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Luddites, the industrial revolution, and the demographic transition

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Technological change was unskilled-labor-biased during the early industrial revolution, but is skill-biased today. This implies a rich set of non-monotonic macroeconomic dynamics which are not embedded in extant unified growth models. We present historical evidence and develop a model which can endogenously account for these facts, where factor bias reflects profit-maximizing decisions by innovators. In a setup with directed technological change, and fixed as well as variable costs of education, initial endowments dictate that the early industrial revolution be unskilled-labor-biased. Increasing basic knowledge then causes a growth takeoff, an income-led demand for fewer but more educated children, and a transition to skill-biased technological change in the long run.

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  1. Although “machine maintenance” is something which occurs within the context of a given stage of technology, rather than being related to technological progress per se.

  2. This has become a rather standard assumption in the labor literature, and is an important one for our analysis later.

  3. Conceptually one could assume either that patent rights to innovation last only one time period, or equivalently that it takes one time period to reverse-engineer the development of a new machine. In any case, these assumptions fit the historical evidence that profits from inventive activity were typically short-lived during the industrial revolution (Clark 2007).

  4. Galor and Mountford (2008) make a rather similar assumption.

  5. Prados de la Escosura (2012) provides evidence that cognitive skills increase more than proportionally as the quantity of education increases. In the returns-to-education literature, the interest is generally in estimating a constant marginal return to years of schooling, but even so some nonlinearities appear to be present, and influential works such as Card and Krueger (1992) and Heckman et al. (2008) could be read in this way. For specific examples of estimates which find increasing returns to years of schooling consistent with our \(k>1\) assumption, we refer the reader to the work of Trostel (2004, 2005). Using the Mincer regression method, this work finds OECD cross-country evidence of increasing returns to years of schooling in the elementary-middle school phase, which possibly then revert to constant or decreasing returns during high-school and college; the results appear stronger in a sample that also includes middle- and low-income economies where there is on average less schooling, and it is these latter findings that might be most comparable to the nineteenth century conditions we have in mind here.

  6. That property appears, for example, in Galor and Mountford (2008), where, under a discrete choice, unskilled or skilled offspring may be created at exogenously fixed time costs \(\tau _u\) and \(\tau _s\), where the latter exceeds the former (generating an exogenous, fixed skill premium on the supply side when both types of offspring are present).

  7. Strong results on schooling (parental income elasticities near 1) emerge from raw data, but not for regressions that include “regional” dummies (e.g., village or county), suggesting that these effects are most clearly visible across locales. In regressions of child literacy on income, regressions for specific towns (London, Macclesfield, Hanley) were unable to detect within-town variation (p. 86). But a national sample using occupational proxies for wages found an parental income elasticity of literacy of 0.72. This last result could be undermined by the inclusion of parental literacy, but the latter is of course highly collinear with income. Mitch also found that income elasticities were falling as incomes rose, suggesting the possibility of threshold effects. In accounts by contemporaries, poor parents themselves were found to cite poverty as the main reason they did not send their kids to school, although their upper-class neighbors were apt to disagree. For the United States, Go (2008) finds a strong correlation between father’s wealth and school attendance by the child in 1850; this correlation disappears in later years after the introduction of free public schools. Go and Lindert (2010) suggest that one of the main reasons why school enrollments in the US North were higher than those in the US South was the fact that the northern schools had lower direct costs relative to income.

  8. Although not Malthusian in nature, the initial static phase in our model is broadly consistent with Malthusian dynamics in the following way. If we consider the pre-Industrial world, one where \(L\) is much larger than \(H\), and maintain the assumption that these factors are grossly substitutable, then any technological change that could have a meaningful influence on average incomes would necessarily be unskilled-labor biased. As the model demonstrates, this will induce a rise in fertility and influence education only modestly. Thus, our model is consistent with the pre-Industrial correlation between brief and temporary bursts of technologically-induced income gains and increases in population.

  9. Of course there are a host of other explanations, including falling death rates related to health improvements, and the passage of various Poor Laws. Naturally we are abstracting from these possibilities without dismissing them as inconsequential.

