THE FLEXIBILITY OF BRITISH APPRENTICESHIP

The important economic contribution of apprenticeship to innovation and to labor mobility has been highlighted over the last two decades (Epstein Reference Epstein1998; Mokyr Reference Mokyr2009; Humphries Reference Humphries, David and Thomas2003, 2010; Wallis Reference Wallis2008; Van Zanden Reference Van Zanden2009, Ch. 5). Another literature has focused on many of the more detailed aspects of apprenticeship, emphasizing its importance in the intergenerational transmission of knowledge that was primarily tacit in nature (De Munck Reference De Munck2010, 2011; Davids Reference Davids, De Munck, Kaplan and Soly2007; Epstein Reference Berlin, Epstein and Prak2013).

The institution of apprenticeship was, of course, not particular to Britain. However, there is reason to believe that it developed into a more flexible and responsive system there than elsewhere. By the eighteenth century Britain had access to a work force of highly skilled artisans that dwarfed anything that other European countries could amass. What happened on the Continent is more complex. Clearly in many areas guilds established the rules of apprenticeship and supervised the actual training (Crowston Reference Crowston, De Munck, Kaplan and Soly2007, p. 46). Yet the contract was notarized (by royal edict of 1691) and as Steven L. Kaplan (Reference Kaplan1993, p. 437) has pointed out, it involved not just the master and the pupil but also the community (i.e., the guild), the government (at various levels), and the potential customers. Nicole Pellegrin-Postel's (Reference Pellegrin-Postel1987, pp. 269–70, 275, 284) detailed analysis of the notarial apprenticeship contracts in the Haut-Poitou area shows that in many cases some of the provisions of the contracts were ignored and that there was a great deal of variability in the duration and other terms of the contract. At the same time there was very little geographical mobility among the apprentice population and it was common for apprentices to choose a trade that was close to that of their father.

The evidence that eighteenth-century French guilds stood in the way of technical progress has been increasingly questioned, and their power to monopolize production was much weakened by the existence of guild-free regions such as the famous Faubourg Saint-Antoine near Paris. Although the guilds survived Turgot's famous but ill-fated attempt to suppress them in 1776, their recovery was slow and gradual (Fitzsimmons Reference Fitzsimmons2010, pp. 14–15). All the same, despite cracks and weaknesses, (Fitzsimmons Reference Fitzsimmons2010, p. 10) concludes that they were still a permanent fixture in French society and that as late as 1750 there was little to indicate their imminent demise. In most places guilds created a relatively rigid institutional framework of rules that stood in contrast to the more agile British system (Ogilvie Reference Ogilvie2014).Footnote ⁶ Robert Darnton's (1984, pp. 114–15) famous observation about mid-eighteenth-century Montpellier—that it was no Manchester, that it produced the same goods on the same scale, and that its journeymen and masters went about their business pretty much in the same way as they had two hundred years earlier—may not be true for the more advanced regions of France. But it is perhaps telling that when the Englishman John Holker was asked by the French government to set up a textile factory in Normandy in 1752, he had to depend on 20 English artisans and mechanics, who were allocated among French workers such that their skills could be disseminated in the most effective fashion among the local workers (Henderson Reference Henderson1954, p. 16; John R. Harris Reference Harris1998, p. 60). With the demise of the French guilds after the revolution, the institutions of apprenticeship in France fell on hard times and attempts to restore it in the nineteenth century “were strangely out of step with economic reality” (Lequin Reference Lequin, Kaplan and Koepp1986, p. 463). This stood in contrast with Britain, where, despite the abolition of the Statute of Artificers in 1814, apprenticeship was alive and well in the nineteenth century (Elbaum Reference Elbaum1989).Footnote ⁷

Three elements were responsible for the flexibility in Britain that allowed it to “produce” large amounts of artisanal human capital. First, by the eighteenth century the guilds in Britain had been weakened and their regulatory powers were limited and further undermined during the civil wars (Epstein Reference Epstein1998, pp. 686–98; Berlin Reference Berlin, Epstein and Prak2008). Of course London and the “old towns” still had guilds (or companies, as they were known), but precisely because so much of the country was guild-free, it became almost impossible to use the guild system to regulate and limit entry into any occupation and maintain exclusionary rents.Footnote ⁸ The London guilds simply no longer had the power to regulate key occupations, including the flows of new workers into them.Footnote ⁹ Second, the strictures of the Statute of Artificers were not strictly enforced so that the length of contract became a decision variable. (Humphries Reference Humphries2010, pp. 268–69) recognizes this flexibility and notes that the contracts could be customized and adapted to particular cases. Finally, eighteenth-century Britain experienced a flourishing of a high degree of social capital, meriting the moniker of an “associational society” (Clark Reference Clark2000). This social capital supported a reputational mechanism that kept both apprentice and master from engaging in excessive opportunistic behavior (Mokyr Reference Mokyr and Helpman2008). The decision to pick a particular master was often driven by family interests made by the family as a whole, and the fairly low incidence of young lads being apprenticed to their own fathers suggests a high level of trust between the two parties, which reduced, but did not entirely eliminate, uncertainty and the chance for opportunistic behavior on either side, (Humphries Reference Humphries2010, pp. 270–71).

