The Evolution of Markets and the Revolution of Industry

Transcription

1 The Evolution of Markets and the Revolution of Industry Klaus Desmet Universidad Carlos III and CEPR Stephen L. Parente University of Illinois and CRENoS April 2008 Preliminary and Incomplete Abstract Why did the Industrial Revolution start sometime in the 18th century in England and not earlier and in some other country? This paper argues that the key to the start of the Industrial Revolution was the expansion and integration of markets that preceded it. Due to less regulation, increasing population, and declining trade costs, markets in England came to support an increasing variety of goods. As such, the demand became more elastic and competition intensi ed. This increased the bene ts to process innovation. Sometime in the 18th century, these bene ts became su ciently large for rms to cover the xed costs of innovation, giving rise to the Industrial Revolution. We illustrate this mechanism in a model with endogenous innovation and population and show that it generates a transition from a Malthusian era to a Modern Economic Growth era as well as a demographic transition and a structural transformation. We provide empirical support for our theory by documenting the evolution in markets in England prior to the Industrial Revolution and by documenting that markets at the start of the 18th century were more developed in England than in the rest of the world. JEL Classi cation: 014, N Keywords: Industrial Revolution, Innovation, Competition, Market Revolution Desmet: Department of Economics, Universidad Carlos III. klaus:desmet@uc3m:es; Parente: Department of Economics, University of Illinois at Urbana-Champaign. parente@uiuc:edu:

2 1 Introduction Sometime in the 18th century, England gradually escaped the Malthusian trap of stagnant living standards as technological progress accelerated and output growth outpaced population growth. One hundred and fty years later, England s transformation from a primarily agrarian society was essentially complete as it emerged as a fully industrialized country with a constant and robust growth rate of per capita output. England is not unique in this experience; although di erent in time and place, other countries have gone through similar revolutions. An important question is why did the world s rst Industrial Revolution have to wait until the 18th century and not occur in some other country? This paper proposes a novel mechanism to explain an economy s transition from a Malthusian era with stagnant living standards, to a modern era, with sustained and regular increases in income per capita, and in doing so provides a novel answer to the question of why England rst. The paper s central hypothesis is that markets need to be su ciently large and competition su ciently strong before an economy can take o. An evolution in markets is thus a precondition for a revolution in industry. In particular, a gradual increase in market size during the Malthusian era, associated with population growth and lower transport costs, spurs greater competition, and sets the industrial revolution in motion, allowing the economy to move from low to high growth. Markets need to be large enough and competition intense enough, or rms will not nd it pro table to innovate. The mechanism from market size and competition to innovation works as follows. A larger market allows an economy to sustain a greater variety of goods and services, making them more substitutable. As a result, price elasticities of demand increase, and mark-ups drop. These changes raise the return to innovation. With a drop mark-ups, rms must sell more units of output in order to break even. Larger rms can cover the xed cost of innovation more easily. Therefore, only after the market reaches a critical size and competition is strong enough, will innovation endogenously take o. The mechanism we highlight is a natural artifact of the address model construct of 1

3 Hotelling (1929) modi ed by Lancaster (1979). With such preferences, each household has an ideal variety that corresponds to its location on the unit circle. As shown by Helpman and Krugman (1985) and Hummels and Lugovskyy (2005), when the population increases, more varieties enter the market. As goods ll up the circle, neighboring varieties become closer substitutes, so that the price elasticity of demand increases and mark-ups fall. Desmet and Parente (2007) exploit this feature and show in a one-period model how the higher elasticity of demand, whether due to a larger population or more liberalized trade, raises the return to process innovation, thereby leading to a larger increase in productivity. 1 The Hotelling-Lancaster construct naturally gives rise to a transition from stagnation to modern growth. As long as market size experiences some minimal growth during the Malthusian phase, the economy will eventually reach a point where innovation will start. As this further expands the market, it adds to the incentives for rms to innovate. This leads to an acceleration in technological change and growth during the industrial revolution. Eventually, the growth rate stops increasing and levels o, in part because the price elasticity of demand increases at a decreasing rate with the population. Our model not only gives rise to a transition from stagnation to modern growth, but also to a structural transformation. In addition to an industrial sector that produces di erentiated goods, our model includes and agricultural sector that produces a subsistence good. This captures the idea that agents need a minimum amount of food to survive. This is a standard way of introducing nonhomotheticities in preferences, implying that as consumers become richer, they dedicate a decreasing share of their incomes to food consumption (Galor and Weil, 2000; Caselli and Coleman, 2001). As economic growth takes o, this leads to a structural transformation, with the share of labor employed in agriculture falling in favor of industry. 1 This mechanism is by construction absent with Spence-Dixit-Stiglitz preferences, since its constant elasticity feature precludes a link between market size, elasticity and innovation. This key di erence is not only theoretically relevant, it is also empirically important. There is ample evidence of a positive relation between market size and demand elasticity. This empirical regularity is present whether markets expand because of population growth (Campbell and Hopenhayn, 2005) or because of trade liberalization (Tybout, 2003; Hummels and Klenow, 2005). 2

