Clans, Guilds, and Markets: Apprenticeship Institutions and Growth in the Preindustrial Economy

Clans, Guilds, and Markets: Apprenticeship Institutions and Growth in the Preindustrial Economy Abstract In the centuries leading up to the Industrial Revolution, Western Europe gradually pulled ahead of other world regions in terms of technological creativity, population growth, and income per capita. We argue that superior institutions for the creation and dissemination of productive knowledge help explain the European advantage. We build a model of technological progress in a preindustrial economy that emphasizes the person-to-person transmission of tacit knowledge. The young learn as apprentices from the old. Institutions such as the family, the clan, the guild, and the market organize who learns from whom. We argue that medieval European institutions such as guilds, and specific features such as journeymanship, can explain the rise of Europe relative to regions that relied on the transmission of knowledge within closed kinship systems (extended families or clans). JEL Codes: E02, J24, N10, N30, O33, O43. I. Introduction The intergenerational transmission of skills and more generally of “knowledge how” has been central to the functioning of all economies since the emergence of agriculture. Historically, this knowledge was almost entirely “tacit” knowledge, in the standard sense used today in the economics of knowledge literature (Cowan and Foray 1997, 71–73; Foray 2004, 96–98). Although economic historians have long recognized its importance for the functioning of the economy (Dunlop 1911, 1912), it is only more recently that tacit knowledge has been explicitly connected with the literature on human capital and its role in the Industrial Revolution and the emergence of modern economic growth (Humphries 2003, 2010; Kelly, Mokyr, and Ó Gráda 2014). The main mechanism through which tacit skills were transmitted across individuals was apprenticeship, a relation linking a skilled adult to a youngster whom he taught the trade. The literature on the economics of apprenticeship has focused on a number of topics we shall discuss in some detail below. Yet little has been done to analyze apprenticeship as a global phenomenon, organized in different modes. In this article, we examine the role of apprenticeship institutions in explaining economic growth in the preindustrial era. We build a model of technological progress that emphasizes the person-to-person transmission of tacit knowledge from the old to the young (as in Lucas 2009; Lucas and Moll 2014). Doing so allows us to go beyond the simplified representations of technological progress used in existing models of preindustrial growth, such as Galor (2011). In our setup, a key part is played by institutions—the family, the clan, the guild, and the market—that organize who learns from whom. We argue that the archetypes of modes of apprenticeship that we consider in the model, while abstract, can be mapped into actual institutions that were prevalent throughout history in different world regions. We use the theory to address a central question about preindustrial growth, namely, why Western Europe surpassed other regions in technological progress and growth in the centuries leading up to industrialization. What is at stake here is that while on the whole medieval Europe was not more advanced than China, India, or the Middle East, at some point before 1700 the seeds of Europe’s primacy were planted, even if they were not to come to full fruition until the Industrial Revolution after 1750. These seeds were of many kinds, and here we will concentrate on one kind only, namely, artisanal skills. In particular, we claim that late medieval and early modern European institutions such as guilds, with specific regulatory features such as apprenticeship and journeymanship, were critical in speeding up the dissemination of new productive knowledge in Europe, compared to regions that relied on the transmission of knowledge within extended families or clans.1 After 1500, many decades before the Industrial Revolution, we can readily observe major advances in European craft production in products as diverse as shipbuilding, textiles, lensgrinding, metalworking, printing, mining, clockmaking, millwrighting, carpentry, ceramics, painting, and so on. Before 1700, few if any of those improvements had much to do with formal codified knowledge; they derived first and foremost from improved artisanal skills—which historians have called “mindful hands” (Roberts and Schaffer 2007)—that disseminated rapidly. Before developing a theory of the modes of institutional organization of apprenticeship and their implications for knowledge dissemination, we address three key issues one should address in modeling. First, the main issue is the extent to which the mode of organizing the transmission of skills was consistent with technological progress. We take the view from the outset that all systems of apprenticeship are consistent with at least some degree of progress. Even when the system has strong conservative elements that administer rigid tests on the existing procedures and techniques, learning by doing generates a certain cumulative drift over time that can raise productivity, even in the most conservative systems. That said, the rates at which innovation occurred within artisanal systems have differed dramatically over time, over different societies and even between different products. Differences in rates of technological progress may in principle have two different sources, namely, the rate of original innovation and the speed of the dissemination of existing ideas. While we discuss implications for original innovation, our theoretical analysis focuses on the second channel. Specifically, we ask how conducive the intergenerational transmission mechanism was to the dissemination of best-practice techniques, and how conducive an apprenticeship system based on personal contacts and mostly local networks was to closing gaps between best-practice and average-practice techniques. Second, the training contract between master and apprentice (whether formal or implicit), for obvious reasons, represents a complicated transaction. For one thing, unless that transmission occurs within the nuclear family (in a father-son line), the person negotiating the transaction is not the subject of the contract himself but his parents, raising inevitable agency problems. Moreover, the contract written with the “master” by its very nature is largely incomplete. The details of what is to be taught, how well, how fast, what tools and materials the pupil would be allowed to use, as well as other aspects such as room and board, are impossible to specify fully in advance. Equally, apart from a flat fee that many apprentices paid up front, the other services rendered by the apprentice, such as labor, were hard to enumerate. This was, in a word, an archetypical incomplete contract. As a consequence, in our theoretical analysis moral hazard in the master-apprentice relationship is the central element that creates a need for institutions to organize the transmission of knowledge. Third, as a result of the contractual problems in writing an apprenticeship agreement, a variety of institutional setups for supervising and arbitrating the apprentice-master relations can be found in the past. In all cases except direct parent-child relationships, some kind of enforcement mechanism was required. Basically three types of institutions can be discerned that enforced contracts and, as a result, ended up regulating the industry in some form. They were (i) informal institutions, based on reputation and trust; (ii) nonstate semiformal institutions (guilds, local authorities such as the Dutch neringen); and (iii) third-party (state) enforcement, usually by local authorities and courts. In many places all three worked simultaneously and should be regarded as complements, but their relative importance varied quite a bit. In our theoretical analysis, we map the wide variety of historical institutions into four archetypes, namely the (nuclear) family, the clan (i.e., a trust-based institution comprising an extended family), the guild (a semiformal institution), and the market (which constitutes formal contract enforcement by a third party). Our theoretical model builds on a recent literature in the theory of economic growth that puts the spotlight on the dissemination of knowledge through the interpersonal exchange of ideas.2 Given our focus on preindustrial growth, the analysis is carried out in a Malthusian setting with endogenous population growth in which the factors of production are the fixed factor land and the supply of effective labor by workers (“craftsmen”) in a variety of trades. Knowledge is represented as the efficiency with which craftsmen perform tasks. While there is some scope for new innovation, the main engine of technological progress is the transmission of productive knowledge from old to young workers. Young workers learn from elders through a form of apprenticeship. There is a distribution of knowledge (or productivity) across workers, and when young workers learn from multiple old workers, they can adopt the best technique to which they have been exposed. Through this process, average productivity in the economy increases over time.3 The central features of our analysis are that the transmission of knowledge (teaching) requires effort on the part of the master; that this leads to a moral hazard problem in the master-apprentice relationship; and that, as a consequence, institutions that mitigate or eliminate the moral hazard problem are key determinants of the dissemination of knowledge and economic growth.4 The “family” in our analysis is the polar case where no enforcement mechanism is available that reaches beyond the nuclear family, and hence children learn only from their own parents. In the family equilibrium, there is still some technological progress due to experimentation with new ideas and innovation within the family, but there is no dissemination of knowledge, and hence the rate of technological progress is low. The “clan” is an extended family where reputation and trust provide an informal enforcement mechanism. Hence, children can become apprentices of members of the clan other than their own parent (such as uncles). The clan equilibrium leads to faster technological progress compared to the family equilibrium, because productive new ideas disseminate within each clan. The “guild” in our model is a coalition of all the masters in a given trade that provides a semiformal enforcement mechanism, but also regulates (monopolizes) apprenticeship within the trade. Finally, the “market” is a formal enforcement institution where an outside authority (such as the state) enforces contracts, and in addition, rules are in place that prevent anticompetitive behavior (such as limitations on the supply of apprenticeship imposed by guilds). In terms of mapping the model into historical institutions, we regard most world regions (in particular, China, India, and the Middle East) as being characterized by the clan equilibrium throughout the preindustrial era. Here extended families organized most aspects of economic life, including the transmission of skills between generations. The distinctive features of Western Europe are a much larger role of the nuclear family from the first centuries of the Common Era; little significance of extended families; and an increasing relevance of institutions that do not rely on family ties (such as cities and indeed guilds) starting in the Middle Ages. Hence, in the language of the model, we view Western Europe as undergoing a transition from the family to the guild equilibrium during the Middle Ages, and onward to the market equilibrium in the centuries leading up to the Industrial Revolution. To explain the emerging primacy of Western Europe over other world regions, we look to the comparative growth performance of the clan and guild institutions. Both the clan and the guild provided for apprenticeship outside the nuclear family, and a count against the guild is the anticompetitive nature of guilds, that is, the possibility that guilds limited access to apprenticeship to raise prices. However, our analysis identifies a much more important force that explains why the Western European system of knowledge acquisition came to dominate. Namely, apprenticeship within guilds was independent of family ties, and thus allowed for dissemination of knowledge in the entire economy, whereas in a clan-based system the dissemination of knowledge was impaired. A different side of the same coin is that in a clan-based system, relatively little is gained by learning from multiple elders, because given that these elders belong to the same clan, they are likely to have received the same training and thus to have very similar knowledge. In contrast, in a guild (and also in the market) family ties do not limit apprenticeship, and hence the young can sample from a much wider variety of knowledge, implying that apprenticeship is more productive and knowledge disseminates more quickly. The historical evidence shows that, indeed, in Europe master and apprentice were far less likely to be related to each other than elsewhere. Moreover, the guild system sometimes included specific features, in particular journeymanship, that had the effect of providing access to a broader range of knowledge and fostering the spread of new techniques and ideas. In a narrower system based on blood relationships, such a wide exchange of ideas was not feasible. Our framework can also be used to explore why institutional change (i.e., the adoption of guilds and, later on, the market) took place in Europe, but not elsewhere. If adopting new institutions is costly, the incentive to adopt will be lower when the initial economic system is relatively more successful, that is, in a clan-based economy compared to a family-based economy. If the cost of adopting new institutions declines with population density, it is possible that new institutions will only be adopted if the economy starts out in the family equilibrium, but not if the clan equilibrium is the initial condition. We also discuss complementary mechanisms (going beyond the formal model) that are likely to have contributed to faster institutional change in Europe. The article engages three recent literatures in economic history that have received considerable attention. One is the debate over whether craft guilds were on balance a hindrance to technological progress, or whether they stimulated it by supporting apprenticeship relations (for a recent summary, see van Zanden and Prak 2013b and Ogilvie 2004). The second new literature is the one emphasizing the ingenuity of artisans and skilled workers in generating knowledge, and minimizing the classic distinction between formal science and practical knowledge. Roberts and Schaffer stress the importance of “local