows these implications for the

1869–1969 period, together with the actual datafor this period (as seen in Figure 1). The modelclearly produces a productivity paradox. In themodel, as in the data, the growth in output perhour gradually accelerates. Over the 1869–1899period, the trend growth rate in output per houris 1.6 percent in both the model and the data.Over the 1899–1929 period, the trend growthrate in output per hour is 2.3 percent in themodel and 2.6 percent in the data. In the model,as in the data, the growth rate in output per hourreaches its new steady state of 3.3 percent bythe mid-1940s.

A convenient summary measure of the speedof transition in our model is the number of yearsthe growth rate of output per hour takes to riseby one percentage point relative to the growthrate of the old economy. Here it takes 50 years.

Next, consider the model’s implicationsfor the diffusion of new technologies. Fig-ure 6 shows this diffusion in the model and inthe data during the 1869–1939 period. For newtechnologies, we make the following compari-son between model and data. For the model, wegraph the percentage of output produced inplants with blueprints dated 1869 and later. Thispercentage is also the percentage of physicalcapital and labor employed in plants with theseblueprints. For the data, we graph the percent-age of total horsepower in US manufacturingestablishments provided by electric motors overthe same period. In this comparison, we areassuming that, in the data, plants that are drivenby electric motors were built in and after 1869and those driven by steam and water were builtbefore 1869. With this interpretation, our modelpredicts a slow pace of diffusion of new tech-nologies quite similar to that for electric motorsin the data. In the model, technologies dated1869 and later take 46 years to diffuse to 50percent; in the data, electric motors take about50 years.

Of course, in measuring diffusion rates, thechoice of initial dates in the data is somewhatarbitrary. To make a comparison of diffusionrates in the model and the data that is not sodependent on initial dates, consider a statisticthat is often used in the diffusion literature: thetime it takes for diffusion to go from 5 percentto 50 percent. This time is roughly 20 years(1899–1919) for electric motors in the data; it is19 years for new technologies in the model.


Thus, either way we measure it, the diffusion inthe model is similar to that in the data.

Note in Figure 6 that our model produces anS-shaped diffusion curve for new embodiedtechnologies. It does so because of the hetero-

geneity across existing plants in the knowledgethat they have built up about their old embod-ied technologies. Plants that have little suchknowledge exit in favor of new plants early inthe transition, while plants with substantial

FIGURES 5–7. The Model’s Reproduction of the Gradual Transition to a New Economy

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FIGURE 5. A SLOW INCREASE IN PRODUCTIVITY GROWTH ...(Log of output per hour and trend growth in manufacturing, 1869–1969, in the data

and the model)

Source: US Department of Commerce (1973).

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1869–1939)



knowledge exit only later in the transition. Thatthe diffusion curve is S-shaped is a quantitativeresult. The shape of the curve reflects the dis-tribution of knowledge across plants implied bythe parameters of our learning process.

Finally, consider our model’s implication forthe extent of ongoing investment in old tech-nologies. We have data on two old technologies,water and steam. So for the model, we considertwo types of old technologies: those used inplants built before 1802, which we identify withwaterpower, and those used in plants built be-tween 1802 and 1869, which we identify withsteam power. This dating of technologies in ourmodel is consistent with the work of Atack,Bateman, and Weiss (1980). Their work sug-gests that the diffusion of steam power in theUnited States started some time between 1800and 1810. We choose to date steam as startingin 1802 so that our model is consistent with thedata on the diffusion of steam power in 1869.That is, in 1869, roughly 67 years after it beganto diffuse, steam power accounts for 50 percentof output in the model and 50 percent of horse-power in the data.

In Figure 7, we graph our model’s predictionsfor the percentages of output produced in plantsusing these old technologies from 1869 to 1939implied by our dating scheme. We also repro-

duce the US data seen earlier, in Figure 2, on thefractions of horsepower derived from water andsteam power over this same time period.Clearly, in those data the fraction derived fromwaterpower declined steadily from 1869 to1939, while the fraction of horsepower derivedfrom steam initially increased from 50 percentto 80 percent between 1869 and 1899 and thendeclined. Our model reproduces both these pat-terns very well.

These results imply that the model has con-siderable ongoing investment in old technolo-gies for at least the first 30 years of thetransition to a new economy. To understand thisimplication, note that in the model, by assump-tion, no new plants are built using either of theold technologies during this time period. Hence,all of the increase in output accounted for bythese old technologies is coming from existingplants that are growing larger by adding capitaland labor. This growth is driven by continuedlearning about these old technologies.