4 By endogenizing the fertility decision, our model also captures the demographic transition. There is no quality decision, however, and so the demographic transition does not involve any human capital. 2 Instead, it is a compositional e ect, due to people moving from the farm to the city, where they face higher costs of raising kids, on account of children being more likely to be involved in home production on a farm than in a factory (Rosenzweig and Evensen, 1977; Hansen and Prescott, 2002). 3 Although higher income raises the demand for children through the preference structure, it also increases the fraction of the population residing in the city, thus lowering the overall demand for kids because of the higher child rearing cost. If this second e ect dominates at higher levels of income, a demographic transition occurs, with higher income reducing population growth. Our paper is part of an emerging literature known as uni ed growth theory that attempts to model the transition from Malthusian stagnation to modern economic growth within a single framework. Important contributions include, amongst others, Kremer (1993), Goodfriend and McDermott (1998), Jones (2001), Galor and Weil (2000), Lucas (2001), Hansen and Prescott (2002), and Voigtlander and Voth (2006). Clearly, the main di erence with our work lies in the novelty of the mechanism we emphasize. For example, whereas Hansen and Prescott (2002) is based on exogenous technological progress, Galor and Weil (2000) relies on increasing returns and externalities associated with human capital production to generate the industrial revolution. Our model, instead, focuses on the link between market size, competition and innovation. In light of the existing empirical evidence, our framework presents a number of advantages over these other theories and models. Voth (2003), for instance, has criticized part of the uni ed growth literature for relying exclusively on a positive link between population size and innovation, as this relation is empirically elusive. He argues that 2 For this reason, our theory avoids the criticism of human capital stories of the industrial revolution made. In particular, Mokyr (2006) and Feinstein (1988) provide evidence that suggest that human capital was not an important factor in the early phase of England s Industrial Revolution. 3 In fact, the laws restricting child labor in 19th century England applied only to factory work, and explicitly excluded farm work (Doepke and Zilibotti, 2005). 3

5 the broader concept of market size is more appropriate, because at the end of the 18th century England was more populous than equally wealthy Holland, and much richer than more populous France. Our model addresses this criticism, since the relevant variable for take-o is the size of the market, and not population per se. While it is certainly true that a country s overall population is a critical determinant of the size of its market and the intensity of competition, other factors matter as well. For example, lower transportation costs and trade barriers, higher per capita income, higher agricultural TFP, and more urbanization all increase market size, and thus imply an earlier take-o date. 4 Needless to say, regulation and institutions also matter, as they a ect the xed cost of innovating. We show via a series of numerical experiments how these di erent factors a ect the timing of an economy s industrial revolution. The rest of the paper is organized as follows. Section 2 describes the model. Section 3 investigates the equilibrium properties of the model. It shows how di erent factors, such as agricultural TFP, population, income per capita and regulation, a ect the timing of an economy s industrial revolution, structural transformation and demographic transition. Section 4 provides empirical support for the theory by documenting the evolution of markets in England and the United States preceding their respective industrial revolutions. Additionally, we provide evidence that suggests that markets were larger and competition was tougher in England at the start of the 18th century, compared to France, Western Europe, and China. Section 5 concludes the paper. 2 The Model In this section we describe the structure of the model economy. Time is discrete and in - nite. There are three sectors: an agricultural sector, an industrial sector, and a household sector. The agricultural sector is perfectly competitive and produces a single non-storable 4 Simon (1977) and Kremer (1999) have emphasized the importance of population growth for development, whereas Williamson and O Rourke (2005) and O Rourke and Findlay (2007) have been at the forefront of the camp that stresses the role of international trade. Schultz (1971), and more recently Diamond (2007), have argued that an agricultural revolution is a precondition for an industrial revolution. 4

6 consumption good. The production function in that sector uses labor and land, and technological change is exogenous. The industrial sector is monopolistically competitive and employs labor to produce a nite set of di erentiated goods, each of which has a unique address on the unit circle. There is both product and process innovation in the industrial sector. The household sector consists of a of one-period lived agents, uniformly distributed around the unit circle. Each agent s location on the circle corresponds to his preferred variety of the industrial good. Households supply their labor to industrial and agricultural rms. They use their income to buy agricultural and industrial goods, and to rear children. Agents chose the number of children, who then constitute the household sector in the next period. In what follows we describe the economy in detail. 2.1 Household Sector At the beginning of period t there is measure N t of households, uniformly distributed around the unit circle. Households live for a single period. Endowments. Each household is endowed with one unit of time, which it uses to work in either the agricultural or the industrial sector, and to rear children. Households are free to work in either sector. Denote by N at and N vt the measure of adults employed in agriculture and industry. The cost of child rearing depends on the sector that employs a household. Let a and x denote the time cost per child for an adult employed in, respectively, the agricultural and the industrial sector. As argued before, it is reasonable to assume that child rearing is cheaper on the farm than in the city, and we thus set x a. Preferences. A household derives utility from children, n t, consumption of the agricultural good, c at, and consumption of the di erentiated industrial goods, fc vt g, where v indexes the variety of the industrial good belonging to the set V t. There is a subsistence level of agricultural consumption c a 0, such that the household s utility depends on the amount by which c at exceeds the subsistence quantity. Preferences are Cobb-Douglas between agricultural goods, industrial goods and 5