technological projects” carried out by the “tacit genius of on-the-spot practitioners”; here they clearly refer to thoughtful and well-trained artisans who advance the frontiers of useful knowledge (Roberts and Schaffer 2007; see also Long 2011). Little in this literature, however, has focused on the intergenerational transmission of the knowledge embedded in such “mindful hands” through the institutions of apprenticeship. The third literature is concerned with understanding economic, institutional, and cultural differences between Europe and other world regions as a source of the relative rise of Europe and decline of other regions in the centuries leading up to the Industrial Revolution (e.g., Voigtländer and Voth 2013a, 2013b; Broadberry 2015). We build in particular on the work by Greif and Tabellini (2017) on the role of clans in China versus “corporations” in Europe (i.e., formal organizations that exist independently of family ties) for sustaining cooperation (see also Greif 2006; Greif, Iyigun, and Sasson 2012). However, Greif and Tabellini do not consider the implications of such institutions for the generation and dissemination of productive knowledge. The article is organized as follows. Section II describes key historical aspects of apprenticeship systems on which we base our theory. Our formal model of knowledge growth is described in Section III. Section IV analyzes the different apprenticeship institutions and derives their implications for economic growth. Section V quantifies the ability of the theory to account for the rise of European technological primacy, and considers endogenous adoption of institutions. Section VI concludes. Proofs for formal propositions, theoretical extensions, and a growth accounting exercise are provided in the Online Appendix. II. Historical Background II.A. Learning on the Shop Floor Through most of history, the acquisition of human capital took the form, in the felicitous phrase of De Munck and Soly (2007), of “learning on the shop floor.” One should not take this too literally: some skills had to be learned on board ships or at the bottom of coal mines. Yet it remains true that learning took place through personal contact between a designated “master” and his apprentice.5 As they point out (2007, 6), before the middle of the nineteenth century there were few alternative routes for acquiring useful productive skills. Some of the better schools, such as Britain’s dissenting academies or the drawing schools that emerged on the European continent around 1600, taught, in addition to the three Rs, some useful skills such as draftmanship, chemistry, and geography. But on the whole, the one-on-one learning process was the one experienced by most.6 The economics of apprenticeship in the premodern world is based on the insight that each master artisan basically produced a set of two connected outputs: a commodity or service, and new craftsmen. In other words, he sold “human capital.” The economics of such a setup explains many of the historical features of the system. The best known, of course, is that the apprentice had to supply labor services to the master in partial payment for his training and his room and board. In some instances, this component became so large that the apprentice contract was more of a labor contract than a training arrangement.7 Such provisions underline the basic idea of joint production, in which the two activities—production and training—were strongly complementary. As Humphries (2003) has pointed out, the contract between the master and the apprentice in any institutional setting is problematic in two ways. First, the flows of the services transacted for is nonsynchronic (although the exact timing differed from occupation to occupation). Second, these flows cannot be fully specified ex ante or observed ex post. The apprentice, by the very nature of the teaching process, is not in a position to assess adequately whether he has received what he has paid for until the contract is terminated. Even if the apprentice himself could observe the implementation of the contract, the details would be unverifiable for third parties and adjudicators. Because the transaction is not repeated, the party who receives the services or payment first has an incentive to shirk. This is known ex ante, and therefore it is possible that the transaction does not take place and that the economy would suffer from serious underproduction of training.8 However, since that would mean that intergenerational transmission of knowledge would take place exclusively within families, some societies have come up with institutions that allowed the contracts to be enforced between unrelated parties. These institutions curbed opportunistic behavior in different ways, but they all required some kind of credible punishment. As we will see in our theoretical analysis below, the more sophisticated and effective institutions led to better quality of training (in a precise manner we will define) and thus led to faster technological progress. II.B. Apprenticeship in Western Europe The evidence suggests that at least in early modern Europe the market for apprenticeship functioned reasonably well, despite the obvious dangers of market failure. A good indicator of the working of the market for human capital, at least in Britain, was the premium that parents paid to a master. Occupations that demanded more skill and promised higher lifetime earnings commanded higher premiums. The differences in premiums meant that this market worked, in the sense that the apprenticeship premium seems to have varied positively with the expected profitability and prestige of the chosen occupation (Brooks 1994, 60). As noted by Minns and Wallis (2013), the premium paid was not a full payment equal to the present value of the training plus room and board, which usually were much higher than the upfront premium. The rest normally was paid in kind with the labor provided by the apprentice. The premium served more than one purpose. In part, it was to insure the master against the risk of an early departure of the apprentice. But in part it reflected also the quality of the training and the cost to the master, as well as its scarcity value (Minns and Wallis 2013, 340). More recently, it has been shown that the premium worked as a market price reflecting rising and falling demand for certain occupations resulting from technological shocks (Ben Zeev, Mokyr, and Van Der Beek 2017). It is telling that not all apprentices paid the premiums: whereas 74% of engravers in London paid a premium in London, only 17% of blacksmiths did (Minns and Wallis 2013, 344). If an impecunious apprentice could not pay, he had the option of committing to a longer indenture, as was the case in seventeenth-century Vienna (Steidl 2007, 143). In eighteenth-century Augsburg a telling example is that a “big strong man was often taken on without having to pay any apprenticeship premium, whereas a small weak man would have to pay more.” It is also recorded that apprentices with poor parents who could not afford the premium would end up being trained by a master who did inferior work (Reith 2007, 183). This market worked in sophisticated ways, and it is clear that human capital was recognized to be a valuable commodity. The formal contract signed by the apprentice in the seventeenth century included a commitment to protect the master’s secrets and not to abscond, as well as not to commit fornication (Smith 1973, 150). The precise operation of apprenticeship varied a great deal. The duration of the contract depended above all on the complexity of the trade to be learned, but also on the age at which youngsters started their apprenticeship. On the continent three to four years seems to have been the norm (De Munck and Soly 2007, 18). As would perhaps be expected, there is evidence that the duration of contracts grew over the centuries as techniques became more complex and the division of labor more specialized as a result of technological progress (Reith 2007, 183). To what extent was the master-apprentice contract actually enforced? Historians have found that often contracts were not completed (De Munck and Soly 2007, 10). Wallis (2008, 839–40) has shown that in late seventeenth-century London a substantial number of apprentices left their original master before completing the seven mandated years of their apprenticeship. The main reason was that the rigid seven-year duration stipulated by the 1562 Statute of Artificers (which regulated apprenticeship) was rarely enforced, as were most other stipulations contained in that law (Dunlop 1911, 1912).9 As Wallis (2008, 854) remarks, “like many other areas of premodern regulation, the tidy hierarchy of the seven-year apprenticeship leading to mastery was more ideal than reality.” Rather than an indication of contractual failure, the large number of apprentices that did not “complete” their terms indicates a greater flexibility in Britain. The number of lawsuits filed against such apprentices was not large (Rushton 1991, 94), and London court records indicate that apprentices wishing to be released from their masters could do so fairly easily in the Lord Mayor’s Court (Wallis 2012). Wallis notes that about 5% of all indentures ended up in this court (2012, 816). It seems that many of the early departures were by mutual consent (see also Wallis 2008, 844). To protect themselves against an early departure, many masters in England demanded and received a lump-sum upfront tuition payment from the parents or guardian of the youngster (Minns and Wallis 2013; Ben Zeev et al. 2017). The flexibility of the contracts in preindustrial England limited the risk each contracting party faced from the opportunistic behavior of the other. This institution, then, would be more successful in terms of transmitting existing skills between generations in an efficient manner. Once an apprentice had mastered a skill, there would be little point in staying on. Moreover, in many documented cases apprentices were “turned over” to another master—by some calculation this was true of 22% of all apprentices who did not complete their term (Wallis 2008, 842–43). There could be many reasons for this, of course, including the master falling sick or being otherwise indisposed. But also, at least some apprentices might have found that their master did not teach them best practice techniques or that the trade they were learning was not as remunerative as some other. The exact mechanics of the skill transmission process are hard to nail down. After all, the knowledge being taught was tacit, and mostly consisted of imitation and learning-by-doing. It surely differed a great deal from occupation to occupation. Moreover, our own knowledge is biased to some extent by the better availability of more recent sources. All the same, Steffens (2001) has suggested that much of the learning occurred through apprentices “stealing with their eyes” (131)—meaning that they learned mostly through observation, imitation, and experimentation. The tasks to which apprentices were put at first, insofar that they can be documented at all, seem to have consisted of rather menial assignments such as making deliveries, cleaning, and guarding the shop. Only at a later stage would an apprentice be trusted with more sensitive tasks involving valued customers and expensive raw materials (Lane 1996, 77). Yet they spent most of their waking hours in the presence of the master and possibly more experienced apprentices and journeymen, and as they aged they gradually would be trusted with more advanced tasks.10 One of the most interesting findings of the new research on apprenticeship, which is central to the theory developed below, is that in Europe family ties were relatively less important than elsewhere in the world, such as India (Roy 2013, 71, 77). In China, guilds existed11 but were organized along clan lines, and it is within those boundaries that apprenticeship took place (Moll-Murata 2013, 234). In contrast, Europeans came to organize themselves along professional lines without the dependence on kinship (Lucassen, de Moor, and van Zanden 2008, 16). Comparing China and Europe, van Zanden and Prak (2013a) write: “In China, training was provided by relatives, and hence a narrow group of experts, instead of the much wider training opportunities provided by many European guilds.” The contrast between Asia and Europe in systems of knowledge transmission is also emphasized by van Zanden (2009): We can distinguish two different ways to organize such training: in large parts of the world the family or the clan played a central role, and skills were transferred from fathers to sons or other members of the (extended) family. In fact, in parts of Asia, being a craftsman was largely hereditary ... In contrast to the relatively closed systems in which the family played a central role, Western Europe had a formal system of apprenticeship—organized by guilds or similar institutions—and in principle open to all. In China, young men were specifically selected and ordered by their families to apprentice with another lineage member. Such apprenticeship relations were routinely formed across patrilines and even branches (Rowe 1990, 75). In Western Europe, despite the fact that within the guilds the sons of masters received preferential treatment and that training with a relative resolved to a large extent the contractual problems, following in the footsteps of the parents gradually fell out of favor (Epstein and Prak 2008, 10). The examples of Johann Sebastian Bach and Leopold Mozart notwithstanding, fewer and fewer boys were trained by their fathers. By the seventeenth century, apprentices who were trained by relatives were a distinct minority, estimated in London to be somewhere between 7% and 28% (Leunig, Minns, and Wallis 2011, 42). Prak (2013, 153) has calculated that in the bricklaying industry, less than 10% continued their fathers’ trades. This may have been a decisive factor in the evolution of apprenticeship as a market phenomenon in Europe but not elsewhere.12 II.C. Mobility and the Diffusion of Knowledge In premodern Europe, as early as fifteenth-century Flanders, artisans were mobile. In England, such mobility was particularly pronounced (Leunig, Minns, and Wallis 2011), with lads from all over Britain seeking to apprentice in London, not least of all the young James Watt and Joseph Whitworth, two heroes of the Industrial Revolution. But as Stabel (2007, 159) notes, towns and their guilds had to accept and acknowledge skills acquired elsewhere, even if they insisted that newcomers adapt to local economic standards set by the guilds. Constraints were more pronounced on the continent, but even here apprentices came to urban centers from smaller towns or rural regions (De Munck and Soly 2007, 17), and mobility of artisans and the skills they carried with them extended to all of Europe. The idea of the “journeyman” or “traveling companion” was that after completing