What was unique in England was that the institution of apprenticeship was regulated by the central government yet these regulations may well have worked in England's favor. The Statute of Artificers (1563) added formal legal regulation of apprenticeship to the customs and rules of the guilds extending the guild practices of the City of London and other corporate towns to urban England, including the seven-year term of service. The Statute did, however, contain some interesting deviations from guild regulations. For example, a legally completed apprenticeship gave a young man the right to practice his trade without distinction of place, that is, he was not required to work and trade in the same place where the term of apprenticeship had been served. According to (Humphries Reference Humphries, David and Thomas2003, p. 96), “this aspect of the Statute, which distinguished it from continental legislation, perhaps recognized that industrial skills had ceased to be a prerogative of the town craftsman and become a characteristic of the intermingled agricultural-industrial life of the countryside.” By making it possible to hire workers outside their city of residence, the Act effectively left masters at liberty to employ as many apprentices as their work demanded (Dunlop Reference Dunlop1911, p. 207; Epstein Reference Epstein1998, p. 689).

The question is whether the clauses of the Statute were indeed enforced, and if so, which of the clauses. Various studies have shown the enforcement of the Statute of Artificers to be incomplete. According to Ron Harris Reference Harris2004, p. 208), incomplete enforcement was a result of the lack of updating and maintenance of the regulations by parliament and as a result “The Statute of Artificers and its offspring became increasingly detached from reality as time went on. This was not a problem of enforcement. Parliament needed to invest time and effort in drafting the regulation in a manner that would be sufficiently detailed and would address the complexities and variety of contexts of real life. It took maintenance work to keep the regulation current. The British parliament often did not do this.” O. Jocelyn Dunlop Reference Dunlop1911, p. 201) has pointed to the lack of enforcement “machinery” claiming that no officers were especially appointed for the enforcement of the Act and that it was beyond the powers of the common informers.Footnote ¹⁰ Notwithstanding the Act, men who had not been regularly apprenticed, but had been merely taught by their fathers, claimed and received admittance to the guilds; the custom of patrimony was preserved everywhere, and it was ranked with apprenticeship as entitling a man to the freedom of his trade association in the ordinances of the guilds. Moreover, Wallis (Reference Wallis2008) has shown that the legal stricture to serve for seven years was rarely observed and that workers left when they felt that the gains from staying longer were less than the opportunity costs. To summarize then, while the Statute of Artificers at first blush may seem a source of rigidity, its practical enforcement on the ground was sufficiently flexible to allow a relatively rapid adaptation to changing economic circumstances.

Apprenticeship was thus a formal method of vocational training in crafts and trade that originated in the guild system of medieval times. Ideally, a master or mistress agreed to train a child in a trade for a specific term of years and in most cases to board and house the child. In return the master was paid an agreed premium and the child committed to serve faithfully and keep the secrets of the trade.Footnote ¹¹ The premium paid, served more than one purpose. In part, it was to ensure the master against an early departure of the apprentice. But in part it reflected the quality of the training and the cost to the master, as well as its scarcity value (Minns and Wallis Reference Minns and Wallis2013, p. 340). The demand side, they show, did not just reflect the increased productivity that apprenticeship conveyed, but also exclusionary rents (Minns and Wallis Reference Minns and Wallis2013, p. 348). “Training premiums,” they write, “were used to address the core tensions in securing pre-industrial training contracts.” This view is consistent with our notion that it is the observed equilibrium price (tuition) in a market in which the masters are the supply side and the apprentices are the demand.

Another important advantage of the British apprenticeship system was its reputational mechanisms that kept both apprentice and master from engaging in excessive opportunistic behavior. Apprenticeship contracts by definition were poorly specified, and much was left open to the discretion of the participants. What made this a self-enforcing contract, in which opportunistic behavior was kept at a minimum, was above all the reputation of both participants, even though they were both operating in the shadow of the law and that legal recourse was possible even if it was highly undesirable and expensive (Humphries Reference Humphries2004; Mokyr Reference Mokyr2009). The knowledge transmitted between master and apprentice was largely tacit in the sense that the learning took place through observation, absorption, and imitation rather than through direct and full instruction. As Bert De Munck, Steven L. Kaplan, and Hugo Soly (Reference Crowston, De Munck, Kaplan and Soly2007, pp. 14–15) put it, apprentices on the shop floor had to “steal with their eyes.” Didactic skills were probably of secondary importance and yet the existence of considerable fees that British masters charged for their services suggests that there were incentives for them to build reputations by exerting efforts and spending resources to better instruct their apprentices.Footnote ¹²

The fee paid to masters was thus dependent on the master's reputation and this placed limits on the degree of opportunism that masters could engage in (Epstein Reference Berlin, Epstein and Prak2013, p. 29). The voluntary termination of so many apprenticeships can be interpreted to mean that at some point the marginal value of the flows between apprentice and master were more or less equal for both and beyond that, neither had much to gain from its continuation. The exact time at which the marginal costs began to exceed the marginal benefits would differ for master and apprentice, and so there was room for negotiation. But precisely because of the self-enforcing institutions of the associational society that made cooperation possible, such differences rarely led to outright conflicts.