  10. Recent studies make a variety of related points which can also explain the demographic transition. Hazan and Berdugo (2002) suggest that technological change at this stage of development increased the wage differential between parental labor and child labor, inducing parents to reduce the number of their children and to further invest in their quality, stimulating human capital formation, a demographic transition, and a shift to a state of sustained economic growth. In contrast, Doepke (2004) stresses the regulation of child labor. Alternatively, the rise in the importance of human capital in the production process may have induced industrialists to support laws that abolished child labor, inducing a reduction in child labor and stimulating human capital formation and a demographic transition (Doepke and Zilibotti 2005; Galor and Moav 2006; Galor 2012).

  11. We can relax this assumption to allow for multiple-step quality improvements each period. Simulation results (not shown) display the same patterns for fertility, education, and relative wages as our main results.

  12. The degree of substitutability between skilled and unskilled labor has been much explored by labor economists. Studies of contemporary labor markets in the US (Katz and Murphy 1992; Ciccone and Peri 2005), Canada (Murphy et al. 1998), Britain (Schmitt 1995), Sweden (Edin and Holmlund 1995), and the Netherlands (Teulings 1995) suggest aggregate elasticities of substitution in the range of one to three. See Katz and Autor (1999) for a detailed review of this literature.

  13. Other parameters simply scale variables (such as \(\Omega \)) or affect the speed of growth (such as \(\alpha \), \(\varepsilon \) and \(\phi \)). Changing the values of these parameters however would not shift the direction of technology, nor would it affect the responsiveness of households. Thus these specific values are not crucial for the qualitative results and our underlying story.

  14. Each period in our model is equivalent to roughly 20 years, so this is equivalent to assuming that initially population grows by about 5 per cent every 10 years.

  15. This produces initial values of \(w_{l} = 0.34\), \(w_{h} = 0.53\), \(A_{l} = 0.20\), \(A_{h} = 0.24\), \(L = 0.75\), \(H = 0.32\), \(e = 0.32\), \(Q_{l} = Q_{h} = 0.04\).

  16. The initial level of \(B\) is chosen such that growth starts after a few periods.

  17. Mokyr and Voth (2010) present a critique of Clark’s skill premium data.


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We acknowledge funding from the European Community’s Sixth Framework Programme through its Marie Curie Research Training Network programme, contract numbers MRTN-CT-2004-512439 and HPRN-CT-2002-00236. We also thank the Center for the Evolution of the Global Economy at the University of California, Davis, for financial support. O’Rourke would like to thank the European Research Council for its financial support, under its Advanced Investigator Grant scheme, contract number 249546. Some of the work on the project was undertaken while O’Rourke was a Government of Ireland Senior Research Fellow and while Taylor was a Guggenheim Fellow; we thank the Irish Research Council for the Humanities and Social Sciences and the John Simon Guggenheim Memorial Foundation for their generous support. For their helpful criticisms and suggestions we thank Gregory Clark, Oded Galor, Philippe Martin, David Mitch, Joel Mokyr, Andrew Mountford, Joachim Voth, two anonymous referees, and participants in workshops at Royal Holloway, University of London; London School of Economics; Universidad Carlos III; University College, Galway; Paris School of Economics; and Brown University; and at the CEPR conferences “Europe’s Growth and Development Experience” held at the University of Warwick, 28–30 October 2005, “Trade, Industrialisation and Development” held at Villa Il Poggiale, San Casciano Val di Pesa (Florence), 27–29 January 2006, and “Economic Growth in the Extremely Long Run” held at the European University Institute, 27 June–1 July, 2006; at the NBER International Trade and Investment program meeting, held at NBER, Palo Alto, Calif., 1–2 December 2006; and at the NBER Evolution of the Global Economy workshop, held at NBER, Cambridge, Mass., 2 March 2007. The latter workshop was supported by NSF grant OISE 05-36900 administered by the NBER. All errors are ours.

