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Federal Reserve Bank of New York
Staff Reports
Accounting for Breakout in Britain:
The Industrial Revolution through
a Malthusian Lens
Alexander Tepper
Karol Jan Borowiecki
Staff Report No. 639 September 2013
Accounting for Breakout in Britain: The Industrial Revolution through a Malthusian Lens Alexander Tepper and Karol Jan Borowiecki Federal Reserve Bank of New York Staff Reports , no. 639 September 2013 JEL classification: N13, N33, O1, O41, O
Abstract
This paper develops a simple dynamic model to examine the breakout from a Malthusian economy to a modern growth regime. It identifies several factors that determine the fastest rate at which the population can grow without engendering declining living standards; this is termed maximum sustainable population growth. We then apply the framework to Britain and find a dramatic increase in sustainable population growth at the time of the Industrial Revolution, well before the beginning of modern levels of income growth. The main contributions to the British breakout were technological improvements and structural change away from agricultural production, while coal, capital, and trade played a minor role.
Key words: Industrial Revolution, Malthusian dynamics, maximum sustainable population growth, development, demographics
Tepper: Federal Reserve Bank of New York (alexander.tepper@ny.frb.org). Borowiecki: University of Southern Denmark (kjb@sam.sdu.dk). The authors thank Knick Harley, Richard Sylla, Bob Allen, Stephen Broadberry, Greg Clark, Bob Lucas, Matthias Morys, Paul Warde, Jan Luiten van Zanden, Michael Best, Joe Rowsell, Charlie Brendon, Nick Howarth, Nick Juravich, Alan de Bromhead, and Stefan Bache for helpful consultations and insightful comments. The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the authors.
model that accounts for the existence of both Malthusian and growth economies, and allows us to draw clear links between some of the factors cited by economic historians and the beginning of growth. It further provides a framework that permits a quantitative assessment of the relative contributions of those factors.
In this paper, we will define a modern or growth economy as one where technological progress at society’s normal rate implies rising living standards. In a Malthusian economy, technological progress at society’s normal rate implies stagnant living stan- dards. We refer to the transition between these two regimes as “takeoff” or equiva- lently “breakout.” This is a more precise statement of Rostow’s (1960) notion that “the takeoff is the interval when (... ) the forces making for economic progress (... ) expand and come to dominate the society. Growth becomes its normal condition” (p. 7).
There exists a modest literature modeling growth in a unified way, to which the three most prominent contributions are Kremer (1993), Galor and Weil (2000), and Hansen and Prescott (2002). Kremer assumes and empirically tests a simplistic rela- tionship between essentially global population size and the global rate of technolog- ical progress and shows how this relationship enables emergence from a Malthusian trap. Galor and Weil construct a complex model that includes assumptions similar to Kremer’s as well as Beckerian assumptions about child quality-quantity tradeoffs to generate an endogenous demographic transition as societies grow richer. Hansen and Prescott assume exogenous technical progress and fertility decisions but include shifting from a Malthus sector that relies on land for production to a Solow sec- tor that does not. The shift is an equilibrium phenomenon driven by diminishing returns to land as the population grows concurrently with technical progress.
The model developed here shares with those papers an emphasis on a phase change generated by a demographic shift and an increase in sustainable population growth, although this is not their terminology. Sato and Niho (1971) also employ a framework
of sustainable population growth in a two-sector model of emergence from Malthu- sian stagnation in a closed economy, concluding that only technological progress in agriculture leads to breakout. Our model could be viewed as a prequel both to the modern “Unified Growth” literature, which is reviewed by Ashraf and Galor (2011), and to the previous generation of literature of which Sato and Niho is an example.