their training, new artisans would travel to another city to acquire additional skills before they would qualify as masters—much like postdoctoral students today (Leeson 1979; Lis, Soly, and Mitzman 1994). As such, journeymanship was traditionally the “intermediate stage” between completing an apprenticeship and starting off as a full-fledged master. Journeymen and apprentices are known to have traveled extensively as early as the fourteenth century, often on a seasonal basis, a practice known as “tramping.” By the early modern period, this practice was fully institutionalized in Central Europe (Epstein 2013, 59). Itinerant journeymen, Epstein argues, learned a variety of techniques practiced in different regions and were instrumental in spreading best-practice techniques. Towns that believed themselves to enjoy technological superiority forbade the practice of tramping and made apprentices swear not to practice their trades anywhere else, as with Nuremberg metal workers and Venetian glassmakers (Epstein 2013, 60–61). Such prohibitions were ineffective at best and counterproductive at worst. Not every apprentice had to go through journeymanship, and relatively little is known about how long it lasted and how it was contracted for. Journeymen have been regarded by much of the literature as employees of masters, and were often organized in compagnonnages, which frequently clashed with employers. Journeymen in many cases were highly skilled workers, but more mobile than masters. Known as “travelers” or “tramps,” they often chose to bypass the formal status of master but prided themselves on their skills, considering themselves “equal partners” to masters (Lis, Soly, and Mitzman 1994, 19). In Elizabethan England, the “number of surplus though fully apprenticed men forced to take the road clearly grew ... the custom of quizzing, registering and entertaining the stranger became more regularized” (Leeson 1979, 56). The letter of the 1562 Statute of Artificers was clearly intended to curtain mobility, but in practice these aspects of the statute were widely disregarded (Leeson 1979, 63–65). The mobility of journeymen lent itself to the creation of networks in the same lines of work, and it stands to reason that technical information flowed fairly freely along those channels of communication. Journeymen are relevant to our story for two reasons: first, because when working in a shop different from the one they were trained in, they were exposed to other skills after they completed their apprenticeship; and second, because the apprentices in the workshops in which they worked after completing their training could learn from them (and thus indirectly from the journeymen’s masters) in addition to their own masters (e.g., Unger 2013, 186). In this way they were an important component of how the European system of apprenticeship allowed learning from more than just one source. But skilled masters, too, traveled across Europe, often deliberately attracted by mercantilist states or local governments keen to promote their manufacturing industries through the recruitment of high-quality artisans. Technology diffusion occurred largely through the migration of skilled workers, or through apprentices traveling to learn from the most renowned masters (and then returning home). Interestingly, such migration seems to have focused mostly on towns in which the industry already existed and which were ready to upgrade their production techniques (Belfanti 2004, 581). II.D. Apprenticeship and Guilds In medieval and early modern Europe, where in most areas third-party enforcement of contracts was still quite weak, the guilds played a crucial role in making apprenticeship relations effective. As late as the eighteenth century, for French bakers, “the guild made the rules for apprenticeship and mediated relations between masters and apprentices ... it sought to impose a common discipline and code of conduct on masters as well as apprentices to ensure good order” (Kaplan 1996, 199). Where third-party enforcement was stronger, or where apprenticeship contracts could be enforced through informal institutions, this role of the guilds became less essential, and consequently market equilibria became more common. There has been a lively debate in the past two decades about the role of the guilds in premodern European economies. Traditionally relegated by an earlier literature to be a set of conservative, rent-seeking clubs, a revisionist literature has tried to rehabilitate craft guilds as agents of progress and technological innovation. Part of that storyline has been that guilds were instrumental in the smooth functioning of apprenticeships. As noted, given the potential for market failure due to incomplete contracts, incentive incompatibility, and poor information, agreements on intergenerational transmission of skills needed enforcement, regulation, and supervision. In a setting of weak political systems, the guilds stepped in and created a governance system that was functional and productive (Epstein and Prak 2008; Lucassen, de Moor, and van Zanden 2008; van Zanden and Prak 2013b). In a posthumously published essay, Epstein stated that the details of the apprenticeship contract had to be enforced through the craft guilds, which “overcame the externalities in human capital formation” by punishing both masters and apprentices who violated their contracts (Epstein 2013, 31–32). The argument has been criticized by Ogilvie (2014, 2016). Others, too, have found cases in which the nexus between guilds and apprenticeships proposed by Epstein and his followers does not quite hold up (Davids 2003, 2007). The reality is that some studies support Epstein’s view to some extent, and others do not. The heated polemics have made the more committed advocates of both positions state their arguments in more extreme terms than they can defend. Guilds were institutions that existed through many centuries, in hundreds of towns, and for many occupations. This three-dimensional matrix had a huge number of elements, and it stands to reason that things differed over time, place, and occupation. Most scholars find themselves somewhere in between. Guilds were at times hostile to innovation, especially in the seventeenth and eighteenth centuries, and under the pretext of protecting quality they collected exclusionary rents by longer apprenticeships and limited membership. But in some cases, such as the Venetian glass and silk industries, guilds encouraged innovation (Belfanti 2004, 576). Their attitude to training, similarly, differed a great deal over space and time. Davids (2013, 217), for instance, finds that in the Netherlands, “guilds normally did not intervene in the conditions, registration, or supervision of [apprenticeship] contracts.” Unger (2013, 203), after a meticulous survey, must conclude that the “precise role of guilds in the long term evolution of shipbuilding technology remains unclear.” Moll-Murata (2013, 256), in comparing the porcelain industries in the Netherlands and China, retreats to a position that “contrasting the guild rehabilitationist [Epstein’s] and the guild-critical positions is difficult to defend ... we find arguments supporting both propositions.” Guilds and apprenticeship overlapped, but they did not strictly require each other, especially not after 1600. Apprenticeship contracts could find alternative enforcement mechanisms to guilds. In the Netherlands local organizations named neringen were established by local government to regulate and supervise certain industries independently of the guilds. They set many of the terms of the apprenticeship contract, often the length of contract and other details (Davids 2007, 71). Even more strikingly, in Britain, most guilds gradually declined after 1600 and exercised little control over training procedures (Berlin 2008). Moreover, informal institutions and reputation mechanisms in many places helped make apprenticeship work even in the absence of guilds. As Humphries (2003) argues, apprenticeship contracts in England may have been, to a large extent, self-enforcing in that opportunistic behavior in fairly well-integrated local societies would be punished severely by an erosion of reputation. Market relationships were linked to social relationships, and such linkages are a strong incentive toward cooperative behavior (Spagnolo 1999). For example, a master found to treat apprentices badly might not only lose future apprentices but also damage relations with his customers and suppliers. The same was true for the apprentices, whose future careers would be damaged if they were known to have reneged on contracts. If both master and apprentice expected this in advance, in equilibrium they would not engage in opportunistic behavior and would try to make their relationship as harmonious as possible.13 The limits to such self-enforcing contracts are obvious. Mobility of apprentices after training would mean that the the reach of reputation was limited, and in larger communities the reputation mechanism would be ineffective. Substantial opportunistic behavior could cause the cooperative equilibrium to unravel. All the same, it has been stressed that despite the convincing evidence that guilds in some cases helped in the formation of human capital and supported innovation, the two economies in which technological progress was the fastest after 1600 were the Netherlands and Britain, the two countries in which guilds were relatively weak (Ogilvie 2016). That such a correlation does not establish causation goes without saying, but it does serve to warn us against embracing the revisionist view of guilds too rashly. In the theory articulated below, the growth implications of the guild system can be assessed according to their next best alternative. If the state is sufficiently strong to enforce contracts and enable apprenticeship without guilds being involved, the anticompetitive aspect of guilds dominates, and thus guilds hinder growth (consistent with faster growth in the Netherlands and Britain after 1600, when the state increasingly took over functions once served by guilds and cities). But when the state is weak, and the choice is between apprenticeship provided via guilds or via clans, the faster dissemination of knowledge associated with guilds dominates. We now turn to the theory that spells out these results in a formal model of knowledge transmission. III. A Model of Preindustrial Knowledge Growth In this section, we develop an explicit model of knowledge creation and transmission in a preindustrial setting. By ``preindustrial,'' we mean that aggregate production relies on a land-based technology that exhibits decreasing returns to the size of the population. In addition, there is a positive feedback from income per capita to population growth, implying that the economy is subject to Malthusian constraints. We do not mean to imply a commitment to a fundamentalist “iron wage” version of this model in which all gains from productivity growth are relentlessly translated into population growth; the assumption is made only for modeling convenience. Compared to existing Malthusian models, the main novelty here is that we explicitly model the transmission of knowledge from generation to generation and the resulting technological progress. This allows us to to analyze how institutions affect the transmission of knowledge, and how this interacts with the usual forces present in a Malthusian economy. III.A. Preferences, Production, and the Productivity of Craftsmen The model economy is populated by overlapping generations of people who live two periods, childhood and adulthood. All decisions are made by adults, whose preferences are given by the utility function:   \begin{equation} u(c, I^{\prime })=c+\gamma \,I^\prime , \end{equation} (1)where c is the adult’s consumption and I΄ is the total future labor income of this adult’s children. The parameter γ > 0 captures altruism toward children. The role of altruism is to motivate parents’ investment in their children’s knowledge. The adults work as craftsmen in a variety of trades. At the beginning of a period, the aggregate economy is characterized by two state variables: the number of craftsmen N, and the amount of knowledge k in the economy. Craftsmen are heterogeneous in productivity, and knowledge k determines the average productivity of craftsmen in a way that we make precise below. We start by describing how aggregate output in our economy depends on the state variables N and k. The single consumption good (which we interpret as a composite of food and manufactured goods) is produced with a Cobb-Douglas production function with constant return to scale that uses land X and effective craftsmen’s labor L as inputs:   \begin{equation} Y = L^{1-\alpha } X^\alpha , \end{equation} (2)with α ∈ (0, 1). The total amount of land is normalized to 1, X = 1. Land is owned by craftsmen.14 At first sight, including land (and hence allowing for decreasing returns) in the technology may appear surprising, because land is usually not an important input for artisans and craftsmen. However, land is still a scarce factor because raw materials used in manufacturing such as wool, leather, timber, grains, grapes, and bricks had a substantial land component. Alternatively, we would get similar results in an economy where there are constant returns for the craftsmen’s technology, but people also consume food, which is subject to the land constraint. In such a setting, aggregate decreasing returns would be reflected in a gradually declining relative price of manufactured output along a balanced growth path.15 The effective labor supply by craftsmen L is a CES aggregate of effective labor supplied in different trades j:   \begin{equation} L=\left(\int _0^1 (L_j)^\frac{1}{\lambda } dj \right)^\lambda , \end{equation} (3)with λ > 1. The elasticity of substitution between the different trades is $$\frac{\lambda }{\lambda -1}$$. The distinction among different trades of craftsmen (watchmaker, wheelwright, blacksmith, etc.) is important for our analysis of guilds below, which we model as coalitions of the craftsmen in a given trade. However, the equilibrium supply of effective labor will turn out to be the same in all trades, so that Lj = L for all j. For most of our analysis, we can therefore suppress the distinction between trades from the notation. We now relate the supply of effective labor by craftsmen L in efficiency units to the number of craftsmen N and the state of knowledge k. Manufacturing is carried out by a set of independent master craftsmen, each one working on their own.16 Craftsmen are heterogeneous in knowledge. The productive knowledge of a craftsman i is measured by a cost parameter hi, where a lower hi implies that the master can produce at lower cost and hence has more productive knowledge. Intuitively, different craftsmen may apply different methods and techniques in their production, which vary in productivity. Specifically, the output qi