7 children. Within the set of industrial goods preferences are based on Lancaster s (1979) model of ideal varieties. A household s location on the unit circle corresponds to its ideal variety, the one it prefers over all others. The further away a particular variety v lies from a household s ideal variety ~v, the lower the utility derived from consuming a unit of variety v. The utility of a household located at point ~v on the unit circle is then U = [(c at c a ) 1 [g(c vt jv 2 V t )] ] (n t ) 1 (1) The subutility function g(c vt jv 2 V ) is c vt g(c vt jv 2 V ) = max[ v2v t 1 + d ] (2) v;~v where d v~v denotes the shortest arc distance between variety v and the household s ideal variety ~v. The term 1 + d v~v is known as Lancaster s compensation function, and can be interpreted as the quantity of variety v that gives the household the same utility as one unit of its ideal variety ~v. The parameter > 0 determines how fast a household s utility diminishes with the distance from its ideal variety. 2.2 Agricultural Sector The agricultural sector is perfectly competitive. It produces a single, non-storeable consumption good via a constant returns to scale technology, with labor and land as the only inputs. The supply of land is xed and normalized to 1. For convenience, we assume that land rents are equally distributed amongst the entire population N t. Let Q at denote the quantity of agricultural output and let L at denote the corresponding agricultural labor input. Then Q at = A at L at 1 > 0 (3) In the above equation, A at is agricultural TFP, which grows exogenously at a rate a Industrial Sector The industrial sector is monopolistically competitive, and produces a set of di erentiated goods, each one of which has a unique address on the unit circle. The technology for producing these goods uses labor as its only input. The existence of a xed cost, which 6

8 takes the form of labor, gives rise to increasing returns. Since the xed cost is not a sunk cost, there is free entry and exit of rms. Additionally, as in Lancaster (1979), rms can costlessly relocate on the circle. Production. Denote Q vt the quantity of variety v produced by a rm, L vt the units of labor it employs, A vt the technology level, or production process, and vt its xed cost. Then the output in period t of the rm producing variety v is Q vt = A vt [L vt vt ] (4) Innovation. Let A xt denote the average level of technology in the industrial sector at the end of period t 1, so that A xt = X v2v 1 n t 1 A v;t 1 (5) where n t 1 is the total number of rms in period t 1. At the beginning of period t, a rm chooses between using the average technology level of the industrial sector in period t 1, A xt, or to allocate some labor to R&D activities in order to improve upon this technology. The upgrade over the previous period s technology level is an increasing function of the amount of labor the rm allocates to R&D. Let G vt denote the factor increase over the previous period s average technology by the rm producing variety v. Thus, A vt = G vt A xt (6) Fixed costs. The xed cost, vt, in equation (4) contains an R&D component as well as an overhead component associated with operating a rm. Thus, even if a rm allocates no labor to innovation, it still incurs a xed cost. In particular, the xed cost of a rm in period t producing variety v and innovating by factor G vt is vt = e [(G vt (1+t[ A xt A x0 1]) 1] ; where > 0; t 2 [0; 1]; and > 0 (7) The above equation, while involved, encompasses a wide range of possibilities. The critical parameter in this equation is t, which indicates the strength of intertemporal spillovers. 7

9 To illustrate the implications of the above equation, consider the extreme values for t. When t = 0, intertemporal spillovers are complete, and the xed cost simpli es to e (Gvt 1). In this case, the component of the xed cost associated with operating a rm is in each period. In addition, the xed cost of innovating by a given factor G is also independent of the time period. As the economy s technology improves over time, innovating does not become more costly. When = 1, intertemporal spillovers are absent, and the expression simpli es to e [(Gvt A xt A x0 of the xed cost associated with production is e [ A xt A x0 1]. In this case, both the component 1], and the xed cost of innovating by a given factor G, are increasing functions of the industry s average technology level. Values for t strictly between 0 and 1 represent intermediate cases where spillovers are incomplete. Note that we index the spillover parameter,, with a time subscript t so as to allow for exogenous changes in the degree of intertemporal knowledge spillovers. For example, if the education system improves over time, facilitating the intertemporal transfer of knowledge, t would become smaller as time progresses. In what follows we assume that spillovers t = (t s)+1 0, where 0 2 [0; 1], > 0, and s is the rst period in which G s > Household Demand Individual household s demand. We start the analysis by deriving an individual household s demand for the agricultural good, for the industrial goods, and for children. The numéraire for the economy is the agricultural good. The di erential cost of rearing children in the city and on the farm implies that the wage rates in the two sectors will be di erent. We therefore distinguish between the agricultural wage, w at, and the industrial wage, w xt. In addition to labor income, each household receives an equal share of the land rents, r t =N t. Let p vt denote the price of variety v 2 V. Then the budget constraint of the household working in sector i 2 fa; xg is w it (1 i n t ) + r Z t = c at + p vt c vt dv (8) N t v2v 8