Most of the parameters of our model arestandard. However, the span of control param-eter, �, and the parameters of the learning pro-cess are not. We ask, therefore, how sensitiveour results are to these parameters.

We find that they are not very sensitive to thevalue of the span of control parameter. We redid

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FIGURE 7. ... AND ONGOING INVESTMENT IN OLD TECHNOLOGIES

(Model’s predicted % of output produced in plants with blueprints dated 1802–1869(steam) and before 1802 (water) versus actual % of horsepower provided by steam

and water power in US manufacturing plants, 1869–1939)



our transition experiments with � � 0.9 and� � 1.0 so that � � �� equals 0.81 and 0.9,respectively. (Recall that our initial values were� � 0.95 and � � 0.85.) These changes led toonly slight differences in the speed of transition.For example, with � � 0.9, the transition isslightly faster: it takes 45 years instead of 50years for the growth rate of output to increaseone percentage point, and 41 years instead of 46years for diffusion to reach 50 percent. With� � 1, the transition is slightly slower: it takes61 years before the growth rate of output in-creases one percentage point and 58 years fordiffusion to reach 50 percent.

B. Learning Experiments

Our model reproduces well the three mainfeatures of the transition to a new economy afterthe Second Industrial Revolution. We find thisresult remarkable because the parameters of thelearning process were not chosen to match anyof these three features. With our approach tomeasuring learning, we have found a learningprocess that is both substantial and protracted.Here, we conduct two experiments to determinewhether this finding is key quantitatively ingenerating our results. We find that it is. In ourfirst experiment, we consider a model in which,on average, there is no learning. In our secondexperiment, we consider a learning processsuggested by other researchers on the basis ofan alternative method for measuring learning.In neither of these experiments does ourmodel reproduce the three main features ofthe transition.

In our first experiment, we set average learn-ing to zero by setting the model’s age-depen-dent means of the shocks to plant-specificproductivity to one (which, with A� � A�, setsthe expected growth rate of A to zero). To getthe transition to converge in this experiment, weincrease the standard deviation of the produc-tivity shocks by a factor of five.6 With theseparameters, the model’s features of the transi-

tion to the new economy are quite differentfrom those seen after the Second Industrial Rev-olution. Productivity and diffusion move swiftlyinstead of slowly, and there is no ongoing in-vestment in old technologies. It takes just fiveyears for the growth rate of output per hour toincrease by one percentage point and only fouryears for technologies dated 1869 and later todiffuse to 50 percent. In this experiment, withour dating scheme, the percentage of outputproduced using old technologies correspondingto steam (those dated 1802–1869) starts at morethan 99 percent at the beginning of the transitionand falls to less than 1 percent over the next 30years.

Now we turn to our second experiment. Re-call that we follow Hopenhayn and Rogerson(1993) in using data on the size of US manu-facturing plants over their life cycle to infer thelearning process. With this procedure, we havefound that learning is both substantial and pro-tracted. Other researchers have not used thesedata to infer learning, but rather have inferred itby using regression estimates of the productiv-ity of plants by age. (See, for example, the workof Jovanovic and Yaw Nyarko 1995; Hornsteinand Krusell 1996; Thomas F. Cooley, Green-wood, and Yorukoglu 1997; and Greenwoodand Yorukoglu 1997, who rely on estimates ofproductivity at the plant level made by Bahkand Gort 1993.) As we have discussed above,there is not much evidence of a systematic re-lationship between plant age and plant produc-tivity. Hence, it is not surprising that thelearning processes used by these researchersimply that learning is much less substantial andprotracted than our procedure implies.

In our second experiment, we consider theimplications of our model for transition whenplants have the learning process discussed byCooley, Greenwood, and Yorukoglu (1997).We do so by setting the age-dependent meansso that, on average, A1 � � grows at 1 percenta year for the first 14 years and is then con-stant. (See the discussion of the Bahk-Gortlearning process in the work of Cooley,Greenwood, and Yorukoglu 1997, 476.) Also,in order to get the transition to converge, weagain increase the standard deviation of theproductivity shocks by a factor of five. In thisexperiment, the model’s transition to a neweconomy is also fast: it takes only eight years

6 We need to increase the standard deviation in order togenerate a smooth transition. If the standard deviation is toosmall, the distribution of organization capital across plantsbecomes lumpy during the transition, and that introducesoscillatory dynamics.


for the growth rate of output per hour to in-crease by one percentage point and only sixyears for technologies dated 1869 and later todiffuse to 50 percent. The percentage of outputproduced using old technologies corresponding tosteam also starts at more than 99 percent at thebeginning of the transition and falls to less than 1percent over the next 30 years.