of a craftsman with cost parameter hi is given by:   \begin{equation} {q}_{i}=h_{i}^{-\theta }. \end{equation} (4) The final-goods technology equation (2) is operated by a competitive industry. Given the Cobb-Douglas production function, this implies that craftsmen receive share 1 − α of total output as compensation for their labor, and consequently the labor income of a craftsman supplying qi efficiency units of craftsmen’s labor is:   \begin{equation} I_{i}=q_{i} \,{(1-\alpha )}\, \frac{Y}{L}. \end{equation} (5)The heterogeneity in the cost parameter hi among craftsmen takes the specific form of an exponential distribution with distribution parameter k:   \begin{equation*} h_{i}\sim \mbox{Exp}(k). \end{equation*} Given the exponential distribution, the expectation of hi is given by $$\mathbb {E}\,[h_{i}]=k^{-1}$$. Hence, higher knowledge k corresponds to a lower average cost hi and therefore higher productivity. We assume that the same k applies to all trades. Given the exponential distribution for hi and equation (4), output qi follows a Fréchet distribution with scale parameter kθ and shape parameter $$\frac{1}{\theta }$$.17 We can now express the total supply of effective labor by craftsmen as a function of state variables. The average output across craftsmen is given by:   \begin{equation} {q}= \mathbb {E}\,(q_{i})=\int _0^\infty h_{i}^{-\theta } (k \exp (-k h_{i})) dh_{i} = k^\theta \Gamma (1-\theta ), \end{equation} (6)where $$\Gamma (t)=\int _0^\infty x^{t-1}\exp (-x)dx$$ is the Euler gamma function. The total supply of effective craftsmen’s labor L is then given by the expected output per craftsman $$\mathbb {E}\,(q_{i})$$ multiplied by the number of craftsmen N:   \begin{equation} L=N \,k^\theta \, \Gamma (1-\theta ). \end{equation} (7)Income per capita can be computed from equation (2) and (7) as:   \begin{equation} y=\frac{Y}{N}= \frac{L^{1-\alpha }}{N} = \Gamma (1-\theta )^{1-\alpha } \,k^{(1-\alpha )\theta }\,N^{-\alpha }. \end{equation} (8) III.B. Population Growth and the Malthusian Constraint So far, we have described how total output (and hence output per adult) depends on the aggregate state variables N and k. Next, we specify how these state variables evolve over time. We start with population growth. Consistent with evidence from preindustrial economies (see Ashraf and Galor 2011), the model allows for Malthusian dynamics.18 The presence of land in the aggregate production function implies decreasing returns for the remaining factor L, which gives rise to a Malthusian trade-off between the size of the population and income per capita. The second ingredient for generating Malthusian dynamics is a positive feedback from income per capita to population growth. While often this relationship is modeled through optimal fertility choice,19 we opt for a simpler mechanism of an aggregate feedback from income per capita to mortality rates. Every adult gives birth to a fixed number $$\bar{n}>1$$ of children. The fraction of children that survives to adulthood depends on aggregate output per adult y, namely:   \begin{equation} n=\bar{n} \, \min [1, s \,y]. \end{equation} (9)Here min [1, s y] is the fraction of surviving children, and n is the number of surviving children per adult. This function captures that low living standards (e.g., malnutrition) make people (and in particular children) more susceptible to transmitted diseases, so that low income per capita is associated with more frequent deadly epidemics. In recent times, we can also envision s to depend on medical technology (i.e., the invention of antibiotics would raise s). However, given that we analyze preindustrial growth, we will assume that s is fixed. We will also focus attention on a phase of development where the mortality trade-off is still operative, so that survival is less than certain and $$n=\bar{n} s \,y$$. The law of motion for population then is:   \begin{equation*} N^\prime = n \, N= \bar{n} \, s \,y \,N=\bar{n} \, s\,\, Y . \end{equation*} Consider a balanced growth path in which the stock of knowledge k grows according to a constant growth factor g:   \begin{equation*} g=\frac{k^{\prime }}{k}. \end{equation*} In such a balanced growth path, the Malthusian features of the model economy impose a relationship between growth in knowledge g and population growth n, as shown in Proposition 1. Proposition 1 (The Malthusian Constraint). Along a balanced growth path, the growth factor of technology g and the growth factor of population n satisfy:  \begin{equation} g^{\theta (1-\alpha )}=n^{\alpha }. \end{equation} (10) Proof. Income per capita y is given by equation (8). Along a balanced growth path, y is constant, and hence equation (10) has to hold in order to keep the right-hand side of equation (8) constant, too. The Malthusian constraint states that faster technological progress is linked to higher population growth. Given equation (10), a faster rate of technological progress is also associated with a higher level of income per capita. Income per capita is constant in any balanced growth path: Malthusian dynamics rule out sustained growth in living standards, because accelerating population growth ultimately would overwhelm productivity growth. Instead, economies with faster accumulation of knowledge will be characterized by faster population growth and hence, over time, increasing population density. III.C. Apprenticeship, Innovation, and the Evolution of Knowledge We now turn to the accumulation of knowledge in our model economy. In a given period, all productive knowledge is embodied in the adult workers. During childhood, people have to acquire the productive knowledge of the previous generation. There are two sources of increasing knowledge across generations. First, craftsmen are heterogeneous in their productive knowledge. Young craftsmen can learn from multiple adult craftsmen and then apply the best of what they have learned. This knowledge dissemination process results in endogenous technological progress. In addition, after having acquired knowledge from the elders, young craftsmen can innovate, that is, generate an idea that may improve on what they have learned, resulting in a second source of technological progress. In order to model the idea that apprentices (or their parents) are subject to imperfect information on the efficiency of the different masters, we assume that the young can observe the efficiency of masters only by working with them as apprentices. Consider an apprentice who learns from m masters indexed from 1 to m (the choice of m will be discussed below). The efficiency hL learned during the apprenticeship process is:   \begin{equation} h_L=\min \left\lbrace h_{1},h_{2},\ldots ,h_{m}\right\rbrace . \end{equation} (11)Hence, apprentices acquire the cost parameter of the most efficient (i.e., lowest cost) master they have learned from. After learning from masters, craftsmen attempt to innovate by generating a new idea characterized by cost parameter hN. The quality of the idea is random, and it may be better or worse than what they already know. As adult craftsmen, they use the highest efficiency they have attained either through learning from elders or through innovation, so that the final cost parameter h΄ is given by:   \begin{equation} h^\prime =\min \left\lbrace h_L,h_N\right\rbrace . \end{equation} (12)As will become clear below, the model can generate sustained growth even if the rate of innovation is 0 (i.e., own ideas are always inferior to acquired knowledge). In that case, the dissemination process of existing ideas is solely responsible for growth. However, allowing for innovation allows for a positive rate of productivity growth even if each child learns only from a single master. Recall that the distribution of the hi among adult craftsmen is exponential with distribution parameter k. The distribution of new ideas is also exponential, and the quality of new ideas depends on existing average knowledge:   \begin{equation*} h_{N}\sim \mbox{Exp}(\nu k). \end{equation*} That is, the more craftsmen already know, the better the quality of the new ideas generated. The parameter ν measures the relative importance of transmitted knowledge and new ideas. If ν is close to zero, most craftsmen rely on existing knowledge, and if ν is large, innovation rather than the dissemination of existing ideas through apprenticeship is the key driver of knowledge. The exponential distributions for ideas imply that, given the knowledge accumulation process described by equations (11) and (12), the knowledge distribution preserves its shape over time (as in Lucas 2009). Specifically, if each young craftsman learns from m masters that are drawn at random we have:20  \begin{eqnarray*} h_L= \min \left\lbrace h_{1},h_2,\ldots ,h_{m}\right\rbrace &\sim\, \mbox{Exp}(m k),\\ h^\prime = \min \left\lbrace h_L,h_N\right\rbrace &\quad \sim \mbox{Exp}(m k+\nu k). \end{eqnarray*} Hence, with m randomly chosen masters per apprentice, aggregate knowledge k evolves according to:   \begin{equation} k^\prime =(m+\nu ) k. \end{equation} (13)The market for apprenticeship interacts with population growth. In particular, if each master takes on a apprentices, and each apprentice learns from m masters, the condition for matching demand and supply of apprenticeships is:   \begin{equation} N^\prime \, m = N\, a. \end{equation} (14)We ignore integer constraints and treat m and a as continuous variables. Below, we will focus on equilibria where each apprentice chooses the same number of masters m, and each master has the same number of apprentices a. We now arrive at the core of our analysis, namely, the question of how the number and identity of masters for each apprentice are determined. Apprenticeship is associated with costs and benefits. While working as an apprentice with a master, each apprentice produces κ > 0 units of the consumption good (this is in addition to the output generated by the aggregate production function). This output is controlled by the master. In turn, a master who teaches a apprentices incurs a utility cost δ(a), where δ(0) = 0, δ΄(a) > 0, and δ″(a) > 0 (i.e., the cost is increasing and convex in a). Incurring this cost is necessary for transmitting knowledge to the apprentices. We assume for simplicity that the function δ(·) is quadratic, that is, $$\delta (a)=\tfrac{\bar{\delta }}{2} a^2$$ and that it is the same for all masters.21 If a master takes on a apprentices but then puts no effort into teaching, the apprentices still generate output κa by assisting the master in production. Thus, there is a moral hazard problem: masters may be tempted to take on apprentices, appropriate production κa, but not actually teach, saving the cost δ(a). Dealing with this moral hazard problem is a key challenge for an effective system of knowledge transmission. The danger of moral hazard is especially severe here because the very nature of apprenticeship defines it as the quintessential incomplete contract (see Section II). In a modern market economy, we envision that such problems are dealt with by a centralized system of contract enforcement. In such a system, a parent would write contracts with masters to take on the children as apprentices. A price would be agreed on that is mutually agreeable given the cost of training apprentices and the parent’s desire, given altruistic preferences in equation (1), to provide the children with future income. Courts would ensure that both parties hold up their end of the bargain. In preindustrial societies lacking an effective system of contract enforcement, other institutions would have to ensure an effective transmission of knowledge from the elders to the young. Our view is that variation in these alternative institutions across countries and world regions plays a central role in shaping economic success and failure in the preindustrial era. After a brief discussion of model assumptions, we analyze specific, historically relevant institutions in the context of our model of knowledge-driven growth. III.D. Discussion of Model Assumptions Our model of growth in the preindustrial economy is stylized and relies on a set of specific assumptions that yield a tractable analysis. We conclude our description of the model with a discussion of the role and plausibility of the assumptions that are most central to our overall argument. Above all, apprenticeship institutions matter in our economy because the knowledge of masters is not publicly observable. This creates the incentive for apprentices to sample the knowledge of multiple masters to gain productive knowledge, and implies that institutions that determine how apprentices are matched to masters matter for growth. To maintain tractability, in the model the lack of information on productivity is severe: nothing at all is known about the productivity of different masters, even though there is wide variation in their actual productivity. Taken at face value, this assumption is clearly implausible. However, possible concerns about its role can be addressed in two ways. First, in our model all knowledge differences between masters are actual productivity differences, that is, masters who know more produce more. A realistic alternative possibility is that at least some variation in knowledge is in terms of “latent” productivity, that is, some masters may know techniques and methods that will turn out to be highly productive and important at a later time when combined with other knowledge but do not give a productivity advantage in the present. A well-known example are the inventions of Leonardo da Vinci, which could not be implemented given the knowledge of his age, but which turned into productive knowledge centuries later. Similarly, the success of the steam engine was based in large part on a set of gradual improvements in craftmen’s ability to work metal to precise specifications; for instance, steam engines work only if the piston can move easily in the cylinder but with a tight fit. Many improvements in techniques would have been of comparatively little value when first invented but then became critical later on. Along these lines, in Online Appendix B we describe an extension of our model where a craftsman’s output can be constrained by the state of aggregate knowledge. This version leads to exactly the same implications as the simpler setup described here, but actual variation in productivity is much smaller than variation in latent productivity, so that imperfect information on underlying productivity appears more plausible. The extended model is also useful for addressing another potential concern about the model, namely, that the support of latent knowledge is unbounded, with a fat-tailed distribution that allows, in principle, for sustained growth based entirely on knowledge diffusion. At face value, this assumption implies that all potential knowledge is already known to at least one person at the beginning of time, which may be regarded as implausible. However, the extended model makes clear that this setting