10 Maximizing (1) subject to (8) yields the following rst order necessary conditions: Z v2v c at = (1 )(w it + r t N t c a ) + c a (9) p vt c vt dv = (w it + r t N t c a ) (10) n t i = (1 )(1 + 1 w it ( r t N t c a )) (11) We make assumptions on the values of inital agricultural TFP, A a0, and the initial average industrial technology, A x0, that ensure that w it + r t =N t > c a for all t 0. The subutility function given by equation (2) implies that each agent consumes a single industrial variety. The variety v 0 that an agent located at ~v buys is the one that minimizes the cost of an equivalent unit of the agent s ideal variety, p vt (1 + d v~v ), so that v 0 = argmin[p vt (1 + d v;~v )jv 2 V ] Using (10), a household located at ~v therefore buys the following quantity of variety v 0 : c v 0 t = (w it + rt N t c a ) p v 0 t (12) Household aggregation. We next determine the aggregate demand for each industrial good, the agricultural goods, and kids. Industrial goods To derive the aggregate demand for an industrial good, we limit our attention to the case of a symmetric equilibrium, where rms are equally spaced around the unit circle, use the same technology, and choose the same price and quantities. Let N at and N xt denote the measure of households that work in the agricultural and industrial sectors. Without loss of generality, we assume that each measure of households is uniformly distributed around the unit circle. Denote by d t the distance between two neighboring varieties in period t, so that d t = 1 (13) n t Given the uniform distribution of both types of households on the unit circle, it follows that d t N at +d t N xt agents consume variety v. As each household spends a fraction 9

11 of their income, net of the subsistence term, on the variety nearest to it, the aggregate demand for a given variety v is Q vt = d t(n vt w vt + N at w at + r t N t c a ) p vt (14) Agricultural good Similarly, aggregate demand for the agricultural good is Q at = (1 )(w at N at + w vt N vt + r t N t c a ) + N t c a (15) Children and population Aggregating the demand for children over households yields the law of motion for the population: N t+1 = (1 )( N at a (1 + 1 w at ( r t N t c a )) + N vt v (1 + 1 w vt ( r t N t c a ))) (16) 2.5 Agricultural Supply The pro t maximizing problems of farms is straightforward, as they are price takers. The rst order condition implies that the agricultural wage rate is w at = A at (L at ) 1 (17) and land rents are r t = (1 )A at (L at ) (18) 2.6 Industrial Supply The xed labor cost implies that each variety, regardless of the technology used, will be produced by a single rm. In maximizing its pro ts, each rm behaves non-cooperatively, taking the choices of other rms as given. Each rm chooses the price and quantity of its good to be sold, the number of workers to hire, and the technology to be operated. As is 10

12 standard in models of monopolistic competition, rms take all aggregate variables in the economy as given. An industrial rm s pro ts can be written as vt = p vt Q vt w xt [e [(G Ax vt (1+t[ 1]) 1] Q A vt x0 + ] (19) A xt G vt where w xt is the wage in the industrial sector. A rm chooses (p vt ; G vt ) to maximize the above equation, subject to aggregate demand (14). The pro t maximizing price is a markup over the marginal unit cost w t =(A xt G vt ), so that p vt = w vt A xt G vt " vt " vt 1 (20) where " vt is the price elasticity of demand for variety v: " vt vt Following the same procedure as in Hummels and Lugovskky (2005), it is easily shown p vt Q vt that in a symmetric equilibrium the elasticity is the same across all varieties: " vt = " t = ( 2 d t ) (21) The rst order necessary condition associated with the choice of technology, G vt, is e [Gvt(1+t[ A xt A x0 1]) 1] + Q vt A xt G vt 2 0 (22) where the inequality in the above expression corresponds to a corner solution, i.e., G t = 1. Equations (20), (21) and (22) are the key to understanding the model s results and the importance of the address construct. From equation (21) it is apparent that as the number of varieties increases, and the distance between rms decreases, the price elasticity of demand increases. With rms being closer, a percentage decrease in the price of one rm s variety can capture more customers away from its nearest competitors because customers are closer to it. Or alternatively, with a more crowded product space, a consumer located at position v e ectively has more goods to choose from, and hence goods become more substitutable. This leads to greater competition. From equation (20), 11

13 it follows that an increase the price elasticity of demand brings about a smaller markup. This implies that the size of rms (in terms of production) must increase. Given the same xed cost, a rm must sell a greater quantity of units in order to break even. Larger rms nd it easier to bear the xed costs of R&D, leading to more innovation. This can be seen in equation (22). 2.7 Symmetric Equilibrium Free entry and exit gives us a zero pro t condition, which for the case of symmetric rms can be written as Ax [Gvt(1+t[ 1]) 1] Q vt = e A x0 Axt G vt (" t 1) (23) Each rm therefore employs L vt = e [Gvt(1+t[ A xt A x0 1]) 1] "t (24) The labor market clearing condition in the industrial sector is then N vt = 1 d t [e [Gvt(1+t[ A st A x0 1]) 1] "t ] (25) The labor market condition in the agricultural sector is The overall labor market clearing condition says that L at = N at (26) N t = N at + N vt (27) Since workers can freely move across sectors, in equilibrium their utilities should be the same: u at = u vt (28) This condition determines the number of agents in the two sectors, N vt and N at. We are now ready to de ne the Symmetric Equilibrium. De nition of Symmetric Equilibrium. A Symmetric Equilibrium is a vector of elements (Q at, Q vt, w at, w vt, r t, N t, N at, N vt, p vt, n t, d t, " t, A xt ; A vt ; and G vt ) that satis es (5), (6), (13), (14), (15), (16), (17), (18), (20), (21), (22, (23), (25), (26), (27) and (28). 12