In other ways, too, the system was well-designed. In principle, the indenture contract guaranteed that the apprentice would make up the difference between the cost of training and the fee by working as a journeyman or servant to his master after the training was complete. In practice, Wallis (Reference Wallis2008) has shown that the traditional view, that the cost to the master and the benefit to the apprentice were heavily concentrated in the first years, may not be the way the institution actually worked by the eighteenth century. He argues persuasively that the flows of costs and benefits to both parties were spaced fairly evenly over the period of the apprenticeship. This is not to say that they were equal: a fee was paid up-front because there was a difference between the present value of the net costs and benefits of both master and apprentice, and this fee can be interpreted as the netprice of the service delivered in a well-functioning market. But it does imply that the fact that many apprenticeships terminated before the legally mandated seven years is evidence for a flexible and mutually advantageous transaction between master and apprentice.

To sum up: the British apprenticeship system worked, and it worked so well that long after the abolition of the Statute in 1814, the institution remained the central mechanism through which Britain trained its skilled craftsmen (Elbaum Reference Elbaum1989; Elbaum and Singh Reference Elbaum and Singh1995). It seems highly plausible that Britain's advantage in highly skilled craftsmen was in large part derived from a more effective training system.

THEORETICAL FRAMEWORK

In what follows, we lay out a deterministic, dynamic partial equilibrium model that can establish a valuable conceptual framework upon which to build the discussion and interpretation of our empirical results in the next section. Notwithstanding the model's simplicity, it will prove instrumental in facilitating our understanding of what we mean by efficiency in the apprenticeship market and the implications this efficiency can have on equilibrium outcomes. We begin the presentation of our model with the supply side of the apprenticeship market, followed by an explanation of its demand side, and we close it by defining and discussing the market equilibrium of the model.

Supply Side

To keep things as simple as possible, we assume there is a representative master. Let us assume the master maximizes the present value of his infinite stream of future profits. The master's revenues are generated by selling apprenticeship contracts, y_t , produced with capital input, k_t , using the production technology y_t = f(k_t). It is assumed that f is continuously differentiable, strictly increasing, strictly concave, and obeys the Inada conditions, f(0)=0, and, . We abstract here from any other activities the master may be undertaking and focus on his activities as an instructor.

The price of an apprenticeship contract is denoted by p_t ; this price is essentially the tuition paid for undertaking the apprenticeship. The master's cost C, is the total cost of investment, which we assume is a function of gross investment, [k_t+1 – (1 – δ)k_t ], where 0 < δ < 1 is the capital depreciation rate. Adding variable labor to this model would not change the main takeaway of this section but would complicate the exposition; hence, we abstract from this aspect in our model. We make the standard assumption that C is strictly increasing, strictly convex, and differentiable, with C(0) = 0. These capital costs are incurred because much of the training costs consisted of materials and equipment. Sven Steffens Reference Steffens2001, pp. 124–25), for example, notes that in Belgium little actual direct instruction was done; the apprentice simply was allowed to try and imitate what the master and more advanced apprentices were doing. In the process, he was likely to waste raw materials and fuel, and may have used up equipment and tools. He also occupied space that had an opportunity costs. Moreover, the master and his apprentice had to establish a rapport, and at first an inexperienced apprentice may have disrupted the normal productive activities in the shop. Note that assuming adjustment costs essentially introduces a capacity constraint on the master and is necessary for facilitating a formal dynamic framework in which the master gradually responds to shocks before moving to new steady state rather than instantaneously reaching it. We can now turn to write the maximization problem facing the master:

(1)

where

0 < β < 1 is the master's subjective discount factor. Note that since k_t is a state variable that is predetermined with respect to period t,k₀ is not a choice variable in the master's maximization problem. It is useful to write down the Bellman equation corresponding to the master's problem:

(2)

where

It is straightforward to apply to our setting standard dynamic programming techniques and obtain the following standard results: (1) uniqueness of the solution; (2) continuity of V(k,p) and the optimal policy function k_t+1 = g(k_t , p_t ); and (3) V is increasing in k and the optimal level of next period's capital is increasing in the level of the current period's capital.Footnote ¹³ Combining the first order condition and envelope condition of Equation 2, we can obtain the following Euler equation characterizing the solution to the master's problem:

(3)

Equation (3) essentially equates the marginal cost (LHS) and marginal revenue (RHS) of using an additional unit of capital. The master's supply of apprenticeship contracts is implicitly determined by this equation and can be shown to be increasing in the price of the contract.Footnote ¹⁴ We can therefore conclude that the solution to the master's dynamic maximization problem generates an upward sloping supply curve.

Given the dynamic nature of the master's problem, it is of interest to ascertain whether there exists a unique and globally stable steady state level of capital. Towards this end, let us write Equation (3) in steady state form in which , and,

(4)

Given the strict concavity of f and strict convexity of C, and the Inada conditions imposed on f, it is straightforward to show that there is a unique and globally stable steady state level of capital. The reason for this is that under these assumptions the term, takes on a value for a unique value of and this unique steady state is independent of the initial value of capital. Furthermore, it is apparent from Equation (4) that the steady state capital stock is increasing in the steady state price level .Footnote ¹⁵ This result and the previous one on the upward slope of the supply curve give us an indication of what will take place following a permanent rise in demand: initially, given that capital is predetermined, capital will not change, but in the subsequent period capital will rise and will continue to gradually rise thereafter until reaching the higher steady state. Importantly, given the capacity constraint facing the master, this new steady state will be characterized by a price level that is lower than that which prevails in the short run. What this means is the apprenticeship supply follows a classical Marshallian pattern: a demand shock drives up the price in the short run, but as adjustment occurs the supply curve becomes more elastic and the adjustment takes place in the quantity space.