can be regarded as a simple analytical approximation to a model with a finite support of knowledge. In particular, if the knowledge distribution is cut off at some upper bound and replaced with a point mass at the bound, we would get the same results for the growth implications of different apprenticeship institutions and overall similar equilibrium outcomes in the short and medium run. Second, it would be possible to relax the assumption of total lack of information about productivity, and instead assume that an informative, but imperfect, signal of each master’s productivity was available.22 In such a setting, more productive masters could command higher prices for apprenticeships, they would employ a larger number of apprentices, and the spread of productive knowledge would be faster. As we document in Section II, the historical evidence for Europe suggests that, indeed, more productive and knowledgeable masters were able to command higher prices and attract more apprentices. However, as long as information on productivity is less than perfect, the basic trade-offs articulated by our analysis and the comparative growth implications of the institutions analyzed below would be the same. Less-than-perfect information about productivity is highly plausible; even in today’s world of instant communication and online discussion boards, for example, graduate students do not have perfect information about which adviser will be the best match for them. We adopt the extreme case of complete lack of observability for tractability; without this assumption the distribution of knowledge would not preserve its shape over time, so that we would have to rely on numerical simulation for all results.23 It should also be noted that in a world of artisans and small workshops there were limits on the number of apprentices that each master could take on. Diseconomies of scale would set in fairly soon, even if there were no guild limitations on the number of apprentices (which often existed). This means that the standard mechanism through which technology diffuses (the more efficient firms expand and take over the industry) was not operative in this period. In addition, the master-apprentice relationship in the model is simplified compared to reality. We use a setting with one-sided moral hazard, that is, masters can cheat apprentices but not vice versa. In reality, moral hazard was a major concern on both sides of the master-apprentice relationship. This assumption is introduced merely to simplify the analysis. It would be straightforward to introduce two-sided moral hazard in our setting, and the role of institutions for mitigating moral hazard would be unchanged.24 We also assume that the only reason why apprentices get differential training is because they work with heterogeneous masters—we do not allow for the apprentices to differ in talent.25 Finally, in the model, apprentices interact in the same way with all of their masters, and they make a one-time choice of the number of masters to learn from. As ever, reality is substantially more complicated; choices of whom to learn from unfolded sequentially over time, and most apprentices generally did only one full apprenticeship (although changing masters was actually not uncommon; see Bellavitis, Cella, and Colavizza 2016; Crowston and Lemercier 2016; and Schalk 2016), followed by other shorter interactions during journeymanship. Once again, these assumptions are for simplicity and tractability but are not central to our main results regarding the role of institutions for knowledge transmission. The key point in the theoretical setup is that apprentices adopt the techniques of the most efficient master they learned from. It is not necessary that apprentices spend equal time with each master; in reality, an interaction may be brief and end once an apprentice ascertains that a given master has nothing new to offer. The model abstracts from such differentiated interactions and imposes symmetrical master-apprentice relations to improve tractability. Having said that, when matching the model to data, care should be taken to account for the fact that “apprenticeships” in the model correspond to a wider range of interactions in reality. Some of these real-world interactions may also consist of horizontal diffusion of techniques in which artisans learn from one another. While we abstract from such interactions in the theoretical model, the historical evidence about the mobility of artisans and journeymen suggests that such horizontal dissemination was an important element in the dissemination of technical knowledge. IV. Comparing Institutions for Knowledge Transmission The crucial question in our theory is how the moral hazard problem inherent in apprenticeship is resolved. If masters do not make an effort to teach their apprentices, parents will have no incentive to send children to learn from masters outside the family. Apprentices would not learn anything, whereas masters would gain the apprentices’ production κ. Parents would be better off keeping children at home, thereby keeping output κ in the family. Thus, for apprenticeship outside the immediate family to be feasible (and thus for knowledge to disseminate), an enforcement mechanism is required in order to provide incentives for masters to exert effort. IV.A. Centralized versus Decentralized Institutions We consider two types of institutions, characterized by centralized versus decentralized enforcement. Under centralized enforcement, people can write contracts specifying that the master must put in effort (and indicating the price of apprenticeship), and there is a centralized system (such as courts) that punishes anyone who breaks a contract. In contrast, in a decentralized system no such central authority exists, and instead people have to form coalitions to maintain a sufficient threat of punishment to resolve the moral hazard problem.26 To allow for the possibility of decentralized enforcement, we assume that each adult can inflict a utility cost (damage) on any other adult.27 However, the punishment that a single adult can mete out is not sufficient to induce a master to put in effort, that is, the punishment is lower than the cost of training a single apprentice. In contrast, coalitions of people can always make threats that are sufficient to guarantee compliance. An effective threat of punishment therefore requires coordination among parents. Coordination, in turn, requires communication: for a master’s shirking to have consequences, the fact of the shirking has to be communicated to all would-be punishers. Thus, the extent to which people are able to communicate with each other partly determines how much knowledge transmission is possible. Over time, societies have differed in the extent and manner in which individuals were connected in communication networks. We consider two different scenarios for decentralized enforcement, the “family” and the “clan,” which we consider particularly relevant for contrasting Europe during the Early Middle Ages with China, India, and the Middle East during the same period and beyond. The decentralized systems correspond to a period when centralized enforcement was not yet sufficiently effective. Even if courts existed, contract enforcement was often costly, slow, and uncertain. More important, for centuries the reach of the state and hence its courts was severely limited. Europe, for example, used to consist of hundreds of independent sovereign entities, and the enforcement of the law outside one’s immediate surroundings (say, the city of residence) was weak. With this in mind, the first centralized enforcement institution that we consider is organized not by the state but by a coalition of all the masters in a given trade: a “guild.” The guild monitors the behavior of its members and enforces the apprenticeship contracts between parents and masters. However, the guild also has anticompetitive features. It can set the price of apprenticeship, thereby exploiting its monopoly in a given trade. Guilds played a central role in European economic life during the Middle Ages, and our theory will allow us to assess their implications for knowledge creation and dissemination. The final institution that we consider is the “market,” where there is a centralized enforcement system for all trades as in a modern market economy. Importantly, under this institution the government not only enforces contracts but also prevents collusion; trades are no longer allowed to form guilds that limit entry and lower competition, and both parents and masters act as price takers. The market institution corresponds to the final stages of the preindustrial economy, when in Europe nation-states became powerful and increasingly abolished the traditional privileges of guilds. IV.B. The Family Decentralized institutions enforce apprenticeship agreements through the formation of coalitions of parents that coordinate on a sufficient threat of punishment for shirking masters. Different decentralized institutions are distinguished by the size of these coalitions and the identity of their members. For the formation of a coalition to be feasible, the members have to be able to communicate with each other about the behavior of masters. Hence, one polar case is where members of different families are unable to communicate with each other, so that no coalitions can be formed. The lack of communication rules out coordinating on punishing shirking masters. As a consequence, apprenticeship outside the immediate family is impossible, that is, each child learns only from the parent. In principle, the moral hazard problem is present even within the family. However, in utility (equation (1)) parents care about their own children, and we assume that the degree of altruism γ is sufficiently high for parents never to shirk when teaching their own children. The result is a “family equilibrium,” that is, an equilibrium where knowledge is transmitted only within dynasties, but there is no dissemination of knowledge across dynasties. Formally, under decentralized institutions we model the knowledge accumulation decisions as a game between the craftsmen of a given generation. The strategy of a given craftsman has three elements: Decide whether to send own children to others as apprentices for training, and if so, which compensation to pay the masters of one’s children. Decide whether to exploit one’s own apprentices (if any). Decide whom to punish (if anyone). We focus on Nash equilibria.28 The strategy profile for the family equilibrium is as follows: All craftsmen train their children on their own. If (off the equilibrium path) a master gets someone else’s child as an apprentice, the master exploits the apprentice. No one ever punishes anyone. If communication outside the immediate family is impossible, the family equilibrium is the only equilibrium. The family equilibrium can also occur as a “bad” equilibrium in an economy where more communication links are available, but people fail to coordinate on a more efficient punishment equilibrium.29 Now consider the balanced growth path under the family equilibrium. We assume that the Malthusian feedback, parameterized by the maximum number of children $$\bar{n}$$ and the survival parameter s, is sufficiently strong for dynamics to lead to a balanced growth path in which income per capita is constant.30 The following proposition summarizes the properties of the balanced growth path. Proposition 2 (Balanced Growth Path in Family Equilibrium). If altruism is sufficiently strong (i.e., γ is sufficiently large), there exists a unique balanced growth path under the family equilibrium with the following properties: Each child trains only with his own parent: mF = 1, and aF = nF. The growth factor gF of knowledge k is:  \begin{equation*} g^{{\bf F}}=1+\nu . \end{equation*} The growth factor nF of population N is:  \begin{equation*} n^{{\bf F}}=(1+\nu )^\frac{(1-\alpha ) \theta }{\alpha }. \end{equation*} Income per capita yF is constant and satisfies:  \begin{equation*} y^{{\bf F}}=\frac{(1+\nu )^\frac{{(1-\alpha )} \theta }{\alpha }}{\bar{n}\,s}. \end{equation*} Proof. See Online Appendix C. The condition for sufficient altruism reflects that parental altruism should be strong enough to overcome the disutility of teaching one’s children. The rate of technological progress is positive in the family equilibrium but small. In the absence of new ideas (ν = 0), there is stagnation (gF = nF = 1). This is because the only source of progress is the new ideas of craftsmen (recall that ν measures the quality of new ideas). New ideas are passed on to children, which makes children, on average, more productive than the parents. However, knowledge does not disseminate across dynasties. Given the growth rate of knowledge gF = 1 + ν, Malthusian dynamics ensure that population grows just fast enough to offset productivity growth and yield constant income per capita. Figure I represents the determination of the balanced growth path in the family equilibrium. The concave curve represents the Malthusian constraint given by equation (10).31 The intersection between this constraint and the line g = 1 + ν gives the balanced growth path under the family equilibrium F. Figure I View largeDownload slide Productivity and Population Growth in the Family (F) Equilibrium Figure I View largeDownload slide Productivity and Population Growth in the Family (F) Equilibrium IV.C. The Clan Next, we consider economies where there is communication within an extended family or clan. While many other structures could be considered, the clan has particular historical significance because of its importance for organizing economic exchange in the major world regions outside Europe. Formally, we consider a setting where all members of a dynasty who share an ancestor o generations back can communicate (here o = 0 corresponds to the family equilibrium, o = 1 means siblings are connected, and so on). Now consider a potential “clan equilibrium” with the following equilibrium strategy profiles: All craftsmen send their children to be trained by each master in the clan, and parents compensate masters for the apprenticeship by paying each δ΄(a) − κ (the marginal cost), where a is the number of apprentices per master. All masters put effort into teaching. If (off the equilibrium path) a master cheats an apprentice, all current members of the clan punish the master. For example, if o = 1, children are trained not only by their parent but also by their uncles. For o = 2, second-degree relatives serve as masters, and so on.32 Along a balanced growth path, the total number of adults (i.e., masters) belonging to the clan is (nC)o, where nC is the rate of population growth in the balanced growth path. For learning from all current masters to be feasible, we assume that all members of the clan work in the same trade. An alternative setup allows for large clans that engage in many trades, in which case a child would be trained only by