14 3 Numerical Results We now analyze the equilibrium properties of the model numerically. We begin by examining whether the model generates a pattern that is roughly consistent with the transition from Malthusian to modern growth. Subsequently, we analyze how various factors or parameters within the model a ect the timing of the industrial revolution. While there are many model parameters that we could analyze, we focus on those for which there is good a priori reason to believe they are potentially important in understanding the timing of the industrial revolution. Those parameters are the initial population, agricultural TFP and its growth rate, the xed cost of operating a rm, and the cost of innovation. Towards this goal, it is instructive to brie y review the pattern of long-run development. Based on the estimates by Maddison (2008), Table 1 reports the growth rates of GDP per capita and of population between 1500 and 2000 for the United Kingdom and Western Europe. In the last decade, many economic historians have challenged the hypothesis that living standards were stagnant before the industrial revolution. Maddison s estimates re ect this new view. As can be seen, the UK living standard rose between 1500 and 1700 at a rate of 0.28 percent per year. Although between 1700 and 1820 the growth rate of GDP per capita did not accelerate, the growth rate of population did. While between 1500 and 1700 the population grew at an annual rate of 0.39 percent, during the 18th century the growth rate averaged 0.76 percent. Between 1820 and 1880 growth in income per capita accelerated signi cantly, averaging 1.19 percent annually, and the population also grew faster. During the 20th century growth in living standards continued to increase, while population growth dropped, due to the demographic transition. Between 1940 and 2000 income per capita grew at an annual rate of 1.81 percent, whereas population only increased at an average rate of 0.35 percent, similar to pre-industrial revolution gures. Both Western Europe and the United States have gone through the same stages of development as the United Kingdom. Taking all factors in consideration, we see the long-run pattern of development to be characterized by an initial era of very low growth 13

15 in the living standard and the population. This is followed by an industrial revolution with a higher and accelerating growth rate of per capita GDP, and with a rising and then falling growth rate of the population. The nal era is characterized by a high rate of growth of per capita GDP and a lower growth of the population. Table 1: England, Western Europe and the United States, Country GDP per capita England 0.28% 0.26% 1.19% 1.14% 1.81% Western Europe 0.13% 0.16% 1.03% 1.30% 2.35% United States 0.73% 1.56% 1.32% 2.36% Population England 0.39% 0.76% 0.82% 0.55% 0.35% Western Europe 0.18% 0.43% 0.71% 0.59% 0.45% United States 1.94% 2.74% 1.62% 1.27% 3.1 Benchmark Model We now parametrize the model and compute the equilibrium path to see if it gives rise to a development and growth pattern similar to the one documented above. In particular, we seek to examine if the model is capable of generating three distinct phases in longrun development: a Malthusian period, with rising population and very slowly increasing living standards; followed by an industrial revolution with still low, but accelerating rates of economic growth, and increasing population growth; culminating in a modern era, with higher but constant GDP per capita growth, and falling rates of population growth. Table 2: Parameter values = 0:6 0 = 0:15 = 4:5 = 0:35 = 0:895 = 0:905 A a0 = 1 A 0 = 1 = 1 a = 0:005 a = 0:045 v = 0:17 c a = 0:235 = 0:0075 N 0 = 20 The parameter values used in the benchmark experiment are given in Table 2. Although this parametrization does not follow a precise calibration procedure, it is still 14

16 useful to motivate our choices. The cost of raising kids as a share of income in the city, v, has been set to 0.17, in line with estimates by Knowles (1999) and Haveman and Wolfe (1995). Since kids on the farm are more likely to contribute to production, we set the equivalent cost in the agricultural sector, a, to a lower number, The exponent on kids in the utility function, 1, has been chosen to generate a population growth rate consistent with the empirical evidence. The share of spending on industrial goods,, has been set to 0.905, empirically a reasonable number. The subsistence constraint on agricultural goods, c a, is chosen so that it is never binding. The parameter value determines the slope of the decrease in utility as a household consumes a variety farther away from its ideal variety. Its precise value is of limited importance. The exogenous TFP growth in agriculture, a, is set to 0.005, so that we get very slow growth in the Malthusian phase. The other parameters values,,, 0 and, refer to the production function in the industrial sector. They are set, so that the model generates a long run pattern of productivity growth consistent with observation. Of particular interest are the values of 0 and, which imply an increasing degree of intertemporal spillovers over time. This captures the idea that, through the improvement of formal education and on-the-job training, the transfer of knowledge has become easier over time. To simplify the analysis, in our benchmark case we assume a constant marginal product of labor in agriculture, and thus eliminate land from the analysis, so that = 1. Figure 1 plots technological progress in the industrial sector over time. As can be seen, prior to the 67 th period, there was no technological progress in the industrial sector. The reason for this is the lack of demand for industrial products, due to both the agricultural subsistence constraint and the small population size. More speci cally, if the market for industrial goods is small, the economy can only support a limited number of varieties, so that the substitutability between them is small, the price elasticity of demand is low, and the markups are high. This implies that rms are relatively small in equilibrium, so that they are unable to spread the xed innovation costs over a large enough customer base. However, since population and income per capita grow gradually over time, at some point the size of the industrial market becomes su ciently large for 15