The results of both of these experiments areconsistent with the idea that the details of ourparticular learning process are primarily respon-sible for this particular model’s ability to repro-duce the main features of the transition to a neweconomy after the Second Industrial Revolution.

IV. Lessons for Other TechnologicalRevolutions

We have built an abstract model of transitionthat can be applied to a variety of technologicalrevolutions. To apply our model to the transi-tion after the Second Industrial Revolution, weused data on growth rates in the late 1800s to setinitial conditions and data on manufacturingplants to set the parameters of the learning pro-cess. We found that, with these initial condi-tions and this learning process, our model couldreproduce the transition after the Second Indus-trial Revolution remarkably well.

David (1990, 1991) and others have arguedthat the transition after that revolution is auseful paradigm for guiding research on thestudy of the transition following the morerecent IT Revolution. Here we examine whatour model can tell us about that idea. Basi-cally, we learn that it is questionable. Instead,the model suggests that the features of a tran-sition after any technological revolution de-pend on the historical context in which therevolution occurs.

To begin our analysis of the IT Revolution,we discuss how to reinterpret the elements ofour model so that it might be applied to thatrevolution. Here we follow David (1990),Bresnahan, Brynjolfsson, and Hitt (2002),Brynjolfsson, Hitt, and Shinkyu Yang (2002),and others in shifting our interpretation of thebasic unit of production from a manufacturingplant to a business organization and our inter-pretation of blueprints from new manufacturingtechnologies based on electricity to new busi-ness practices based on information technology.

While the two revolutions clearly have somequalitative parallels, they are also likely to havesome quantitative differences that will shape thenature of their particular transition to a neweconomy. Specifically, our model predicts aslow transition after a technological revolutiononly if agents have accumulated a large stock ofbuilt-up knowledge of old technologies beforethe transition begins. For the Second IndustrialRevolution, we argued, agents did have a largestock of built-up knowledge about plants basedon steam and waterpower. For the IT Revolu-tion, then, our model will likely predict a slowtransition only if, at the start of that revolution,agents had a large stock of built-up knowledgeabout business practices based on old informa-tion technologies.

Due to the lack of adequate data about the ITRevolution, we cannot use our model to evalu-ate that period in the same way we did theearlier period. Instead, we conduct two experi-ments with our model to examine which factorsdetermine the extent of built-up knowledge inequilibrium. In the first experiment, we learnthat the faster the pace of technical change inthe old economy, the smaller is the extent ofbuilt-up knowledge and, hence, the faster the tran-sition after a technological revolution. In the sec-ond experiment, we learn that the more substantialand protracted the learning process, the larger isthe extent of built-up knowledge and the slowerthe transition after a technological revolution.

Our experiments suggest, then, that the extentto which the transition after the Second Indus-trial Revolution is a paradigm for the transitionafter the IT Revolution depends heavily on theextent of knowledge about business practicesthat business organizations had built up beforethe IT Revolution. Currently there is little directevidence on the extent of that built-up knowl-edge. Our model does, however, suggest datafrom which it might be measured.

A. Reinterpreting the Model

Our model can be reinterpreted for the ITRevolution by shifting the basic unit of produc-tion from a manufacturing plant to a businessorganization. We assume that each new busi-ness organization starts with a set of businesspractices that embody the current frontier ofsuch practices and then learns to become more


productive with these practices over time. Spe-cifically, we reinterpret our three main techno-logical assumptions as follows:

● New business organizations embody newbusiness practices. This assumption is mo-tivated by the work of Bresnahan, Brynjolf-sson, and Hitt (2002) and Brynjolfsson,Hitt, and Yang (2002), who argue that theeffective use of new information technol-ogy requires a redesign of the business or-ganization.

● Improvements in the design of business prac-tices are ongoing. This assumption is moti-vated by the observation that increases incomputing and networking capability haveled to an increasing array of new types ofbusiness practices and is consistent with theobservation of Michael S. Scott Morton(1991).