those masters in the clan who work in the child’s chosen trade. In either case, we envision that in the clan equilibrium children obtain the knowledge of a handful of masters who belong to the same clan and to the same trade. The following proposition summarizes the properties of the balanced growth path in the clan equilibrium. Proposition 3 (Balanced Growth Path in Clan Equilibrium). There is a threshold omax  > 0 such that if o < omax  and if altruism is sufficiently strong (i.e., γ is sufficiently large), there exists a balanced growth path in the clan equilibrium with the following properties: The number of masters per child m is given by the numberof adults in the clan, mC = (nC)o, and the number ofapprentices per master is aC = (nC)o + 1. The growth factor gC of knowledge k is the solution to:  \begin{equation} g^{{\bf C}}=1+\frac{\nu \,{(n^{{\bf C}})}^o}{g^{{\bf C}}-\nu }. \end{equation} (15) The growth factor nC of population N is given by:  \begin{equation*} n^{{\bf C}}=(g^{{\bf C}})^\frac{{(1-\alpha )} \theta }{\alpha }. \end{equation*} Income per capita is constant and satisfies:  \begin{equation*} y^{{\bf C}}=\frac{(g^{{\bf C}})^\frac{{(1-\alpha )} \theta }{\alpha }}{\bar{n}s}. \end{equation*} For o = 0, the balanced growth path coincides with the family equilibrium, whereas for o > 0 knowledge growth, population growth, and income per capita are higher compared to the family equilibrium. The growth gC of knowledge k is increasing in the size of the clan o. Proof. See Online Appendix D. Parallel to the family equilibrium, the condition on sufficiently high altruism ensures that parents find it worthwhile to pay for the training of their children.33 The upper bound omax  on the size of the clan limits productivity growth to a level where the Malthusian feedback is sufficiently strong to generate a balanced growth path with constant income per capita. The clan equilibrium leads to a higher growth rate compared to the family equilibrium because children learn from more masters. In particular, they benefit not just from the new ideas of their own parent but also from the new ideas of their uncles and other current members of the clan. Thus, new knowledge disseminates more widely compared to the family equilibrium. However, there is still no dissemination of knowledge across clans. Equation (15) implies that as long as ν > 0 (there is some innovation), a higher o (larger clans) leads to faster growth. However, if there are no new ideas, ν = 0, the growth rate in the clan equilibrium is 0. Intuitively, in a clan the masters of a given apprentice all trained with the same masters when they were apprentices, which implies that they all started out with the same knowledge. If the masters do not have new ideas of their own, studying with multiple masters does not provide any benefit over studying with only one of them. Hence, knowledge does not accumulate across generations. Another way of stating this key point is that learning opportunities in the clan are limited, because the knowledge of the available masters is correlated. This correlation arises from the fact that the available masters once learned from the same teachers, and hence acquired the same pooled knowledge present within the clan. As we will see, this issue of correlated knowledge across masters is the key distinction between the clan and institutions such as the guild and the market that extend beyond blood relatives. Figure II represents the determination of the balanced growth path in the clan equilibrium. In addition to the Malthusian constraint (10), we have drawn the function   \begin{equation} n=\left(\frac{(g-1)(g-\nu )}{\nu }\right)^\frac{1}{o}, \end{equation} (16)which is derived from equation (15). This function is equal to 1 when g = 1 + ν, increases monotonically with g for g > 1 + ν, and ultimately crosses the Malthusian constraint. The function (16) captures the relationship between population growth and the size of the clan. When n = 1, every person has one child, and hence there are no siblings and no uncles. Therefore, children can learn only from their own parent, who is the sole adult member of the clan. At higher rates of population growth, the clan is bigger, and hence there are more masters who generate ideas and whom the young can learn from, resulting in faster technological progress. Figure II View largeDownload slide Productivity and Population Growth in the Clan (C) Equilibrium Figure II View largeDownload slide Productivity and Population Growth in the Clan (C) Equilibrium IV.D. The Market At the opposite extreme (compared to the family) of enforcement institutions, we now consider outcomes in an economy with formal contract enforcement (as in the usual complete-markets model). All contracts are perfectly and costlessly enforced, so that masters who promise to train apprentices do not shirk.34 There is a competitive market for apprenticeship. Given market price p for training apprentices, masters decide how many apprentices to train, and parents decide how many masters to pay to train their children. In equilibrium, p adjusts to clear the apprenticeship market. A craftsman’s decision to take on apprentices is a straightforward profit maximization problem. In particular, given price p a master will choose the number of apprentices a to solve:   \begin{equation*} \max _a\lbrace p\, a +\kappa \,a -\delta (a) \rbrace . \end{equation*} The benefit of taking on apprentices derives from the price p as well as the apprentices’ production κ, and the cost is given by δ(a). Optimization implies that in equilibrium the price of apprenticeship equals the marginal cost of training an apprentice:   \begin{equation*} p=\delta ^\prime (a)-\kappa . \end{equation*} Now consider parents’ choice of the number of masters m that their children should learn from. Given p, parents will choose m to maximize their utility from equation (1):   \begin{equation*} \max _m \left\lbrace -p\, m\,n +\gamma \, \mathbb {E}\,I^\prime \right\rbrace , \end{equation*} where n is the number of children and I΄ is the income of the children, which is given by equation (5). Each child’s expected income depends on m, because learning from a larger number of masters increases the expected productivity (and hence income) of the child. The objective function is concave, because as m rises, the probability that an additional master will have the highest productivity declines. Lemma 1. The first-order condition for the parent’s problem implies:   \begin{equation} \delta ^\prime (a)-\kappa = \gamma \, \theta {(1-\alpha )} \frac{1}{m+\nu }\frac{Y^{\prime }}{N^{\prime }}. \end{equation} (17) Proof. See Online Appendix E. Notice that the decision problem implicitly assumes that the young apprentice gets m independent draws from the distribution of knowledge among the elders, as though the masters were drawn at random. The possibility of independent draws from the knowledge distribution is a key advantage of the market system over the clan system. In a clan, the potential masters have similar knowledge (because they learned from the same “grand” master), and hence the gain from studying with more of them is limited (there is still some gain because of the new ideas generated by masters). Of course, it would be even better to study only with masters known to have superior knowledge. We assume, however, that a master’s knowledge can be assessed only by studying with them; hence, choosing masters at random is the best one can do. The market equilibrium gives rise to a unique balanced growth path, which is characterized in the following proposition. Proposition 4 (Balanced Growth Path in Market Equilibrium). The unique balanced growth path in the market equilibrium has the following properties: The number of apprentices per master aM solves equation (17):  \begin{equation} \delta ^\prime (a^{{\bf M}})-\kappa = \gamma \, \theta {(1-\alpha )}y^{{\bf M}}\left(\frac{a^{{\bf M}}}{n^{{\bf M}}}+\nu \right)^{-1}, \end{equation} (18)and the number of masters per child mM is given by $$m^{{\bf M}}=\frac{a^{{\bf M}}}{ n^{{\bf M}}}$$. The growth factor gM of knowledge k is given by:  \begin{equation*} g^{{\bf M}}=m^{{\bf M}}+\nu . \end{equation*} The growth factor nM of population N is given by:  \begin{equation*} n^{{\bf M}}=(g^{{\bf M}})^\frac{{(1-\alpha )} \theta }{\alpha }. \end{equation*} Income per capita is constant and satisfies:  \begin{equation*} y^{{{\bf M}}} =\frac{(g^{{\bf M}})^\frac{{(1-\alpha )} \theta }{\alpha }}{\bar{n}\,s}. \end{equation*} The market equilibrium yields higher growth in productivity and population and higher income per capita than do the clan equilibrium and the family equilibrium. Proof. See Online Appendix F. To analyze the equilibrium, we can plug the expressions for aM, mM, and yM into equation (17) to get:   \begin{equation} \delta ^\prime ((g^{{\bf M}}-\nu )n^{{\bf M}})-\kappa = \gamma \theta {(1-\alpha )} \frac{1}{g^{{\bf M}}}\,\,\,\, \frac{n^{{\bf M}}}{\bar{n}\,s}. \end{equation} (19)This equation describes a relationship between gM and nM which we call the “apprenticeship market,” as it is derived from the demand for apprenticeship and the equilibrium condition on the apprenticeship market. Equation (19) can be rewritten as:   \begin{equation} n^{{\bf M}}=\frac{\kappa }{\bar{\delta }(g^{{\bf M}}-\nu )- \displaystyle \frac{\gamma \theta {(1-\alpha )}}{\bar{n}\,s\,g^{{\bf M}}}}. \end{equation} (20)This function of gM is plotted in Figure III. The negative relationship between population growth and the rate of technical progress in equation (19) can be interpreted as follows. When fertility is higher, the market for apprenticeships is tighter, the equilibrium price of apprenticeship is higher, and parents demand fewer masters. Hence faster population growth is associated with lower productivity growth. Notice that such a feedback does not arise in the family equilibrium, because there apprenticeship is limited by the fact that only parents can serve as masters, rather than being constrained by market forces. Figure III View largeDownload slide Productivity and Population Growth in the Market (M) Equilibrium Figure III View largeDownload slide Productivity and Population Growth in the Market (M) Equilibrium The market equilibrium leads to faster growth than the clan equilibrium does because knowledge is disseminated across ancestral boundaries throughout the entire economy. The masters teaching apprentices represent a wider range of knowledge, implying that more can be learned from them.35 All of this is made possible by having a different enforcement technology for apprenticeship contracts, namely courts rather than punishment by clan members. IV.E. The Guild Historically, economies did not transition directly from the family or clan equilibrium to the market equilibrium; rather, there were intermediate stages of semiformal enforcement through institutions other than the state. In Europe, the key intermediate institution was the guild system, which for centuries regulated apprenticeship and knowledge transmission, at a time when state power was still weak. Craft guild is a generic term for an organization of craftsmen and manufacturers who shared an occupation and hence a training. Yet while they can be found everywhere, their function and power varied enormously both over time and across different regions. In Europe, continental craft guilds in most areas were politically powerful and used this power not only to organize the industry but also to monitor its operations and enforce rules. In England, guilds were less powerful and their political influence was much more limited. In the Ottoman Empire, guilds emerged in the sixteenth century but seem to have acted mostly as trade cartels and lobbying bodies, which did little to enforce industry regulations (Faroqhi 2009, 30–40). In China guilds emerged fairly late, and as noted above, often coincided with people of common origin rather than people sharing an occupation. We now provide a formal characterization of a “guild equilibrium” as an intermediate step between the family equilibrium and the market equilibrium. We envision a guild as an association of all masters involved in the same trade. In the production function (3), the effective labor supply from many different trades is combined with limited substitutability across trades, so that market power can arise. Allowing for heterogeneous labor supply by different trades, the labor income of a craftsman i in trade j is:   \begin{equation*} I_{ij}=q_{ij} \,{(1-\alpha )}\, \frac{Y}{L}\left(\frac{L_j}{L}\right)^{\frac{1}{\lambda }-1}. \end{equation*} Apprentices choose the most attractive trade. In equilibrium, the net benefit of joining as an apprentice is equalized across trades, so that for all j we have:   \begin{equation} \mathbb {E}\,I^{\prime }_{ij} - p_j m_j = \mathbb {E}\,q^{\prime }_{ij} \,{(1-\alpha )}\, \frac{Y^{\prime }}{L^{\prime }} -p \, m. \end{equation} (21) Collusion among masters in a given guild leads to social costs and benefits compared to the clan equilibrium. The costs are the usual downsides from limited competition; the guild has an incentive to raise prices and limit entry. Guilds enforced labor market monopsonies, and as a result often limited the number of apprentices that each master was allowed to take on at one time, specified the number of years each apprentice had to spend with his master, or even stipulated time periods that had to elapse between taking on one apprentice and the next (Kaplan 1981, 283; Trivellato 2008, 212). The purpose of these constraints was to limit supply and increase exclusionary rents, which for our analysis means that technological progress is slowed down compared to a market equilibrium.36 However, guilds operated across different dynasties and thus represented the full range of knowledge in the given trade. If the guild also enforced apprenticeship contracts (in the same fashion as in the clan equilibrium above), there was more scope for knowledge accumulation. Thus, in the absence of strong centralized contract enforcement institutions (i.e., if the clan and not the market was the relevant alternative), the guild had a genuinely positive role to play.37 Consider the choice of a guild j of setting the price of apprenticeship pj within the trade, or equivalently, of choosing the number aj of apprentices per master. The guild maximizes the utility of the masters in the trade. If the guild lowers aj, the effective supply of craftsmen’s labor in trade j in the next generation goes down. Due to limited substitutability across trades, this increases future craftsmen’s income in the trade, and thus the price pj that today’s apprentices are willing to pay. Thus, as in a standard monopolistic problem, the guild will raise pj to a level above the marginal cost of training apprentices. The maximization problem of the guild can be expressed as:38  \begin{equation} \max _{ a_j}\lbrace p_j\, a_j-\delta (a_j)+\kappa \,a_j \rbrace \end{equation} (22)subject to:   \begin{eqnarray*} S_j