Demand Side

Prospective apprentices, indexed by i are assumed to derive economic value from undertaking the apprenticeship, which we denote by v_i,t .Footnote ¹⁶ This variable represents the additional utility gained by the acquisition of a skilled trade. This utility could be seen as the present value of the expected markup in income over the wage of an unskilled worker, the higher social status of a skilled artisan, and possibly the pride and satisfaction of producing more sophisticated goods. This additional utility is explicitly defined as:

(5)

where, 0 < β < 1 is the prospective apprentice's subjective discount factor, which we assume for simplicity to be equal to that of the master's, and w_i,t is the expected payoff at period t from undertaking the apprenticeship. One reason for the assumed heterogeneity in v_i,t across different apprentices is that different prospective apprentices are likely to possess different levels of talents. Given that the decision taken by the prospective apprentice is a binary one, we define a binary variable x_i,t that takes the value of one if the apprenticeship is decided to be pursued and zero if it is forgone by the prospective apprentice. Moreover, since the cost of taking part in the apprenticeship is p_t , the apprentice's net payoff function is v_i,t – p_t if the apprenticeship is pursued and zero if it is foregone.Footnote ¹⁷ Therefore, we can describe the solution to the prospective apprentice's problem simply as follows:

(6)

Equilibrium

For the purpose of defining the market equilibrium, let us first assume there is a total number of N masters each offering y_t contracts so that the total number of offered apprenticeships is Ny_t .Footnote ¹⁸ Market equilibrium will take place when aggregate supply of apprenticeships equals the aggregate demand for apprenticeships, that is, . For a sufficiently large number of prospective apprentices as well as a sufficiently large level of heterogeneity as manifested in the variation in v_i , , would be a standard downward-sloping demand curve; the simple reason for this is that, under these conditions, raising the tuition level would drive at least one prospective apprentice out of the market.

Note that in this setting shifts in the aggregate demand for apprenticeships are caused by variation in the value of v_i,t . The main potential economic demand shifter is technological changes in the relevant sector; for example, technological improvements raise the expected earnings from the specific trade thus raising demand. It is important to stress that the actual diffusion of the innovation (which may take years) is less relevant than the knowledge of the new technique has arrived. Informed people will anticipate its diffusion and thus adjust their demand for apprenticeship accordingly. Another possible demand shifter is health; for instance, deterioration in the health of prospective apprentices is likely to reduce their expected earnings (and a shortening of the period in which they have higher earnings) and as a result cause a decrease in the demand for apprenticeships.

The equilibrium of this Marshallian model is conveniently depicted by Figure 1.Footnote ¹⁹ Let us assume the initial position of the market is some steady state (point A). Technological change will normally cause the demand curve for skills to shift to the right.Footnote ²⁰ Since there is no change initially in the level of apprenticeship contracts given that capital is predetermined (that is, capacity is constrained), we will move to point B.

Note: Curve S' represents the supply curve that corresponds to the subsequent period after the demand shock takes place; S is the supply curve that corresponds to the long run. The demand curve shifts rightward from curve D0 to D1. Point A represents the initial steady state, point B is where the equilibrium will be immediately after shock, point C is where the equilibrium will be one period after the shock, and point E is the new steady state.

Figure 1 The Dynamics of the Apprenticeship Market Following a Demand Shock

In the following period the new equilibrium will be to the right of the initial one reflecting both a higher tuition level as well as a higher quantity of apprenticeships, putting the market equilibrium at point C. Subsequently the number of apprenticeship contracts will gradually rise along the new demand curve until reaching the new steady state of point E. The figure demonstrates our notion of efficiency in the context of this shift in demand and movement along the supply curve. A bigger increase in the long-term quantity of apprenticeships was highly important for economic growth. An elastic supply of skills meant not only that the total national “stock” of skilled labor could increase, but that its composition could change relatively rapidly, adapting the distribution of skills to the needs of the changing economy.

Empirical Analysis

Descriptive Statistics

Summary statistics for the number of apprentices and the tuitions in our various occupations are displayed in Appendix Table 1a. As the table shows the average number of new apprentices in every occupation per year were 36.7 and the tuition 27.1 pounds. The number of new apprentices was obviously larger in more common occupations, including for example, house carpenters (174.2), tailors (173.4), shoe-makers (284), bakers (82.6), butchers (95.5), and weavers (99.5) and the tuition was higher in certain occupations with various barriers to entry such as lawyers (108.5 pounds), surgeons (70.7 pounds), merchants (75.4 pounds), and brewers (77 pounds).

Feldman and van der Beek (Reference Feldman and van der Beek2016) have shown that the number of new apprenticeships increased in response to inventions in the years 1710–1772, with the strongest increase being in among carpenters and machine making occupations, which were most strongly affected by technological changes.Footnote ²⁷ What we are interested in in this article, is the response of tuitions. Figure 2–Figure 3 illustrate the number of new apprenticeships and the level of nominal and real tuitions relative to their level in the years 1710–1720 (in average) in various occupations, grouped by larger occupational categories. The figures indicate that apprenticeship tuition levels remained stable in the long run. Tuitions responded moderately to changes in the annual number of new apprenticeships in the short run but always returned to their equilibrium level.Footnote ²⁸ This feature, which will be shown to be statistically significant in the econometric analysis, suggests a high level of elasticity of the supply side of the apprenticeships system in this period, and was characteristic of almost all the occupations. Figure 2 depicts the changes in the aggregate number of new apprenticeships. As the figure shows, there were no major shocks to the number of apprenticeships at this level as the main changes were in the occupational distribution of apprenticeships rather than on their total number.