17 innovation to endogenously take o. This happens in period 67. After that, technological progress continues to grow over time, before peaking at around 2.1 percent. The exact shape of the path of technological progress depends on a number of forces, in particular, the rate of population growth, the degree of intertemporal spillovers, and the responsiveness of the price elasticity of demand to increases in the size of the industrial market. Once technological progress takes o, population growth accelerates, at least initially, and income per capita growth increases. Both e ects give further incentives for rms to innovate. Technological progress accelerates because of the self-reinforcing nature of it: the size of the market increases innovation, and innovation increases the size of the market. The eventual slowdown in technological progress occurs because the demographic transition slows down population growth and because the responsiveness of the demand elasticity decreases as the market becomes larger. However, if intertemporal knowledge spillovers become greater over time, this slowdown is mitigated, and the rate of technological progress remains close to constant. 2.5% Technological Progress Industry 2.0% Annual Growth Rate 1.5% 1.0% 0.5% 0.0% 0.5% Period Figure 1: Technological Progess Industry The model generates a pattern for GDP per capita that is consistent with the historical record. Figure 2 shows how in the period leading up to the industrial revolution 16

18 Growth GDP per capita 2.5% 2.0% Annual Growth Rate 1.5% 1.0% 0.5% 0.0% Period Figure 2: Growth GDP per capita Agricultural Employment Share 39.0% 37.0% 35.0% Agricultural Share 33.0% 31.0% 29.0% 27.0% 25.0% Period Figure 3: Agricultural Employment Share 17

19 per capita GDP increases, albeit at the low rate of around 0.10 percent per period. There is positive growth prior to the industrial revolution for two reasons. First, there is exogenous technological change in agriculture. Second, with the increase in population, the average cost of industrial goods falls. With the start of the revolution, technological progress takes o in the industrial revolution, leading to accelerating GDP per capita growth, before reaching a maximum of roughly 2 percent in period 150. Thereafter, the growth rate remains essentially constant. The growth path in Figure 2 closely resembles that of technological progress in Figure 1, and therefore, its exact shape depends on the same forces that determine innovation. The pattern of structural change is also largely in line with empirical evidence. Because of the subsistence constraint, the increase in GDP per capita leads to a relative decrease in the demand for agricultural goods. Figure 4 shows how the share of labor employed in agriculture steadily declines. As can be seen, the structural transformation starts prior to the start of the industrial revolution, because there is already some growth in GDP per capita during the Malthusian era. Although the magnitude is somewhat o, this is consistent with the historical record of England, where according to Allen (2000), the agricultural population decreased from 94 percent in 1300 to 84 percent in Note furthermore that the structural transformation slows over time. This is to be expected: the higher is income per capita, the closer preferences are to being homothetic. The model also gives rise to a demographic transition that is qualitatively consistent with the historical record. Figure 4 depicts the population growth rate over the rst 200 periods. It starts out very low and then increases, until reaching a peak prior to the start of the modern growth era. After that, it gradually decreases over the remainder of the time horizon. Population dynamics are the result of two opposing forces. On the one hand, the increase in GDP per capita increases the demand for children. On the other hand, the move of people from the farm to the city, decreases the overall demand for children, as the time cost of child rearing is higher in the city. For the rst 100 periods, the rst e ect dominates, in part because the subsistence constraint is more binding when the living standard is low. In this respect, our model economy resembles Galor and 18

20 Population Growth 1.4% 1.2% 1.0% Annual Growth Rate 0.8% 0.6% 0.4% 0.2% 0.0% Period Figure 4: Population Growth Weil (2000). After period 100, the second e ect dominates and the population growth decreases. 3.2 Population We now explore how various parameters in the model a ect the timing of the industrial revolution. We begin by considering the initial population of the economy. Before doing so, we emphasize that a country s population is not necessarily a good measure of its market size. 5 More speci cally, the real world counterpart of population in the model is the number of people that can access a market. Clearly trade and transportation costs a ect this. Although not included in our model, it is easy to show that lower transportation costs or lower trade barriers have the same e ect on innovation as an increase in the population. 6 5 Voth (2003) is critical of uni ed growth models that rely exclusively on population size to generate the industrial revolution, and argues that historical evidence points to market size being a more relevant factor. 6 In Desmet and Parente (2007) we explore the e ects of the reduction in trade barriers and the improvement in transportation infrastructure on innovation in a static model with Hotelling-Lancaster 19

21 Industrial Revolution and Population Size 2.5% 2.0% Annual Growth Rate 1.5% 1.0% 0.5% Technological Progress, N=20 Technological Progress, N=25 0.0% 0.5% Period Figure 5: Industrial Revolution and Population Size In this experiment we increase the initial population, N 0, by 25 percent. The e ect of this change on technological progress is depicted in Figure 5. As can be seen, a larger population hastens the start of the industrial revolution by about 20 years. The reason for this is straightforward. Since a larger population supports a greater variety of goods, the distance between neighboring varieties is smaller. As a result, the price elasticity of demand rises, and rm size increases. This makes it easier for rms to bear the xed costs of innovation, and hence technological progress takes o earlier. 3.3 Institutions We next explore how the timing of the industrial revolution depends on the xed costs in the model. In the real world, the xed costs rms incur to operate and to innovate depend to a large extent on institutions and policy. We therefore interpret changes in the parameters that lower this xed cost to re ect better institutions and policies. In our model, the xed cost is made up of two parameters,, which determines the xed cost of operating the benchmark technology, and, which determines how much preferences. Not surprisingly, we nd that freer trade and lower transport costs have the same positive e ects on innovation as an increase in population size. 20