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Appendix 1: Limit pricing and the gains from innovation

Here we solve for the price new innovators would charge for newly invented machines in the face of competition from producers of older machines. First, let us describe the producers of the unskilled-intensive good, \(A_{l}L\); analogous results will hold for the skill-intensive good. The production function for these goods are

$$\begin{aligned} \left( \frac{1}{1-\beta }\right) Q_{l} L^{\beta } \int \limits _{0}^{1}M_{l}(j)^{1-\beta }dj. \end{aligned}$$

Producers wish to maximize profits or, equivalently, to minimize unit costs. The unit costs for producers who buy new machines, denoted as \(uc\), can be written as

$$\begin{aligned} uc = \beta ^{-\beta }\left( 1-\beta \right) ^{\beta }\left( \frac{1}{\varepsilon Q_{l}}\right) w_{l}^{\beta } \int \limits _{0}^{1}p(j)^{1-\beta }dj, \end{aligned}$$

where \(p(j)\) is the price of machine \(j\) and \(w_{l}\) is the wage of \(L\).

The question for us is, what maximum price could an innovator charge and drive out the competition at the same time? The “competition” in this case are those who hold the blueprints of the next highest-quality machines of quality \(Q_{l}\). The lowest price they can charge is their marginal cost, \(Q_{l}\); if all old machine-producers charge this, unit costs can be written as

$$\begin{aligned} uc_\mathrm{{old}} = \beta ^{-\beta }\left( 1-\beta \right) ^{\beta }\left( \frac{1}{Q_{l}}\right) w_ {l}^{\beta } Q_{l}^{1-\beta }. \end{aligned}$$

Traditional endogenous growth theories that use quality ladders typically have producers of new machines charge a monopolistic mark-up over marginal cost. In our case producers of new machines would charge a price \(p_\mathrm{{monop}} = \frac{\varepsilon Q_{l}}{\left( 1-\beta \right) }\) for a machine of quality \(\varepsilon Q_{l}\). However, in order for this to be a profitable strategy, unit costs for producers of \(A_{l}L\) must be at least as low when they buy new machines compared with when they buy the older, cheaper machines. In other words, \(uc_\mathrm{{old}} \ge uc_\mathrm{{monop}}\), which requires that

$$\begin{aligned} \beta ^{-\beta }\left( 1-\beta \right) ^{\beta }\left( \frac{1}{Q_{l}}\right) w_ {l}^{\beta } Q_{l}^{1-\beta } \ge \beta ^{-\beta }\left( 1-\beta \right) ^{\beta }\left( \frac{1}{\varepsilon Q_{l}}\right) w_{l}^{\beta } \left( \frac{\varepsilon Q_{l}}{\left( 1-\beta \right) }\right) ^{1-\beta }. \end{aligned}$$

This simplifies to the condition \(\varepsilon \ge \left( 1-\beta \right) ^{\frac{\beta -1}{\beta }}\). Thus, in order for monopoly pricing to prevail, quality improvements must be large enough for goods producers to be willing to pay the higher price. If this condition does not hold, the monopoly-priced machine will be too expensive, and producers will opt for the older machines.

However, producers of newer machines can charge a price lower than this and still turn a profit. How low would they have to go to secure the market? They certainly could go no lower than \(\varepsilon Q_{l}\), which is their own marginal cost of machine production. Fortunately they would not have to go that low; they could charge a price \(p_\mathrm{{limit}}\) low enough such that \(uc_\mathrm{{old}} \ge uc_\mathrm{{limit}}\) (see Barro and Sala-i-Martin 2003 and Grossman and Helpman 1991 for similar limit-pricing treatments). That is, producers of new machines could undercut their competition so that goods producers would prefer the higher-quality machines to the older lower-quality machines. And to maximize prices, new machines producers would charge a price such that this held with equality, so that

$$\begin{aligned} \beta ^{-\beta }\left( 1-\beta \right) ^{\beta }\left( \frac{1}{Q_{l}}\right) w_ {l}^{\beta } Q_{l}^{1-\beta } = \beta ^{-\beta }\left( 1-\beta \right) ^{\beta }\left( \frac{1}{\varepsilon Q_{l}}\right) w_{l}^{\beta } p_\mathrm{{limit}}^{1-\beta }. \end{aligned}$$

Solving for this limit price gives us

$$\begin{aligned} p_\mathrm{{limit}} = \varepsilon ^{\frac{1}{1-\beta }}Q_{l} > \varepsilon Q_{l}. \end{aligned}$$

Thus, producers will always opt for newer machines, no matter the size of quality steps. So our approach would be valid for any values of \(\varepsilon > 1\) and \(0 < \beta < 1\). Given our paramerization described in Sect. 2.3, we assume this limit pricing strategy is used.