Notes: 10-year moving average. Sources: The Stamp Tax Registers

Figure 2 Aggregate number of new apprentices and tuition levels: 1710–1805

As can also be observed in Figure 2, there are some serious drops in the number of entries in the registers, in both series (“City” and “Country”), in the years 1726–1740, and more moderate falls in the years 1745–1751. These falls in the number of entries seem to be partly due to register losses but since they become more frequent in years of high death rates which were mainly caused by bad harvests and smallpox outbreaks as identified by E. A. Wrigley and R. S. (Schofield Reference Wrigley and Schofield1981, p. 162), they may also represent a real decrease in the number of apprenticeship contracts.Footnote ²⁹ Since the exact reason for these strong declines in the number of entries is unknown, we concentrated on controlling for the possible effects they may have on our results, dropping years with small numbers of entries and controlling for changes in the composition of entries from “City” and “Country” registers, as will be explained in what follows. We also examine the effect of the drops on our results by estimating our model in periods that are not characterized by such drops in the number of entries (1750–1805) and obtain very similar estimates for the elasticity of supply of apprenticeship.Footnote ³⁰ In addition, we include a variable that measures the ratio of entries from London relative to Country to capture possible effects of changes in the composition of entries that are not constant over time due to drops in the number of entries in one of the series. We also use annual death rates and the log of the population of the 15–24 year olds (the relevant age for apprenticeships) to instrument for the number of apprentices given the simultaneous relationship between this variable and tuitions, as we will be discussing more extensively in the next section.Footnote ³¹

Notes: 10-year moving average. Sources: The Stamp Tax Registers.

Figure 3 Number of new apprentices and tuition levels by occupation: 1710–1805

Figure 3 displays the same variables in various occupational groups. It is clear from this figure that both in occupations in which the number of new apprenticeships remains almost unchanged and in those in which they increased significantly as in machine making, carpenters, building, and leather production, real tuitions seem to have responded moderately and remain unchanged in the long-run. The number of new apprenticeships in machine making, carpenters, building, and leather production occupations increased by 50–150 percent in the mid-eighteenth century and yet real tuitions remain stable in the long run. The only case in which we observe a significant and ongoing increase in real tuitions is in the services sector, which includes a very heterogeneous group of occupations including physicians and lawyers, occupations that were changing quite drastically in the eighteenth century.

In the case of apprenticeship in the machine making occupations, the number of new apprenticeships increased by more than 200 percent in the 1750s while tuitions increased by less than 20 percent and returned to their initial level. Similarly, the number of apprenticeships to carpenters and joiners increased by nearly the same percent while tuitions increased by about 30 percent until the 1760s when real tuitions declined and returned to their initial level in the end of the period. In the case of the building trades and the leather products trades, again, the number of apprenticeships increased by 150–200 percent, tuitions responded moderately and real tuitions soon returned to their initial level. In all these cases there was a long-run increase in nominal tuitions.

These figures reflect very clearly the high level of flexibility of the supply in this market and its capacity of absorbing strong changes in demand for skill acquisition. In the next section, we provide more formal econometric evidence for this claim.

Instrumental Variables (IV) Regression Analysis

We now turn to the analysis of the elasticity of the tuition payments with respect to the number of apprenticeships:

(7)

where each observation represents an occupation i (in London/Country) in year t.Footnote ³² Our dependent variable of interest is the logarithm of the tuition of occupation i in year t, ln(tuition_i,t ). The lagged value of this variable is included on the right-hand side to capture the persistence in tuitions.Footnote ³³ The X matrix contains a set of covariates: CPI, the logarithm of unskilled wages (the wages of day laborers) and the logarithm of the number of war recruits, the percent of observations from London, and a linear time trend.Footnote ³⁴ All the covariates in X vary only over time.Footnote ³⁵ The parameter γ_i denotes a full set of London_occupational effects, which capture common shocks to tuitions of all occupations, and, ∊_i is an error term, capturing all other omitted factors. Our main variable of interest, ln(apprentices_i,t ), is the number of new apprentices in occupation i in year t. The parameter β₁ therefore, measures the elasticity of tuition with respect to the number of apprentices and the reciprocal of the standard elasticity of supply. However, β₁ cannot be consistently estimated using OLS since, as is typical when studying demand and supply, prices and quantities are mutually determined and observed in equilibrium. We therefore use an Instrumental Variable approach.Footnote ³⁶

In what follows, we propose death rates and the size of youth population (in logarithm) as instruments for the number of new apprentices. Apprentices were usually bound at the age of 14 and their number was affected by changes in the size of their cohort. One of the important factors that affected the size of cohorts in eighteenth century England was outbreaks of smallpox, which mostly affected children in the ages of 0–10.