22 Industrial Revolution and Institutions 2.5% 2.0% Annual Growth Rate 1.5% 1.0% 0.5% Technological Progress, kappa=0.35 Technological Progress, kappa= % 0.5% Period Figure 6: Industrial Revolution and Institutions: E ect of lower kappa 2.5% Industrial Revolution and Institutions II 2.0% Annual Growth Rate 1.5% 1.0% 0.5% Technological Progress, phi=4.5 Technological Progress, phi= % 0.5% Period Figure 7: Industrial Revolution and Institutions: E ect of lower phi 21

23 the xed cost increases when adopting better technologies. Decreases in and should have similar e ects. Figure 6 shows that if we decrease from 0.35 to 0.25, the industrial revolution starts 30 years earlier, in period 37 instead of 67. Figure 7 shows how a drop in from 4.5 to 4 speeds up the industrial revolution by about 20 years. 2.5% Industrial Revolution and GDP per capita 2.0% Annual Growth Rate 1.5% 1.0% 0.5% Technological Progress, A0=1 Technological Progress, A0= % 0.5% Period Figure 8: Industrial Revolution and GDP per capita 3.4 Agricultural Revolution Some authors, such as Schultz (1971) and Diamond (1997), have argued that an agricultural revolution is a precondition for an industrial revolution. Figure 8 shows that if we increase initial agricultural TFP by 10%, the industrial revolution starts 15 years earlier, in period 52 instead of 67. Note that as long as agricultural labor productivity does not exhibit decreasing returns, changing agricultural TFP only a ects the timing of the industrial revolution, and never the fact that it eventually occurs. However, if we set < 1, so that the marginal product of labor is decreasing, it is possible for the industrial revolution never to occur. In particular, if in that case we set agricultural TFP growth to zero, population growth peters out over time. If this happens before endogenous innovation in the industrial sector takes o, the economy gets stuck in a Malthusian 22

24 trap. 4 Empirical Support In this section we use the model to interpret the historical experience of various regions and countries to show that our theory provides a reasonable answer to the question of why the Industrial Revolution did not start earlier in history and in some country other than England. Recall that at the core of our theory is the mechanism by which market size a ects competition and innovation. Our theory isolates several variables that determine the size of the market: the size of the population, openness to trade, transport costs, and agricultural TFP. In addition, regulation and barriers to entry directly a ect the returns to innovation. We focus on two aspects of the historical record: the time series and the cross section. The time series evidence concentrates on England, the world s most productive country from 1820 to 1890, and the United States, the world s most productive country since Historians date the start of the industrial revolution around 1750 in England and around 1840 in the United States. In particular, we concentrate on the developments in agriculture, transportation and trade, population and institutions in the periods preceding their respective industrial revolutions. The cross section compares other countries and regions to England along these same dimensions on the eve of England s industrial revolution. 4.1 Time Series England, Between 1300 and 1800 there were important improvements in England s institutions, agriculture, and transportation, in addition to large increases in the number of people living in urban areas. These developments were almost surely related. For instance, Acemoglu et al. (2005) argue that the rise in North Atlantic trade was an important factor shaping institutions in England and other parts of Europe. A key date for improvements in English institutions is the Glorious Revolution of North and Weingast (1989), in particular, have argued that the Glorious Revolution 23

25 was an important development because it made it far more di cult for the crown to expropriate wealth, raise customs and sell monopolies. Ekelund and Tollison (1981) claim that the balance of power brought on by the events of 1688 weakened the e ects of mercantilism, primarily by reducing e ective regulation. In fact, Ekelund and Tolllison characterize the situation in England as one of free trade. There were also large increases in agricultural productivity in England between 1300 and According to Allen (2000, Table 8, p 21), agricultural output per agricultural worker in England was stagnant from 1300 to 1600, but roughly doubled between 1600 and Historians point to a number of factors to explain this, in particular, land enclosure, mechanization, selective breeding and crop rotation. It is generally agreed that each of these developments allowed for a signi cant population increase in England. Land enclosure has also been related to the large increase in the urban population as tenant farmers were evicted. Further contributing to the size of the market, the transportation system in England was improved in the period leading up to the Industrial Revolution. In England, both roads and canals were important. According to Szostak (1991, p. 60), a network of turnpikes was put into place in the rst half of the 18 th century, linking almost every town. The turnpike was a fairly recent development, with the rst one being built in the 17 th century. Turnpike trusts constituted an important institutional change, as they replaced local parishes as the main body responsible for the maintenance of roads. While local parishes relied on property taxes and the requirement of up to six days of unpaid labor by local residents, trust paid for the maintenance by levying tolls and issuing debt. By 1770, turnpikes covered 15,000 miles and non-turnpike roads covered approximately 60,000 miles. In addition to roads, canals were an important means of transporting goods in the period. England was, in fact, blessed with a geographical advantage in this respect. The abundance of natural waterways and the lack of dramatic changes in elevation and seasonal temperatures made water tra c pro table. According to Szostak (1991, p 55), England had 1,100 kilometers of navigable rivers in 1660, rising to 1,900 in 1725, and 24