● New organizations improve their practicesthrough a period of learning. This assumptionis consistent with the work of Brynjolfsson,Amy Austin Renshaw, and Marshall Van Al-styne (1997) and Brynjolfsson, Hitt, andYang (2002), who argue that the process ofimproving an organization structure may in-volve a protracted period of learning beforethe payoffs from this investment are fullyrealized.

B. The Transition Experiments

We now conduct two experiments to investi-gate how important the stock of built-up knowl-edge is for the speed of transition and how thisstock varies with the model parameters.

A First Experiment.—Our first experimentdemonstrates how our model’s implications forthe three main features of transition depend onthe initial pace of technical change and, hence,the growth rate in the old economy. We thenexplain that this dependency arises because thestock of built-up knowledge varies with thepace of technical change.

In the experiment, we simulate the model re-peatedly, varying the growth rate in the old econ-omy, but holding fixed the assumption that growthis 1.7 percentage points higher in the new econ-omy than in the old. Each time, we also hold fixedall other parameters of the model, including the

learning parameters. Implicitly, here we are as-suming that the learning process is the same as wefound for manufacturing plants.

We summarize the results of these simula-tions in Figure 8A. This figure shows thenumber of years that pass before the growthof measured productivity has risen by onepercentage point, as well as the number ofyears until technologies that are new at thestart of the transition have diffused to 50percent. Clearly, as the growth rate in the oldeconomy increases, two of the key features ofthe transition after the Second Industrial Rev-olution disappear: the extent of the productiv-ity paradox decreases, and new technologiesdiffuse more rapidly.

The third feature disappears as well: accord-ing to the model, as the initial growth rate in theold economy increases, less ongoing investmentin old technologies occurs during the transitionto a new economy. Recall that after the SecondIndustrial Revolution, the percentage of outputproduced using old technologies correspondingto steam power rose from 50 percent to 80percent in the first 30 years of the transition.Here, to make our analysis of old technologiesparallel to that of steam after the Second Indus-trial Revolution, we report on the percentage ofoutput produced using technologies that are upto 67 years old at the start of each simulatedtransition, as well as the fraction of output pro-duced using these same technologies 30 yearslater. The model implies that when the initialgrowth rate is 1.5 percent, the percentage ofoutput accounted for by old technologies risesfrom 42 percent to 78 percent in the first 30years of transition. In contrast, when the initialgrowth rate is 3.5 percent, the percentage ofoutput accounted for by old technologies fallsfrom 97 percent to 1 percent in the first 30 yearsof transition.

Why does the model produce such differentresults for these transitions, when all thatdiffers is the economy’s initial growth rate?The answer lies in the extent of built-upknowledge that exists in the old economy. Inthe model, as we increase the initial growthrate, the diffusion rate of new technologies inthe old economy also increases. Hence, thestock of built-up knowledge that agents haveabout existing technologies in the old econ-omy naturally decreases. With less built-up


knowledge at the start of the transition, agentsare more willing to abandon old technologiesin favor of new ones.

In our model, the stock of built-up knowledgeis characterized by the distribution of organiza-tion capital across productive units. A conve-nient aggregate measure of this stock of built-up

knowledge, relative to the frontier blueprints, is(A� t/t)

1��. Note that the ratio A� t/t is the averageof the specific productivity across productiveunits relative to the frontier blueprints availableto new productive units. The exponent 1 � �expresses this ratio in units of the Solow resid-ual of a standard growth model.

0

10

20

30

40

50

60

1.5 2.0 2.5 3.0 3.5

Growth rate in the old economy (%)

Years

Years until productivity up 1% point

Years until diffusion reaches 50%

FIGURE 8. INITIAL GROWTH RATES MATTER

A. FOR THE SPEED OF TRANSITION ...(Model’s predictions, with various initial steady-state growth rates, for the time until

productivity growth increases 1% point and the time until diffusion reaches 50%)

0

.5

1.0

1.5

2.0

2.5

1.5 2.0 2.5 3.0 3.5

Growth rate in the old economy (%)

In old steady state

In new steady state

( /

B. ... AND THE STOCK OF BUILT-UP KNOWLEDGE

(Model’s predictions, with various initial steady-state growth rates, for the amountof built-up knowledge, (A� /)1��, in the old and new steady states)


How this ratio changes with growth rates canbe demonstrated by the model. For example, inour transition experiment corresponding to theSecond Industrial Revolution, this ratio was2.23 in the old economy and only 1.25 in thenew. Thus, built-up knowledge was nearly 80percent higher in the old economy than in thenew. In that transition, the initial growth rate inthe old economy was 1.6 percent. In contrast,suppose that the initial growth rate had been 3.5percent. Then, the model implies that these ra-tios would have been 1.17 in the old economyand 1.03 in the new, so that built-up knowledgewould have been only about 14 percent higherin the old economy than in the new.