The model presented here has several advantages over previous attempts to model the transition process. First, it is much simpler and allows easy access to the intu- ition that can be obscured by a more complex model. While Sato and Niho, and Hansen and Prescott require two sectors, which essentially doubles the number of variables, and Galor and Weil employ four simultaneous difference equations, the present model combines one production function and one differential equation gov- erning population growth in a simple, intuitive way. It thus highlights the most important and fundamental dynamics of the transition from a Malthusian regime to a Solovian one, showing that the many assumptions and complexities of the liter- ature are not necessary to generate both a qualitatively and quantitatively correct story. Second, unlike Galor and Weil, and Kremer, this model’s assumptions do not dictate that takeoff can only occur in societies of a certain size or level of technolog- ical advancement. Given that the first takeoff actually did occur in Britain, rather than in much larger France or China, this result is to be viewed as an advantage. Third, in this model, most of the underlying causes of growth are exogenous. We view this as an advantage both because it avoids arbitrary and simplistic assump- tions about social behavior and because many of the important factors for takeoff are driven by processes that are as much political, historical, or social in nature as they are economic. By remaining agnostic about the relationships between the elements of a breakout, the model can accommodate a rich array of development strategies and can apply to a wider range of societies.
to sustain a rise in living standards is robust to a wide variety of estimates for the various components of economic growth. Although the pace of transition varies, the qualitative story stays the same. Finally, along the way to compiling MSPG estimates we come up with new estimates for total factor productivity during the Industrial Revolution. These generally follow Crafts and Harley but employ im- proved estimates of factor shares and natural resource growth. The new estimates point to a somewhat larger role for TFP than the most recent estimates put forth by Crafts and Harley.
The MSPG estimates presented here also carry two further implications that are at variance with the conventional wisdom. First, the effect of trade on the ability of the British economy to transition to modern growth is probably exaggerated. Second, we will see that short- or even medium-term economic growth is a different phenomenon than the ability to sustain a breakout in living standards. If we want to understand the end of the Malthusian era, just asking which factors contributed to growth does not necessarily shed light on this question. Rather, the question we must answer is “What allowed the British economy to transition, possibly fairly abruptly, from a regime where per capita income was trendless to one where it was growing at 1% per year?” The difficult thing to understand is not the “growth” but the “transition.”
Finally, it is important to recognize that this analysis does not purport to investi- gate the ultimate causation of the Industrial Revolution. Rather, it is an accounting exercise in the spirit of Solow, linking the economic changes that were part of the Industrial Revolution to the accompanying rise in living standards. While it would be correct to consider the factors identified in this paper as the direct causes of a breakout, they are likely to be linked to each other as part of the broader underly- ing process of the Industrial Revolution. Although some cursory thought is given to these links here, a thorough examination of them is beyond the scope of this
research.
Section 2 lays out our basic framework for modeling transitions from Malthusian regimes to modern growth. Section 3 explains data sources and estimation methods for the various components of MSPG. Section 4 combines the data to estimate MSPG in Britain. Section 5 discusses some implications of the results and how they relate to the previous literature. Section 6 concludes.
2 The Basic Model
We employ a very simple Malthusian model, with a production function of popula- tion and resources.^1 Resources are fixed and population is endogenous. Technology is exogenous, for we wish to examine the role of technology in the transition from a Malthusian economy to a growth economy, and to do this we would like to exoge- nously vary the rate of technological progress.
We begin with Cobb-Douglas production function (though we shall later present a more general form), and the birth and death rates are taken to be exogenous functions of per capita income:
Y = ALαR^1 −α^ (1) L˙ L =^ b^ −^ d^ ≡^ g(Y /L)^ (2)
The birth rate rises with income until income reaches some critical level and sub- sequently falls, while the death rate falls with income. Defining per capita income y = Y /L, the functions b(y), d(y), and g(y) look like figure 1. The justification for the qualitative functional form of g(y) in Britain is discussed in some detail in appendix A, but is consistent with Lucas’ (2004) results on the relationship of (^1) The basic results do not change if endogenous accumulation of capital is included in the model.
will rise. The same analysis holds for population shocks.^3
The mechanism is classically Mathusian: A technology shock leads to higher incomes, causing population growth to rise and encountering diminishing returns to land. Diminishing returns combined with a population that is growing faster than the maximum sustainable population growth cause falling incomes and a return to a Malthusian equilibrium.
Figure 2: The Dynamics of the Economy
In this economy the level of income is determined by the growth rate of technology. The situation is analogous to pouring water into a leaky bucket—the faster the water is poured in, the higher the steady-state level of water in the bucket, but if the faucet is turned off, the water leaks out to a lower level. This leads to a prediction that in pre-modern societies, higher income levels should be associated with periods of technological advancement (or high MSPG for other reasons) but should dissipate once the technological advancement ends.