26 reaching 3,400 by The natural ports, provided by England s coastline, constituted an additional advantage. This contributed to the growth in international trade over the period between 1300 and Acemoglu et al. (2005), for example, show that in the 18 th century there was a roughly 8-fold increase in the number of Atlantic voyages per year. Lastly, there was a large increase in England s urban population between 1400 and In terms of total population, the English population in 1700 stood at approximately the same number as in 1300, as it took 400 years for the total population to recover from the Black Death in 1347 that killed o half of England s population. While population size was approximately the same in 1700 and 300, the distribution of the population across rural and urban areas was radically di erent. In 1300, there were 220,000 people living in urban areas, which represented 4 percent of the population. In 1700, this number was 880,000, representing almost 14 percent of the population. This increase in urbanization occurred before the start of the Industrial Revolution, and is partly attributed to the English Acts of Enclosure, which turned many common parcels of land into private holdings. To understand the Industrial Revolution within the framework of our theory, all of these developments are important. One should therefore not look at each development in isolation. Clark (2005), for instance, has challenged the branch of the literature that favors institutional developments, since the Glorious Revolution occurred 100 years before the Industrial Revolution. However, such a lag may not be surprising. In our theory, the Glorious Revolution contributed to the Industrial Revolution happening earlier than it otherwise would have, without predicting the take-o should happen immediately. Another example of an event that may have a ected the timing of the Industrial Revolution is the Black Death. Without the plague, the revolution would have likely occurred earlier. How much earlier is a di cult question to answer because institutions, openness, and urbanization in England were very di erent in 1300 than in

27 The United States, The industrial revolution in the United States happened later than in England. According to Gallman (2000), there was a marked increase in the growth rate of per capita GDP starting in In particular, income per capita increased at an annual rate of 0.3 percent between 1774 and 1800, 0.9 percent between 1800 and 1834, 1.3 percent between 1834 and 1869, and reaching 2.4 percent between 1869 and There is a vast literature that documents the evolution in US markets from 1750 and Sellers (1991) goes so far as to actually call this a market revolution. 7 An important turning point was the War of 1812 with Britain. Although there were large increases in urban populations before 1812, 8 leading to some degree of specialization, most manufactured goods were still imported. The domestic manufacturing sector was small, and interregional trade was limited, with rural populations manufacturing many of their goods at home. The trade embargo with Britain during the War of 1812 had a short-run impact on industrialization as domestic manufacturers sprung up to supply the local market. Some of those survived after the embargo was lifted. The War of 1812 was also important for the evolution in markets because it was the start of a huge increase in transportation infrastructure. With strong public support, between 1810 and 1820 the number of road miles in New York state alone increased from 1,000 to 4,000, and the cost of transporting goods by roads was cut in half. The expansion in the canal system was even more impressive. The Eerie Canal reduced the price of shipping from $100 a ton to $9 a ton. In this era canals were more important to the integration of markets than roads, as transportation costs by road were still prohibitive for a large class of goods. In addition to the canal miles, improvements in transport technology were important for reducing transportation costs. The steam ship was invented in 1787 by John Filtch and signi cant 7 Howe (2007) believes this is a bit of an overstatement for in his view the integration of markets had been gradually evolving since Philadelphia, which was the largest city in 1790, experienced a 110 percent increase in its population over the next 20 years; New York City experienced an even larger increase, close to 200 percent; and Baltimare grew 156 percent. 26

28 improvements were made in the decades that followed. The e ects were dramatic. For example, according to Howe (2007, p 214), it took 26 days to reach Louisville from New Orleans in By 1825, the trip could be made in 8 days. The transportation revolution resulted in an integration of regional markets, bringing about specializing in agriculture and manufacturing between the urban east and the rural west. Consistent with our theory, rms in urban areas were larger than their rural counterparts and their productivity was higher (Engerman and Sokolo, 2000). Moreover, average size of these rms grew over the period. 4.2 Cross-Section We now present evidence that England on the eve of the Industrial Revolution was far more advanced in the factors identi ed by our theory as being important than other countries and regions. It is certainly true that England had a smaller land mass and smaller total population than many other countries at the beginning of the 18th century. However, as we shall argue, it compensated for this in terms of better transport, better institutions, more open trade, and greater urbanization. These factors meant that markets in England tended to be more national in coverage, whereas markets in the larger nations were much more regional. In fact, as we shall argue, in the case of China, the relevant comparison is not with China as a whole, but with the Jiangsu and Zhejiang regions in the Lower Yangzi Province. France and Western Europe. We begin with evidence in the form of price data from Shiu and Keller (2007) that suggests that markets in England were far more national in nature compared to France, and the rest of Western Europe. Shiue and Keller (2007) compute the variance of grain prices across regions in Europe and China for the 17th, 18th and 19th centuries. They nd that grain prices in the 17th century were far less volatile in England, compared to the rest of Europe and China. By the 19th century, this volatility declined for Europe, but remained more or less the same for China. Why were markets more national in England and more regional in the rest of the world? One reason is that England possessed a much more developed system of roads 27