According to Romola Davenport, Leonard Schwarz, and Jeremy Boulton (2011) smallpox was the single most lethal cause of death in the eighteenth century, accounting for 6–10 percent of all burials. More importantly, although the knowledge of the geography of smallpox epidemics and mortality in eighteenth century England remains extremely fragmentary, smallpox was a childhood disease. For example, in London in 1752–1766 almost 80 percent of the deaths from smallpox were amongst children between the ages of 0 and 10 (about 70 percent amongst children between 0 and 4), and in 1775–1799, 94.2 percent (about 85 percent between 0 and 4).Footnote ³⁷ In Kilmarnock, Scotland, 94 percent of smallpox victims between 1728 and 1763 were aged under seven, and in Manchester only one adult (aged over 10) was recorded as dying, of 589 smallpox victims in the period 1769–1774.Footnote ³⁸ Changes in death rates can therefore be assumed to have had a stronger effect on the demand for apprenticeships (availability of children and willingness to send them to cities where smallpox hit harder) than on the supply of apprenticeships (supply of masters). Figure 4 illustrates the correlation between the number of apprentices and death rates, mainly when we look at the five year lag which was chosen to capture the high death rates from smallpox of children aged 0–10, about five years before becoming apprentices. As the first stage Angrist-Pischke F statistics of weak identification in our regressions show, these IVs are strongly correlated with the number of new apprentices.

Sources: The number of apprentices is from the Stamp Tax Registers; for death rates see footnote 25.

Figure 4 Death Rates and the Number of New Apprenticeships

Note that since our instruments and all the covariates in X vary only over time and not over occupation, we cannot add time fixed effects to regressions where these covariates are included.Footnote ³⁹ Nevertheless, as the results in columns (2) and (3) of Table 1a show, the covariates manage to capture most of the variation over time and are as good as using year fixed effects. As previously mentioned we control for changes in the composition of entries from “City” and “Country” registers in the analysis by adding the ratio of observations from “City” (Percent_London).

Table 1a OLS and IV estimates of the elasticity of tuitions with respect to the number of apprentices

Significant at 10 percent level.

Significant at 5 percent level.

Significant at 1 percent level.

Notes:

Dependent variable in second stage is the logarithm of tuitions. Columns (2)–(4) report the results of OLS regressions with fixed effects on the London-occupation level, with standard errors clustered at the year and occupation level. Columns (5)–(7) report IV regression results. The regression in column (7) does not control for the changes in the composition of the observation (the variable Percent_London) nor are the years with low numbers of observations dropped. F-statistic for excluded instruments gives the Angrist-Pischke statistic. The null hypothesis is rejected at the 1 percent level in all cases. See Appendix Table 1b for variable definitions. Standard errors in parentheses.

Column (1) in Table 1a presents the pooled OLS relationship between tuitions and the number of new apprentices. The elasticity of tuitions with respect to the number of new apprentices is statistically significant at the 1-percent level (all the standard errors are robust for arbitrary heteroscedasticity and clustering of the standard errors at the year and occupational level). The estimated elasticity increases when we add the London_occupation fixed effects. The estimate of β₁ in column (2) is 0.08 with a standard error of 0.008. If causal, this estimate would imply that a percentage increase in the number of apprentices increased tuitions by 0.08 percentage points. Column (3) is identical to column (2) except for the year fixed effects which are replaced by the set of time varying covariates in X. The estimate of β ₁ is very similar (0.088), suggesting that our covariates capture most of the annual common shocks to tuitions. The effects of the control variables on the tuitions are all as expected with an elasticity of 0.1 of tuitions with respect to prices. The coefficient estimate of the labor's nominal wages is not statistically significant due to the high degree of colinearity between wages and prices. It becomes significant at the 1-percent level once prices are dropped. The results remain practically unchanged when the lagged dependent variable is omitted as presented in column (4).

Since the number of apprentices is simultaneously determined and therefore endogenous, the estimates of β ₁ in columns (1)–(4) are not consistent. Columns (5) and (6) present the two-stage least-squares estimate of β ₁ which is now consistently estimated and is, as expected in cases of simultaneity, higher at the level of 0.2 in the dynamic setting in column (5) and 0.19 when we drop the lagged dependent variable in column (6). The results in column (7) are obtained after including all the years in the data without restricting for the annual number of entries and after dropping the variable Percent_London that we use to control for possible effects of the sharp declines in the number of entries in the data. The resulting estimate of β ₁ in this case is much lower (0.047) and not significant. Panel B presents the first stage results for the regressions in columns (5)–(7). Our instrumental variables are shown to be highly correlated with the number of apprentices and, as the Angrist-Pischke F-statistic shows, the null hypothesis that the equation is weakly identified is rejected.Footnote ⁴⁰

Table 1b presents our robustness checks to the two-stage least-squares estimates obtained in Table 1a. To test whether the results are mainly representative of apprenticeship in London, we run separate regressions for London and Country. The results in columns (1) and (2) show that tuitions in London responded more strongly to changes in the number of apprentices (a 0.39 estimated elasticity for London vs. 0.16 in the Country), yet, elasticities are still small and significantly lower than unity. This is an interesting result which may be interpreted as reflecting the stronger presence of guilds in London. Moreover, it may be reflecting London's concentration of apprenticeships to occupations with strong guilds (e.g., pewteres and goldsmiths) and with high entry costs (e.g., high setting up costs, prestiege), such as rich merchants and attorneys.

Table 1b The elasticity of tuitions with respect to the number of apprentices: robustness checks

Significant at 10 percent level.

Significant at 5 percent level.

Significant at 1 percent level.