In essence, maximum sustainable population growth is a reservoir that can be used to support a growing population or rising living standards. In a Malthusian soci- (^3) Point G in the figure is also an equilibrium, albeit an unstable one. If the economy finds itself to the right of point G, income will rise, causing fertility to fall resulting in further income rises, fertility falls, and sustained growth. In practice, however, point G tends to occur at a high enough income that it is not attainable by pre-industrial societies. If the economy is to the left of G, it will fall back to the Malthusian equilibrium at point M.
ety, the maximum sustainable population growth rate is below the peak population growth rate. All growth in productivity is used to support a larger population, fully exhausting the reservoir. But once MSPG rises above that peak, people do not want to reproduce fast enough to “use up” all the productivity advances being discovered in the economy. Some of these advances can be used to increase per capita income, effecting the transition to modern growth. Returning to the leaky bucket analogy, modern growth is equivalent to pouring water into the bucket so fast that, despite the leaks, the bucket overflows.
These results do not depend on the Cobb-Douglas functional form or on having just two factors of production. Consider the very general production technology or, even more generally, an income function:
Y = F (L, Ri, Xj , sk) (5)
which is assumed to have constant returns to scale in the extensive inputs L, Ri, and Xj. Here, Ri are different types of fixed resources, Xj are variable factors of produc- tion such as capital or human capital, and sk are parameters of the economy, such as the terms of trade and level of technology. Then, if we take logs and differentiate, per capita income growth is given by:
y˙ y =^
i
ηiR R^ ˙ii + ∑ j
ηjx x^ ˙jj + ∑ k
ηks s^ ˙kk − ηRg(y) (6)
where ηi and ηj are the elasticities of income with respect to each of the fixed re- sources and variable factors of production, and ηk are the elasticities of income with respect to the parameters sk. Lowercase letters denote per capita amounts or inten- sive properties of the economy, and ηR = ∑ i ηi is the total share of output paid to fixed factors. Maximum sustainable population growth is then determined, as before,
share, it may increase MSPG even in the face of a decline in income or income growth. The intuition is that a lower resource share raises the ultimate steady-state income level even as it decreases the rate of growth toward that equilibrium.
We shall illuminate this effect in more detail as we explore the effect of an opening to trade on the economy. In a world with no trade, a poor country must produce its own food, which requires labor and land. It might have a production function as previously denoted in equation (1). The process of opening to trade raises the value of α, reducing the resource share in the economy.^4 This trade effect on the transition to growth can be seen in figure 3.
Figure 3: The Effect of Trade on MSPG
The increase in α raises the level of population growth that can be sustained in a Malthusian equilibrium.^5 If the increase is large enough, as shown in the figure, the change can be enough to lift the resource constraint entirely and set off the transition to modern growth.
For large countries, there is an additional complication that a large productivity (^4) It is recognized that as a mathematical matter the production functions for the non-tradeable and tradeable sectors should simply be added. Given that Cobb-Douglas is already an abstraction that does not apply to the real world, it is hoped that the reader will accept the further abstraction that combining two industries with Cobb-Douglas production functions will be taken to yield a Cobb-Douglas with intermediate factor shares. Even an economy that specializes completely into another good requires at least some small share of non-tradeable resources, such as drinking water, living space or land on which to build factories. 5 This depends on at least some part of technology being non-resource augmenting. Otherwise we have A(1−α)^ in the production function and moving away from resource-intensive production hurts technological progress as well as lifting the Malthusian constraint, and these effects offset each other.
improvement in the export sector, precisely what occurred in Britain during the Industrial Revolution, will affect the terms of trade. In the appendix B we provide a basic analysis of the case when the terms of trade depend on trade volumes. There we show that if an economy is experiencing income gains, MSPG may increase while income growth decreases. Similarly, in an economy that experiences income declines, MSPG may decrease while income growth increases. Therefore, trade may increase income growth while making it harder to escape from the Malthusian trap, or vice versa. Later, we will see that this odd result is not just theoretical but in fact likely applied to Great Britain during the Industrial Revolution: Britain was experiencing income gains, but was nonetheless suffering immiserating trade that increased the sustainability of its growth.