More generally, Figure 8B shows the model’spredictions for the stock of built-up knowledgein the old and new economies as a function ofthe growth rate in the old economy. Note thatthe stock of built-up knowledge in both econo-mies declines as the growth rate in the old econ-omy rises. Comparing Figures 8B and 8A, then,we see the close link between the stock of built-upknowledge and the subsequent speed of transition.

A Second Experiment.—Our first experimentthus indicates that our model does not producea slow transition after a technological revolu-tion unless agents have a large amount ofbuilt-up knowledge about old technologies atthe start of the transition. It further indicates thatan economy does not have much built-upknowledge if the initial growth rate is fast. Wenow find that in order to get a slow transitionwhen the initial growth rate is high, we needlearning to be extremely substantial and pro-tracted, much more so, for example, than wefound from data on US manufacturing plants in1988.

To demonstrate this point, we conduct a finaltransition experiment in which we increase theamount of learning in organizations by increas-ing the means of the idiosyncratic shocks toorganization-specific productivity by a constantfactor independent of age. Recall that theseshocks have a lognormal distribution, so thatlog �s � N(ms, �s

2). Specifically, we increase themean of these shocks to m�s � ms � with �0.1133. With this change in parameters, thelearning process is much more substantial andprotracted than that seen in data on US manu-facturing plants.

With this change in the learning process, weconduct the following transition experiment.We suppose that the old economy starts with arelatively high growth rate of 3.3 percent andthen agents suddenly learn that the growth offrontier blueprints has increased once and forall, so that the economy grows 5 percent per yearon the new balanced growth path. The transitionin this experiment is now very similar to the onewe found after the Second Industrial Revolution:it takes 49 years for the growth rate of output perhour to rise one percentage point and 46 years fornew technologies to diffuse to 50 percent. Interms of ongoing investment in old technolo-gies, we find that technologies up to 67 yearsold account for 51 percent of output at the start ofthe transition and that these same technologiesaccount for 81 percent of output 30 years later.

Inferring the Extent of Built-Up Knowledge.—By the preceding experiments, we have shownthat, in our model, the extent of built-up knowl-edge is critical for generating a slow transitionand that this extent of knowledge varies with theinitial growth rate assumed in the old economy.While we cannot yet measure built-up knowl-edge directly, we can ask what variables in themodel vary with the initial growth rate and howthese variables might be used to infer the exist-ing extent of built-up knowledge. Theory sug-gests that two variables in the old economy areparticularly relevant: the speed of the diffusionof technologies and the life cycle of the relevantproductive units (plants or business organiza-tions).

In our model, the speed of diffusion of tech-nologies in the old economy, before the transi-tion even begins, increases with the initialgrowth rate. For example, in our model, in theold economy, technologies take 72 years to dif-fuse to 50 percent if the initial growth rate is 1.5percent, but only 21 years if the initial growthrate is 3.5 percent. In our Second IndustrialRevolution experiment, the growth rate in theold economy is 1.6 percent, and in that oldeconomy, technologies take 67 years to diffuseto 50 percent. This slow diffusion of steam isconsistent with the work of Atack, Bateman,and Weiss (1980), who suggest that steam tookroughly 70 years to diffuse to 50 percent. In thecontext of our model, this slow diffusion im-plies that agents had built up a large stock of


knowledge about old technologies before theSecond Industrial Revolution.

In our model, the life cycle of productiveunits in the old economy also varies with theinitial growth rate. As the growth rate in the oldeconomy increases, the fraction of the laborforce employed in productive units with oldertechnologies shrinks and the fraction employedin those with the newest technology increases.For example, in our simulations underlying Fig-ure 8, in the old economy, when the initialgrowth rate is 1.5 percent, over 98 percent of thelabor force is employed in productive units atleast 25 years old and only 0.02 percent in thoseusing the newest technologies. In contrast,when the initial growth rate is 3.5 percent, 45percent of the labor force is employed in pro-ductive units at least 25 years old and 2.8 per-cent in those using the newest technologies. (Interms of entry and exit, note that the fractionemployed with the newest technology is theemployment-weighted rate, which, at leastalong a balanced growth path, is also the em-ployment-weighted exit rate.)