Notes:

Dependent variable in the second stage is the logarithm of tuitions. All regressions are IV 2SLS regressions with fixed effects on the London-occupation level, with standard errors clustered at the year and occupation level. The specification of the regressions is the same as in coumn (6) of Table 1a but uses only observations from London (column (1)), only observations from the Country (column (2)), only observations from the years after 1750 (column (3)), columns (4)–(5) break the results of the two sub-periods: 1710–1770 (column (4)) and 1770–1805 (column (5)). In column (6), we omit the years of the Napoleonic wars (from 1792) and the column (7), we omit the occupational group machines. F-statistic for excluded instruments gives the Angrist-Pischke statistic. The null hypothesis is rejected at the 1 percent level in all cases. See Appendix Table 1a for variable definitions. Standard errors in parentheses.

The regression in column (3) tests whether the estimates depend on the strong variation in the number of apprentices during the first half of the century, in which there are strong falls in the number of entries, by dropping the years 1710–1750 and shows this not to be the case. Columns (4)–(5) test for structural change examining whether the estimated elasticity changes throughout the period and present a moderate increase in the response of tuitions during the later part of the century, with an estimated elasticity of 0.16 between 1730 and 1770 and 0.24 between 1770 and 1805. The results of an estimation excluding the years of the Napoleonic wars between France and Britain are presented in column (6) and column (7) presents the estimation excluding occupations related to machine making (the occupational group machines in Appendix Table 1). In both cases the estimated elasticity of tuitions with respect to the number of apprentices is low and significant (0.12 and 0.2, respectively).

To test whether the estimated elasticities that we obtain vary across occupational groups we re-estimated our baseline regression from column (6) of Table 1a with the addition of an interaction term between the number of apprentices and a dummy variable representing the occupational category. The interaction of our two instruments with the same dummy variable was used to instrument for the additional endogenous variable. Table 2 presents the two-stage least-squares estimates for the elasticity of the tuition in the 13 occupational groups which include machinery, carpenters, building, shipbuilding, clothing, leather, wood, yarn, metal, victualing, services, trade, and other trades.Footnote ⁴¹ It is interesting to note that in almost all occupational categories we find no significance of the interaction term, implying that there is no significant difference in the elasticities between the different groups. The estimated elasticity in the leather and wood categories came out significantly different than the average, however this should be interpreted with caution as the probability of obtaining sigificant results for 2 out of 13 by chance is high and there is no apriori reason to expect different results in these two groups.Footnote ⁴² This does not mean however that there were no differences in elasticities within groups, between the occupations composing them.

Table 2 The elasticity of tuitions with respect to the number of apprentices: various occupational groups

Significant at 10 percent level.

Significant at 5 percent level.

Significant at 1 percent level.

Notes:

Dependent variable in the second stage is the logarithm of tuitions. All regressions are IV 2SLS regressions with fixed-effects on the London-occupation level, with standard errors clustered at the year and occupation level. The specification of the regressions is the same as in column (6) of Table 1a with the addition of an interaction of our variable of interest, log(apprentices) with an occupational group (containing a number of occupations specified in Appendix Table 1b). F-statistic for excluded instruments gives the Angrist-Pischke statistic. The null hypothesis is rejected at the 1 percent level in all cases.

The regression analysis presented in this section leads us to two important conclusions. The first is that the supply of apprenticeships in eighteenth century England was highly elastic. The system of apprenticeship could absorb important changes in the demand, as was the case with machinery workers and carpenters, without a strong response of the tuition. Our second conclusion is that this capacity was representative of the system as a whole and did not vary significantly between trades, while demand for apprenticeship did vary with the nature of final demand and the shocks to technology.

IDENTIFYING DEMAND SHOCKS USING A VAR

We now employ a VAR to test the short-run and long-run response of both the number of apprentices and the tuition to technological changes, for which we use the innovation in the textile technology series.Footnote ⁴³ We perform the analysis in the aggregate level, as well as in specific occupational groups. The results are summarized in Table 3. The table shows the sectoral responses of the quantities and prices of apprenticeships to a one unit increase in textile technological innovations (that is, one more significant invention in the textile industry) from VARs that examine the impact of these innovations on sectoral apprenticeship quantity and tuition series.Footnote ⁴⁴

The response horizon reported in column 1 of the table is the number of years following the shock at which each peak quantity response is obtained; this is the horizon which corresponds to the reported quantity and tuition responses (columns 2 and 3, respectively). The table shows that the number of apprenticeships responded significantly to inventions in most occupational sectors, mainly in the sectors relevant to the inventions in this period, including, metalwork and leather that were directly required for machine construction, in yarn and clothing, in which production increased and in building (including carpenters), due to increase in construction. It can be seen that machinery demonstrated the largest quantity responses (65 percent). This is not surprising as this sector includes occupations that are highly skilled and directly relevant to the machinery production and maintenance and are therefore expected to be in demand when technological change take place.Footnote ⁴⁵ .

Table 3 Sectoral Responses and Implied Supply Elasticities Induced by a One Unit Increase in Textile Technological Innovations

Significant at 10 percent level.

Significant at 5 percent level.

Significant at 1 percent level.

Source: See text.

Notes:

The table shows the sectoral responses of the quantities and prices of apprenticeships to a one unit increase in textile technological innovations from VARs that include the textile technological innovations series along with sectoral apprenticeship quantity and tuition series. The response horizon reported in the first column is the number of years following the shock at which each peak quantity response is obtained; this is the horizon which corresponds to the reported quantity and tuition responses (columns 2 and 3, respectively). The fourth column reports the implied price elasticities, computed as the ratio of the tuition response to the quantity response.