Appendix 2: Additional robustness analysis

Here we present simulation results with alternative parameter values. We first try lower values of \(k\), which governs the human capital returns from education. Specifically, \(k\) is lowered from its baseline value of 1.5, first to a small, diminishing-returns level value of 0.5 in Fig. 12, and then raised to the constant-returns level of 1 in Fig. 13. (In order to keep the skill premium at a reasonable number slightly less than 2, we also increase \(\tau \) to 0.63 and 0.53, respectively, in these cases, and we adjust \(\delta \) to keep the transition in the same 10 year window). Again, we see that general patterns for fertility, education and wages remain the same. Thus our results are not sensitive to the specific rate of return from education.

Fig. 12
figure 12

Robustness Check 5. The figure shows the model simulation when \(k=0.5\)

Fig. 13
figure 13

Robustness Check 4. The figure shows the model simulation when \(k=1\)

Figure 14 displays simulation results for the case of even greater increasing returns to education that in the baseline case. Specifically, the parameter \(k\) is increased from its baseline value of 1.5 to a level of 2. (To set a reasonable starting value for the skill premium in this case, \(\tau \) is lowered to 0.37, and we again adjust \(\delta \) to keep the transition in the same 10 year window). In this case the skill premium actually rises initially, before falling later. This shows that the model can qualitatively match the data on wage levels, fertility, education and so on, while producing differing results for the skill premium. Our main results do not therefore require us to take a position on the dispute regarding the direction of change in the skill premium during the early industrial revolution.

Fig. 14
figure 14

Robustness Check 6. The figure shows the model simulation when \(k=2\)

Figure 15 displays simulation results for the case of a larger “fishing-out” effect. In this case innovation dramatically raises the costs for future innovations. Notice that this makes growth in unskilled technologies sporadic. Despite this, the evolution for fertility, education and wages echo those of prior simulations, albeit with some added choppiness.

Fig. 15
figure 15

Robustness Check 6. The figure shows the model simulation when \(\alpha =5\)

Finally, Fig. 16 displays simulation results for the case where exogenous changes in the mortality rate are imposed on the demographic dynamics so as to match the actual changes in mortality rates in the British data over the period. Our baseline model makes no attempt to model mortality or its impact on household choice: for every 1 single parent alive at time \(t\) there are \(n\) offspring in the new generation at time \(t+1\), and \(n\) is interpreted as a fertility choice variable, with, in effect, constant zero mortality. But this will not match the data from the eighteenth and nineteenth century very well because in reality the demographic transition not only featured a fertility boom and bust, but a secular mortality decline as well.

Fig. 16
figure 16

Robustness Check 6. The figure shows the model simulation with exogenous mortality changes taken from the historical data, so population growth \(n - (m_0 - z)\) is now different from the birth rate in the third panel, the difference being the decline in mortality from the initial period \(z\)

To capture this we run a simulation where we impose an exogenous mortality term \(z\) on the population dynamics so that for every 1 single parent alive at time \(t\) there are \(n - (m_0 - z) \) offspring in the new generation at time \(t+1\), where \(z\) is a time-varying mortality decline parameter known to adults making their education and fertility choices at time \(t\) and which is chosen to match the actual historical data, and \(m_0\) is a constant equal to initial mortality. Thus, as \(z\) rises over time from 0, the difference between population growth under constant mortality \(n - m_0 \) and actual population growth is equal to \(z\).

In this case Fig. 16 shows paths that are similar to the baseline but with more pronounced swings. In the early phase of industrialization, directed technical change favors abundant unskilled labor, which responds with more supply via endogenous education choices, while due to mortality declines, more parents arrive each period and the labor pool grows even further. Per capita output growth is slower since population growth rates are higher at all times, and the education transition is delayed and slowed. But when the education transition finally begins it is more rapid, as mortality declines continue and now additional labor supply is fed into the skilled pool.

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O’Rourke, K.H., Rahman, A.S. & Taylor, A.M. Luddites, the industrial revolution, and the demographic transition. J Econ Growth 18, 373–409 (2013).

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