The effect of trade on the Malthusian economy when terms of trade are not constant is therefore ambiguous. Trade may help or hurt an economy’s ability to escape the Malthusian trap, and it provides a channel for breakout to be exported even without the prospect of technology transfer. Even more surprisingly, the analysis provides a graphic demonstration that factors increasing income growth may not necessarily make it easier to escape from Malthusian stagnation.
3 Estimating the Building Blocks of MSPG
We now estimate MSPG in Britain during the period 1300-1850. For this purpose we utilize equation (7), which allows us to include capital in the model as follows:
M SP G =^1 γAA^ ˙ + βγkk^ ˙ + RR˙ (10)
where γ is the resource share in the economy and β is the capital share. We will thus require estimates of total factor producivity A, the factor shares β and γ, effective land area R, and capital intensity k.
real GDP growth, Wrigley and Schofield’s (1981) population estimates, Feinstein’s (1988) estimates of capital stocks, and our own estimates of natural resource growth and factor shares as described in sections 3.2 and 3.3 below. Combining these figures with the numbers from Allen gives estimates of TFP growth from 1300 to 1860. This time series is shown in table 2, and it will serve as our estimate of TFP growth for the rest of this paper.
1300- 1400- 1500- 1600- 1700- 1760- 1780- 1800- 1830- 1400 1500 1600 1700 1760 1780 1800 1830 1860 Allen/Tepper and 0.06 0.03 -0.07 0. Borowiecki Crafts/Harley/ 0.31 0.04 0.41 0.57 0. Tepper and Borowiecki Sources: see text. Table 2: Annual Growth Rates of Total Factor Productivity (Percent)
These estimates of TFP growth are close to Crafts’ original (1985) estimates and are generally somewhat higher than Crafts and Harley’s revised figures. This does not stem from any fundamental disagreement with Crafts and Harley over the progress of the economy but rather reflects the need to treat land and capital as separate factors.
The results indicate that prior to the scientific revolution in the mid-17th century TFP growth was extremely slow and may have been dominated by exogenous events like climate change. The 150 years from 1650, including the agricultural revolution, saw modest but consistently positive rates of TFP growth in England. Then, begin- ning with the Industrial Revolution in the first half of the 19th century, TFP growth slowly accelerated to modern levels.
3.2 Structural Change
Structural change is linked to breakout because it reduces the dependence of the economy on land and other natural resources that are constrained in the Malthusian
sense.^8 While there are many measures of structural change, the one that matters for breakout is the factor shares in the economy. Specifically, the inverse resource share acts as a multiplier on MSPG, so that reducing the importance of fixed factors in the economy can have a large effect on sustainable population growth.
Structural change may encompass not only a shift to less resource-intensive pro- duction but also a shift to more capital-intensive production. In equation (10) we observe that as the resource share, γ, falls (if the move is into capital-intensive pro- duction), then β increases at the same time, magnifying the effect. Estimating the production elasticities β and γ is fraught with pitfalls. The simplest way to do so, and the approach taken by most authors, is to assume that the pre-Industrial and Industrial Revolution British economy was approximately competitive and to proxy the elasticity of production by the share of GDP paid to each factor. That is the approach taken here, although it is recognized that this is a strong assumption.
We construct our own rent share coefficients prior to 1700. For the rent share after 1700, we obtain two separate series: using Clark et al.’s (2012) and Allen’s (2009b) estimates or Broadberry et al.’s (2013) figures.
The estimation methodology is as follows. We assume that all land rents derive from agriculture prior to the 18th century, as rents paid on coal mines even in 1860 were at most 4% of agricultural rents, and were negligible before this time.^9 We then combine data on the share of agricultural income paid to land (Allen, 2005)^10 , (^8) Although it is not modeled as part of the main paper, it is easy to create a feedback loop so that structural change is endogenous in the model. Intuitively, if agricultural productivity in- creases slowly, then the entire productivity growth is absorbed into supporting a larger population. However, if agricultural productivity increases more quickly, then as incomes rises, people consume more non-agricultural goods (the income elasticity of food demand is less than one). This leads to people moving off the land, decreasing the rent share, which increases per capita income growth, leading to a lower share of agriculture in GDP and more people moving off the land, which leads to a lower rent share, in other words a virtuous circle. 9 10 See Clark and Jacks (2007) for data on coal rents. We obtain from Allen (2005) estimates of the agricultural income paid to land for 1300, 1500, and 1700. The share of agricultural income to land in 1400 is assumed to be the same as the estimate for 1500, as all the change in economic structure between 1300 and 1500 is assumed to be due to the Black Death in 1348-51. We further use the share from 1700 for 1650, as it is the closestavailable estimate. The later assumption is further motivated by the observation that the share
an implausibly rapid structural change in the English economy from 1660 to 1700. Until new and better evidence becomes available, it is not clear which point of view will stand the test of time (Leunig, 2013), and as such, it is not obvious which estimates are the right ones. Therefore, we construct two separate rent share series for the period of the disagreement.