Statistical significance results are based on Hall (Reference Hall1992) confidence bands generated from a residual based bootstrap procedure repeated 2,000 times.

Moreover, the evidence for the sectors for which there are statistically significant responses is consistent with our interpretation of the technology shocks as demand shocks: tuition levels rise considerably following all shocks, indicating that there is a strong shift in demand for apprenticeships that pushes prices up along with quantities. For example, tuitions in the metalwork, building trades, and clothing and upholstery rise by 15.6, 7.2, and 16.2 percent, respectively.

The fourth column of the table reports the implied price elasticities, computed as the ratio of the tuition response to the quantity response. By and large, we can see that the elasticity of prices was sufficiently low so as to allow for quantities to rise considerable following the technology shock. These results are broadly consistent with those presented in Table 1a and it is encouraging that despite the very different methodologies employed the order of magnitude of the estimated (inverse) supply elasticity of 0.2 reported in column 5 of Table 1a, is quite similar to the sectoral elasticities obtained by the VAR analysis and reported in column 4 of Table 3. Note that the elasticities computed in column 4 of Table 3 are not the same parameter as those estimated in Table 1a; the latter are the marginal elasticities, whereas the former can be viewed as the accumulated elasticities over a particular number of years. Notwithstanding this difference, it is encouraging that these two types of estimated elasticities are broadly similar. Both point to a highly elastic supply curve of skills, and thus indicate a high degree of adaptability of the economy to technological shocks.

We now examine the dynamics of tuition and apprenticeship quantities following the technology shocks. Towards this end, we also present the estimated impulse responses for the aggregate apprenticeship quantity and tuition series (Figure 5) as well as for the instrument and machines sector and the carpenters and joiners sector (Figure 6 and Figure 7). We focus on these two sectors for conciseness reasons but also because these two sectors seem to be most sensitive to technology shocks exhibiting the largest quantity responses.

Note that the aggregate VAR is different from the sectoral VARs only in that aggregate quantity and price series are used instead of sectoral ones. Figure 5 depicts the estimated impulse responses of the textile technological innovations series and the aggregate apprenticeship quantity and tuition series to a positive one standard deviation unanticipated technology shock, along with the 5th and 95th percentile confidence bands. Turning first to the aggregate apprenticeship quantity series, it is evident that the impact response is overall statistically insignificant, after which the quantity rises in a hump-shaped manner peaking at 8.2 percent after four years. Following the technology shock, the number of inventions rises significantly on impact by 0.26 inventions, after which it exhibits a hump-shaped response that peaks after one year at 0.55 inventions. Moreover, the impact response of the aggregate tuition series is at first insignificant, but becomes significant after three years and peaks after 6 years reaching 2.7 percent.

Sources: See text.

Figure 5 Impulse Responses to a One Standard Deviation Technology Shock (Solid Lines): Overall Aggregate Economy

Figure 6 depicts the estimated impulse responses of the textile technological innovations series and the instrument and machinery apprenticeship quantity and tuition series to a positive one standard deviation unanticipated technology shock, along with the 5th and 95th percentile confidence bands. The number of inventions significantly rises in a hump-shaped manner peaking after four years at 0.55 inventions. The responses of the quantity and tuition series, however, are considerably stronger than those of the aggregate series. In particular, the quantity of apprenticeships rises by 10.6 percent on impact, after which it continues to increase peaking at 16.9 percent four years following the shock. The response is both and statistically and economically significant. The tuition series also exhibits a similar hump-shaped response, although it is smaller relative to the quantity series and only becomes significant after four years. The tuition peak response takes place after six years reaching 1.5 percent. Overall, it is apparent that the instruments and machinery apprenticeship market reacts in a significant manner to the technology shock.

Sources: See text.

Figure 6 Impulse Responses To A One Standard Deviation Technology Shock (Solid Lines): Instruments And Machinery Sector

Figure 7 depicts the estimated impulse responses of the textile technological innovations series and the carpenters apprenticeship quantity and tuition series to a positive one standard deviation unanticipated technology shock, along with the 5th and 95th percentile confidence bands. The responses of all variables are generally similar to those in Figure 6, although the tuition response is much stronger than the tuition response in the instruments and machinery sector, indicating a higher sensitivity of the level of tuition in the carpenters apprenticeship market relative to the instruments and machinery apprenticeship market. Moreover, the quantity response is both statistically significant as well as economically significant (the peak response of carpenters' apprenticeships is 15.1 percent and takes place after one year).

Sources: See text.

Figure 7 Impulse Responses To a One Standard Deviation Technology Shock (Solid Lines): Carpenters and Joiners

Table 4 Sectoral Responses and Implied Supply Elasticities Induced by a One Unit Increase in Patents

Significant at 10 percent level.

Significant at 5 percent level.

Significant at 1 percent level.

Sources: See text

The table shows the sectoral responses of the quantities and prices of apprenticeships to a one unit increase in the patent series from VARs that include the textile technological innovations series along with sectoral apprenticeship quantity and tuition series. The response horizon reported in the first column is the number of years following the shock at which each peak quantity and tuition responses (columns 2 and 3, respectively). The fourth column reports the implied price elasticities, computed as the ratio of the tuition response to the quantity response.

Statistical significance results are based on Hall (Reference Hall1992) confidence bands generated from a residual based bootstrap procedure repeated 2000 times.