In our second learning experiment, we foundthat our model could generate a slow transitionstarting from a high initial growth rate, if learn-ing is much more substantial and protracted

than we found for US manufacturing plants. Togive a feel for the implications of the learningprocess we discussed above (where we in-creased the mean of these shocks by �0.1133), in Figure 9 we show the distribution ofemployment across productive units of differentages implied by the model at the start of thattransition, along with the actual data for USmanufacturing plants. We see in this figure that,in the model, employment is concentrated inproductive units using very old technologies.Here, over 50 percent of employment is in pro-ductive units that use technologies that are atleast 67 years old. This is clearly not consistentwith the learning process measured at US plantsin 1988. Moreover, the model’s relatively moresubstantial and protracted learning process im-plies a very slow diffusion rate of new technol-ogies: it takes 67 years for a new technology todiffuse to 50 percent.

These results indicate a final lesson from ourmodel. The transition to a new economy afterthe Second Industrial Revolution can legiti-mately be viewed as a paradigm for the transi-tion after the IT Revolution only if, before therevolution, organizations had substantially morebuilt-up knowledge about business practicesthan manufacturing plants had about production

Age of plants or organizations in years

0

20

40

60

80

100

120

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

%Data: US manufacturing plants

Model: Organizations withmore substantial learning

FIGURE 9. THE DISTRIBUTION OF EMPLOYMENT WITH MORE SUBSTANTIAL LEARNING

(Cumulative distribution of employment by age of plants or organizations: Modelspredicted for organizations with substantial and protracted learning versus actual data

for US manufacturing plants in 1988)

Source: US Census Bureau 1988 Longitudinal Research Database.


processes in the recent data. That level ofbuilt-up knowledge would correspond to a lifecycle of business practices much longer than thelife cycle of US manufacturing plants.

V. Conclusion

Many historians and economists view the pe-riod after the Second Industrial Revolution as aparadigmatic example of a slow transition to anew economy after a technological revolution.We have presented a quantitative model of thattransition, which generates what many see asthe three main features of that paradigm: a pro-ductivity paradox, a slow diffusion of old tech-nologies, and ongoing investment in oldtechnologies after the revolution. We find thattwo characteristics of the model are particularlyimportant in generating this result: learningmust be substantial and protracted, and built-upknowledge in the old economy must be large.We use data on the life cycle of US manufac-turing plants to argue that learning about plant-specific technologies is indeed substantial andprotracted. And we point to the slow diffusionof steam before the Second Industrial Revolu-tion as indirect evidence consistent with thehistorians’ claim that manufacturers had builtup a large stock of knowledge with existingtechnologies before that revolution.

The paradigm may not fit all transitions, how-ever. We are not able to apply the model in thesame way to the effects of the more recent ITRevolution because of the lack of data needed tomeasure learning and built-up knowledge inbusiness organizations, the type of productiveunit that faced the choice of adopting the newtechnology. But our model has provided someinsight into how the recent transition may differfrom that after the Second Industrial Revolu-tion. Our experiments suggest that a transitionto a new economy after a major, sustained in-crease in the pace of technical change will notalways be slow, as it was after the SecondIndustrial Revolution. The speed of the transi-tion will depend on the existing pace of techni-cal change. When that pace is quite fast, thetransition will be also.

Clearly, then, no simple analogy exists be-tween the transition after the Second IndustrialRevolution and the transition that we shouldexpect after the IT Revolution. Instead, the main

lesson from this analysis is that the nature of thetransition after any technological revolution de-pends in an important way on its historicalcontext. The Second Industrial Revolution hap-pened to come at a time when the pace ofembodied technical change was relatively slow.

Of course, before any definitive analysis ofthe impact of the IT Revolution can be fleshedout in a quantitative model such as ours, somequestions must be answered. Where are the newtechnologies embodied? How long is the periodof learning after they are adopted? And howmuch built-up knowledge do existing organiza-tions have with their current technologies? (Fordiscussion of these questions, see the work ofBrynjolfsson and Hitt 2000.) With regard toinformation technologies, questions like theseare not easy to answer quantitatively, but wehave suggested how theory can be used to guidethe search for these answers.

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