N^{\prime } m_j &=& N \, a_j,\\ p_j &=&\gamma \frac{\partial \mathbb {E}\, I^{\prime }_{ij}}{\partial m_j},\\ \mathbb {E}\, I^{\prime }_{ij} -p_j m_j &=& (1-\alpha )\, \frac{Y^{\prime }}{N^{\prime }}- p\, m. \end{eqnarray*} Here Sj is the endogenous relative share of apprentices choosing to join trade j. We have Sj = 1 in equilibrium; however, the guild solves its maximization problem taking the behavior of all other trades as given, so that Sj varies with pj and aj in the maximization problem of the guild. The second constraint represents the optimal behavior of parents sending their children to trade j (equalizing pj to the marginal benefit of training with an additional master). The third constraint stems from the mobility of apprentices across trades (from equation (21)). These two equations represent the two market forces limiting the power of the guild. Notice that $$\frac{Y^{\prime }}{N^{\prime }}$$ is exogenous for the guild j, because each trade is of infinitesimal size. Lemma 2. In the symmetric equilibrium, the solution to the maximization problem (22) satisfies:   \begin{equation} \delta ^\prime (a)-\kappa =\Omega (m) \,\,\gamma \theta {(1-\alpha )}\frac{1}{m+\nu } \, \frac{Y^{\prime }}{N^{\prime }} \end{equation} (23)with Ω(m) < 1. Proof. See Online Appendix G. Thus, the condition determining equilibrium in the apprenticeship market is of the same form as in the market equilibrium (see Lemma 1), but with the benefit from apprenticeship scaled down by a factor strictly smaller than 1. Hence, the extent of apprenticeship (and productivity growth) will be lower compared to the market equilibrium. In the limit where trades become perfect substitutes, λ → 1, we have that Ω(m) → 1, that is, guilds have no market power and the problem of the guild leads to the same solution as the market (Lemma 1). We can now characterize the balanced growth path in the guild equilibrium. Proposition 5 (Balanced Growth Path in Guild Equilibrium). The unique balanced growth path in the guild equilibrium has the following properties: The number of apprentices per master aG solves equation (23):  \begin{equation} \delta ^\prime (a^{{\bf G}})-\kappa =\Omega \left( \frac{a^{{\bf G}}}{n^{{\bf G}}}\right)\,\, \gamma \theta (1-\alpha ) y^{{\bf G}}\left(\frac{a^{{\bf G}}}{n^{{\bf G}}}+\nu \right)^{-1} , \end{equation} (24)and the number of masters per child mG is given by $$m^{{\bf G}}=\frac{a^{{\bf G}}}{n^{{\bf G}}}$$. The growth factor gG of knowledge k is given by:  \begin{equation*} g^{{\bf G}}=m^{{\bf G}}+\nu . \end{equation*} The growth factor nG of population N is given by:  \begin{equation*} n^{{\bf G}}=(g^{{\bf G}})^\frac{{(1-\alpha )} \theta }{\alpha }. \end{equation*} Income per capita is constant and satisfies:  \begin{equation*} y^{{{\bf G}}} =\frac{(g^{{\bf G}})^\frac{{(1-\alpha )} \theta }{\alpha }}{\bar{n}\,s}. \end{equation*} The guild equilibrium yields lower growth in productivity and population and lower income per capita than does the market equilibrium. Proof. See Online Appendix H. The guild equilibrium is represented in Figure IV, where the apprenticeship market is described by equation (24). This relationship is similar to the apprenticeship market condition in the market equilibrium, but with a shift to the left because of the market power of the guild, represented by the term Ω(·). Figure IV View largeDownload slide Productivity and Population Growth in the Guild (G) Equilibrium Figure IV View largeDownload slide Productivity and Population Growth in the Guild (G) Equilibrium For explaining the rise of European technological supremacy, the key comparison is between the growth performance of the guild equilibrium (which we view as representing Europe for much of the period from the Middle Ages to the Industrial Revolution) and the clan equilibrium (a feature of other regions such as China, India, and the Middle East). There are forces in both directions; guilds foster growth compared to clans because knowledge can disseminate across ancestral lines, but at the same time the anticompetitive behavior of guilds may limit access to apprenticeship. For this reason, the ranking of growth rates depends on parameters. The guild will lead to faster growth if λ is sufficiently small, because a low λ (close to 1) implies that guilds have little market power, so that the guild equilibrium is close to the market equilibrium. Moreover, the guild also generates faster growth if the rate of innovation ν (i.e., the relative efficiency of new versus existing ideas) is close to 0. In this case, most growth is due to the dissemination of existing ideas rather than to the generation of new knowledge, and guilds dominate clans in terms of dissemination (recall that the growth rate in the clan equilibrium is 0 if ν = 0). Perhaps the most important comparison is that the guild would always lead to more growth than the clan if the number of masters m were the same in both systems. In the guild, conditional on m, masters are selected in the best possible way (namely, as independent draws from the distribution of knowledge, which maximizes the probability that something new can be learned from an additional master). While the guild may limit access to apprenticeship, it does benefit from allowing for an efficient choice of masters, because this raises the expected benefit of learning from masters and hence the price apprentices are willing to pay. Put differently, the guild distorts only the quantity, but not the quality of apprenticeship. In contrast, in the clan the knowledge of the multiple masters that a given apprentice learns from is necessarily correlated, given that all masters started out with the same initial knowledge available in the clan. Thus, for a given m, in a clan apprentices are exposed to a smaller variety of ideas, and (on average) they learn less. Hence, the only scenario where the clan could generate more growth than the guild is where the market power of guilds is so strong that they would reduce m to well below the level prevalent in the clan. If anything, the historical evidence points in the opposite direction. Through the multiple interactions that apprenticeship and journeymanship provided, the European guild system is likely to have offered at least as many learning opportunities as the contemporary clan-based system did. From the perspective of our model, faster technological progress in Western Europe compared to other world regions would then be the necessary consequence. V. The Rise of Europe’s Technological Primacy A central question about preindustrial economic growth is how, in the centuries leading up to the Industrial Revolution, Western Europe came to achieve technological primacy over the previous leaders. We argue that this technological primacy was due to the synergistic growth of both tacit (artisanal) and codified (formal) knowledge. In many branches of production the skills of the craftsman and the engineer, learned through apprenticeship, were needed to carry out and scale up the ideas of inventors. Artisanal knowledge could progress on its own with cumulative incremental advances in productivity, but if it was to avoid running into diminishing returns, conceptual breakthroughs were required. Conversely, macroinventions depended crucially on the craftsmen that could turn new ideas from blueprints to functioning devices. Every James Watt required a set of brilliant artisans familiar with state-of-the-art workmanship such as the ironmaster John Wilkinson and the engineer William Murdoch to carry out his plans. As our analysis above makes clear, in our view the adoption of apprenticeship institutions that promoted the dissemination of knowledge, namely the guild and later on the market, lay at the heart of Western Europe’s success.39 Many of the guild arrangements supported the spread of technological knowledge beyond the boundaries of individual guilds, a critical factor in the diffusion of technology across the European continent.40 In addition to the practice of tramping during the Wanderjahre, guilds also supplied waystations or Herbergen to host itinerant journeymen, who sometimes were lodged at the expense of the guild. Local artisans would interview these artisans, and sometimes hire them (Farr 2000, 212). Trained artisans were a mobile element in Europe. Some were highly mobile journeymen who moved across linguistic and national boundaries; others were permanent immigrants, lured by incentives or earlier immigrants to new settlements. Technology diffused through Europe with skilled craftsmen in search of a livelihood. Given the localized nature of control wielded by guilds, there seems to be no serious way they could have prevented this diffusion from happening (Reith 2008). To shed further light on the role of apprenticeship institutions in the rise of European primacy, in this section we address two issues. First, we ask whether the theoretical mechanisms developed above could be sufficiently strong to account, in a quantitative sense, for the observed acceleration of European productivity growth relative to other world regions. We focus in particular on the comparison of Western Europe with the previous technological leader: China. Second, we consider mechanisms that may explain why Western Europe adopted superior apprenticeship institutions, while other world regions failed to do the same. V.A. Accounting for Divergence in Productivity Growth between Western Europe and China In this section, we provide a quantitative assessment of the importance of apprenticeship institutions based on a parameterized version of the model economy. While the model is stylized, we still aim to choose parameter values that are realistic for the evidence from the period considered. For parameters where little evidence is available, we choose conservative values so as not to exaggerate the importance of the role of apprenticeship institutions. One period (generation) is interpreted as 25 years. Consider first the aggregate technology. Voigtländer and Voth (2013b) argue that based on the historical evidence a land share in agricultural output of 40% is reasonable in the preindustrial era. Given that the land share in manufacturing would be substantially lower, we choose an aggregate land share of $$\alpha =\frac{1}{3}$$. The elasticity-of-substitution parameter λ determines the market power of guilds. While direct historical estimates of this parameter are not available, in modern studies this parameter is pinned down by observations on markups. To give a sizable role to the anticompetitive aspect of guilds we set λ = 1.3, which would correspond to a markup of 30%, at the upper end of modern estimates. The shape parameter θ determines the dispersion of craftsmen’s productivity. Lucas (2009) sets this parameter to θ = 0.5 to match the dispersion in earnings observed in modern U.S. data. Given a lack of good inequality measures for the preindustrial era, we use the same value. Notice that most available indicators suggest that inequality declined substantially from the industrialization period until a few decades ago, which suggests that inequality was likely to be higher in preindustrial times and, hence, that θ = 0.5 is a conservative choice. For demographics, we set $$\bar{n}=2$$ and s = 7.5. These two parameters do not affect results, because the upper bound on fertility turns out not to be binding and (given the choice of a linear relationship between population growth and income per capita) the choice of s amounts to a choice of the units in which income is measured.41 Next, we turn to parameters that affect growth rates. In the family equilibrium, growth is driven by the relative efficiency of new ideas ν. We set this parameter to reproduce a growth rate of population of 0.86% per generation in the family equilibrium, which matches the estimated growth of population between 10,000 BCE and 1000 CE in Clark (2007), Table 7.1. This yields ν = 0.0086. In the clan equilibrium, growth is driven by the size of clans. Given the lack of hard information on this we use o = 6, a large value that implies that apprenticeship is possible even involving fairly distant relatives. For given remaining parameters, growth in the guild and market equilibria is jointly determined by altruism γ, the production of apprentices κ, and the cost of training apprentices $$\bar{\delta }$$. Our strategy is to preset two of these parameters (γ and κ) and then use the third ($$\bar{\delta }$$) to match specific targets. For altruism, we use γ = 0.1, which corresponds to an annual discount factor of 0.91 (given a period/generation length of 25 years). For the output of apprentices we set κ = 0.02, which implies that in the family equilibrium, apprentices are about one-third as productive as adults. For the training cost $$\bar{\delta }$$, we start by choosing this value such that the number of masters per apprentice m is identical in the clan and guild equilibria, which yields $$\bar{\delta }=0.019$$. While this is not necessarily the most realistic value, equalizing m across the institutional regimes allows us to isolate the additional growth in the guild equilibrium, compared to the clan equilibrium, that arises solely out of the increased variety in masters’ knowledge. Any growth effects due to a higher m in the guild would be in addition to this effect. Table I displays the balanced growth rates for total factor productivity, given by kθ(1−α), and population N under each apprenticeship institution, together with the number of masters per apprentice, m. Notice that since income per adult is constant on the balanced growth path, the growth rate of total output Y is equal to the growth rate of population N. We find that productivity growth, population growth, and output growth are all increasing as we proceed from family to clan, guild, and ultimately the market. In terms of the growth performance of the different institutional regimes, we notice that the growth advantage of the clan compared to the family is small, with a productivity growth rate of close to 0.3% in either case. In contrast, the guild yields a substantially higher growth rate (above 2% per generation) than either family or clan. The guild yields substantially higher growth than the clan even though (given our parametrization) the number of masters per apprentice is exactly the same; it is the higher efficiency of knowledge transmission in a system unconstrained by bloodlines rather than more learning opportunities that explains the advantage of the guild. Moving from guild to market yields an additional growth effect through a higher m (because in the market system, guilds are not able to restrict access to apprenticeship). The variation in m between the apprenticeship institutions is fairly small (from 1 in the family to 1.08 in the market).42 TABLE I Balanced Growth Paths for Different Apprenticeship Institutions in the Parameterized Economy Equilibrium  Number of masters  Productivity growth  Population growth  Family F  