Based on the earliest estimates, which are provided for 1381 and come closest to 1400, we calculate the average agricultural share in employment for 1400. Since there is no estimate available for the share of workforce in agriculture in 1300, we approximate it with the estimate from 1400, an assumption supported by the near- constant share of agricultural employment from 1381-1650. Broadberry’s figure for 1522 is used for 1500 and Clark’s estimate for 1652-60 is employed for 1650. From then on their estimates diverge significantly and we construct two separate series for the period post 1700. The first one takes rent share estimates directly from Allen (2009b) for the period after 1760 and calculates the rent share for 1700 as the average between Allen’s figure for 1760 and our estimate for 1650. The second series is based on Broadberry’s estimates that are closest to 1700, 1760, 1800 and 1841. Table 3 summarizes the calculations.
We turn next to the estimation of productivity differences between the agricultural sector and the rest of the economy. Broadberry et al. (2013) estimate that produc- tivity outside agriculture was higher than productivity in agriculture by a factor 1.6 in 1381, 2.11 in 1522, and 1.74 in 1700. We use these figures to translate our agricultural share in employment into GDP share estimates for 1400 and 1500, and interpolate the productivity difference for 1650. We then multiply the share of GDP in agriculture by the share of agricultural production paid as rent to obtain the share of GDP paid to land. To determine the rent share in 1600, we use Clark’s (2002) rent index combined with the assumption that gross land area under cultivation was constant over the half-century from 1600 to 1650. Linked with data on population
Allen: Rent Share of Ag. Inc. 0.39 0.19 0.19 0.51 0.51 0.48 0.51 0. Clark/Broadberry/Allen: Share of Pop. in Ag. 57% 57% 58% 59% Share of GDP in Ag. 46% 46% 40% 46% Rent Share in GDP 0.18 0.09 0.08 0.29 0.23 0.23 0.22 0.17 0. Broadberry: Share of Pop. in Ag. 39% 37% 32% 24% Share of GDP in Ag. 27% 30% 31% 19% Rent Share in GDP 0.14 0.14 0.16 0. Table 3: Rent Share in National Income Estimates Sources: Rent share in agricultural income from Allen (2005). Share of population in agriculture from Broadberry et al. (2013); Clark (2013); Clark et al. (2012). Share of GDP in agriculture and rent share in GDP own calculation based on Broadberry’s et al. and Clark’s et al. data on share of population in agriculture. See text for calculation methods.
growth and the rent share in 1650, this uniquely determines GDP per capita growth, which is estimated to have been 0.02% per annum from 1600 to 1650.^11 Broadberry et al. (2012) report a comparable figure for annual GDP per capita growth rate of -0.04%. Our estimates imply a rent share of 29% in 1600 and, by taking the average of the rent share for 1650 (based on Clark’s estimates) and Allen’s estimate for 1760, we find a rent share of 23% in 1700. Calculating the rent share using Broadberry’s numbers, one would end with a low estimate of 14%.
As a check on these figures, one could conduct a bottom-up approach: multiplying the rent per acre by the number of acres (Clark, 2002) and dividing by nominal GDP (Lindert and Williamson, 1982). This yields a rent share in GDP of 23% in 1700, 24% in 1760 and 13% in 1800. The 1700 estimate is practically the same as the rent share coefficient obtained in our framework when Clark’s agricultural share in employment is used; the estimates for the following years come very close to Allen’s rent share.
To get averages over a period, we simply average the endpoints of the period. The (^11) See appendix C for the details of this calculation.