1.00  0.29  0.86  Clan C  1.06  0.30  0.91  Guild G  1.06  2.14  6.43  Market M  1.08  2.87  8.60  Equilibrium  Number of masters  Productivity growth  Population growth  Family F  1.00  0.29  0.86  Clan C  1.06  0.30  0.91  Guild G  1.06  2.14  6.43  Market M  1.08  2.87  8.60  Notes. One period corresponds to 25 years. Growth rates are in percent per period. Number of masters is m; productivity growth is θ(1 − α)(g − 1), where g is knowledge growth factor. View Large In the results displayed in Table I, the training cost δ was chosen such that the number of masters is equated between clan and guild, which is useful for highlighting the mechanism, but is not necessarily empirically realistic. Next, we ask whether the mechanism could quantitatively account for the empirically observed acceleration in growth in Western Europe relative to other world regions after Europe adopted the guild equilibrium. In matching the model to long-run growth data we confront two difficulties. First, given the distant time periods involved there is a lot of uncertainty about exactly what income and population levels were. We use Maddison (2010) as our baseline data source, but also explore robustness to using alternative statistics from Broadberry, Guan, and Li (2014). Second, predictions for population growth and income levels depend not just on productivity growth (which our model focuses on) but also on the Malthusian link between income per capita and population growth (which is a linear relationship in our model for analytical convenience). Mapping the model predictions into data for both population and income per capita is especially difficult if the income-population link shifts over time, which the evidence suggests is relevant for China and Europe in this period.43 We deal with this issue by focusing directly on productivity. Specifically, we use the available data on population and income levels in China and Western Europe to do a growth accounting exercise and back out productivity growth. Then, we show what it would take for the model to account for the observed differences in productivity growth.44 The underlying data and the details of the productivity calculations are described in Online Appendix J. The growth accounting exercise brings out the main facts that motivate the study, namely, a rise in productivity growth in Europe but not China after the year 1000. Using data from Maddison (2010) on total population and GDP per capita in Western Europe and China, we find that in the period from 1 to 1000, China led Western Europe in total factor productivity growth by 0.9% per generation (25 years). Subsequently, productivity growth accelerated substantially in Western Europe, resulting in a gap between the productivity growth rate of Western Europe and China of about 2.5% per generation from 1000 to 1820, right at the onset of the Industrial Revolution. Using instead Broadberry, Guan, and Li (2014) for historical estimates of income per capita leads to similar conclusions for Western Europe, but a more pessimistic view of productivity growth in China after 1000 (due to higher estimates of GDP per capita early on). Consequently, the estimated gap in productivity growth between Western Europe and China is even larger, amounting to 4.8% per generation from 1000 to 1500, and 7.4% from 1500 to 1820. From the perspective of our model, we interpret the gap in productivity growth between Western Europe and China as being due to a transition of Western Europe from the family to the guild equilibrium, whereas China remains in the clan equilibrium throughout. To assess whether this mechanism could possibly explain the data, Table II displays the values of the training cost of apprentices $$\bar{\delta }$$ and the corresponding equilibrium number of masters per apprentice m in the guild equilibrium that would need to be imposed to match the observed gap in productivity growth in each period (recall that $$\bar{\delta }$$ affects the balanced growth path in the guild equilibrium but not the clan equilibrium, where instead apprenticeship is limited by the size of the clan).45 The switch to the guild equilibrium is assumed to occur in 1250, so that Western Europe spends half of the period 1000–1500 and all of the period 1500–1820 in the guild equilibrium. TABLE II Accounting for Observed Differences in Productivity Growth between Western Europe and China     Model variables to match gap  Period  Gap in TFP growth  Training cost  Number of masters  1000–1500  2.5 (Maddison 2010)  0.016  1.15  1000–1500  4.8 (Broadberry, Guan, and Li 2014)  0.013  1.29  1500–1850  2.4 (Maddison 2010)  0.018  1.07  1500–1850  7.4 (Broadberry, Guan, and Li 2014)  0.014  1.22      Model variables to match gap  Period  Gap in TFP growth  Training cost  Number of masters  1000–1500  2.5 (Maddison 2010)  0.016  1.15  1000–1500  4.8 (Broadberry, Guan, and Li 2014)  0.013  1.29  1500–1850  2.4 (Maddison 2010)  0.018  1.07  1500–1850  7.4 (Broadberry, Guan, and Li 2014)  0.014  1.22  Notes. TFP growth is in percent per period (25 years). Details on computation of TFP growth in the data are given in Online Appendix J. The training cost displayed is the parameter $$\bar{\delta }$$ that matches the observed gap in TFP growth between an economy that is continuously in the clan equilibrium (as displayed in Table I) and an economy that starts out in the family equilibrium and then is in the guild equilibrium from 1250 onward. The number of masters is the m in the guild equilibrium corresponding to the displayed training cost. View Large The results in Table II show that the observed gap in productivity growth can be matched with training costs that still imply a low number of masters per apprentice. For matching Maddison (2010), the number of masters in the guild equilibrium is 1.15 for the first period and only 1.07 for the second period. If we fix the training cost at the level estimated based on the first period (1000–1500), the model actually overpredicts the gap in productivity growth between Western Europe and China in 1500–1820. One possible interpretation is that our assumption that Western Europe remained in the family equilibrium until 1250 is too pessimistic. Given the larger growth differential, matching the Broadberry, Guan, and Li (2014) numbers requires a lower training cost and results in a larger number of masters per apprentice, but even here the number of masters remains low, implying that only a minority of apprentices had multiple training opportunities. Clearly, it is not possible to quantify the relative importance of apprenticeship institutions for explaining the preindustrial rise in productivity growth in Western Europe with great precision: there is considerable uncertainty about the historical statistics, we lack direct historical measures for key statistics such as the number of masters per apprentice and the dispersion in craftsmen’s productivity, and we also lack precisely quantified measures of other sources of productivity growth (such as scientific breakthroughs and improvements in agriculture).46 Still, the results here do suggest that the apprenticeship channel has at least the potential to explain a substantial fraction of the rise of European productivity. V.B. Endogenous Transitions between Apprenticeship Institutions In the quantitative assessment above, we took the transition of Europe from the family to the guild equilibrium as well as the continued prevalence of the clan equilibrium in China as given. We now consider mechanisms that could explain why the two regions adopted different institutions. The importance of clans in China has recently been emphasized in the work of Avner Greif with different coauthors (e.g., Greif and Tabellini 2010; Greif, Iyigun, and Sasson 2012; Greif and Iyigun 2013; and Greif and Tabellini 2017). “[In China] clans relieved the poor, the elders and the orphans, lent money to members in need, educated the young, conducted religious services, built bridges, constructed dams, reclaimed land, protected property rights, and administered justice” (Greif and Tabellini 2017, 8). The importance of clans and kinship relations in Chinese economic history was far larger than in Europe, where society was organized along nuclear families.47 More generally, Kumar and Matsusaka (2009) report an array of historical evidence documenting the preindustrial importance of kinship networks in China, India, and the Islamic world. In contrast to the rest of the world, in Europe the nuclear family came to dominate (corresponding to the family equilibrium in our model). It is clear that by the High Middle Ages, extended families (or what we might call “clans”) had largely disappeared in Europe, and especially in the Western part (Shorter 1975, 284; Mitterauer 2010, 72). Peter Laslett, who has done more than anyone to establish this view, referred to the typical European family as the conjugal family unit, couple plus offspring (Laslett and Wall 1972). When, and even more so why, this pattern became so dominant in Europe remains to this day a debated question.48 To some extent it may have been encouraged by policies of the Western Christian church, as Greif and Tabellini argue. In Europe the Christian church actively discouraged practices that sustained kinship groups. The existence of institutions that encouraged the cooperation among nonkin, such as manors and monasteries, may have been equally important. By the early Middle Ages the nuclear family already dominated in some areas.49 Why did (nuclear) family-based Europe adopt better institutions over time, while clan-based regions did not? One potential explanation is that it is precisely Europe’s starting point in the low-growth family equilibrium that fostered the more rapid adoption of superior institutions. If adopting the guild or market systems is costly, the incentive for adoption depends on the the performance of the existing institutions. In our view, other world regions had less to gain from adopting new institutions, given that the clan-based system performed well for most purposes. Moreover, Europe was the only place in which the idea of a “corporation” took root—a rule-setting nonstate organization of people united by common interest and occupation, not blood ties. Guilds were only one example of such a corporation; monasteries and universities were in that regard quite similar. In many places, guilds formed an alliance with the crown and were even known as choses du roi in France, yet formally they remained autonomous. In the absence of the legal concept of such corporations, it is not clear that craft guilds of the type that developed in Europe were ever a realistic option elsewhere, except when they coincided with family ties. To formalize this possibility, consider the option of adopting the guild system at fixed per family cost of μ(N). We let this cost depend on the density of population, with μ΄(N) < 0 reflecting the idea that the adoption of guilds is cheaper when density is high (in line with the fact that the incidence of guilds increases with population density, see De Munck, Lourens, and Lucassen 2006). The cost μ(N) can be seen either as an aggregate cost of setting up guilds or courts, or linked to an individual decision, that is, the cost of moving from a small town to a larger city where contract enforcement institutions are in place. Formally, we need to compare the utilities of the parents from keeping the current system, uF → F and uC → C, with the ones from adopting the guild, uF → G and uC → G. Let us consider two economies having the same population N0 and knowledge k0, one in the family system, the other in the clan system. The distribution of income is thus the same in these two economies, as is mean income y0 and the number of children n0. Adults have to decide whether to pay the cost μ to adopt the guild. If the guild is adopted, the equilibrium price of apprenticeship will be p0, the number of apprentices per master will be a0, and the number of masters teaching one apprentice will be m0. The income of the children under the guild system will be given by: $$y^{{{\bf F}}\rightarrow {{\bf G}}}=y^{{{\bf C}}\rightarrow {{\bf G}}}\equiv y^{{\bf G}}_1$$. Let us now write the utility in the four cases:   \begin{eqnarray*} u^{{{\bf F}}\rightarrow {{\bf F}}} & =& y_0+\gamma \, n_0\, y^{{\bf F}}_1 +\kappa \, n_0 -\delta (n_0)\\ u^{{{\bf F}}\rightarrow {{\bf G}}} & = & y_0+\gamma \,n_0\, y^{{\bf G}}_1 +\kappa \, a_0-\delta (a_0)-\mu (N_0)\\ u^{{{\bf C}}\rightarrow {{\bf C}}} & = &y_0+\gamma \,n_0 \,y^{{\bf C}}_1 +\kappa \, (n_0)^{o+1} -\delta ((n_0)^{o+1})\\ u^{{{\bf C}}\rightarrow {{\bf G}}}& =&y_0+\gamma \, n_0 \,y^{{\bf G}}_1 +\kappa \, a_0-\delta (a_0)-\mu (N_0).\\ \end{eqnarray*} The following propositions gives the main result. Proposition 6 (Transition from Family and Clan to Guild). Consider two economies with the same initial knowledge and population, one in the family equilibrium, and one in the clan equilibrium. If limN→0μ(N) = ∞ and limN→∞μ(N) = 0, there exist population thresholds $$\underline{N}$$ and $$\overline{N}$$, with $$\underline{N}<\overline{N}$$, such that: if $$N_0<\underline{N}$$, none of the economies adopt the guild institution. if $$\underline{N}\le N_0\le \overline{N}$$, only the economy in the family equilibrium adopts the guild institution. if $$\overline{N}<N_0$$, both economies adopt the guild institution. Proof. See Online Appendix I. Given equal populations, the incentive to pay the fixed cost will be lower when the initial economic system is more successful, that is, a clan-based economy will be less likely to adopt than a family-based economy.50 Now take two hypothetical economies starting with the same low level of population. Suppose that one of them starts in the family equilibrium, whereas in the other the clan equilibrium prevails. In both economies, population is low and the guild equilibrium is not adopted, but there is still some technical progress and population growth. Given Proposition 3, population growth is higher in the clan economy. The question is which economy will first reach the population threshold that makes adopting the market optimal. The family economy has a lower threshold value, but, as it grows more slowly, it is not clear that it will adopt the guild first. A possible trajectory is the one shown in Figure V. Here, the family economy adopts the guild earlier, at date t1, which allows it to catch up and overtake the clan economy. Figure V View largeDownload slide Possible Dynamics of Two Economies Starting from the Same N0 Figure V View largeDownload slide Possible Dynamics of Two Economies Starting from the Same N0 Later on, the clan economy may or may not reach its own threshold above which it is optimal to adopt the guild, depending on the properties of the cost function μ(·), and in particular how it behaves when population becomes large. If limN→∞μ(N) = 0, the guild will be adopted for sure (which is the case covered in Proposition 6). But if limN→∞μ(N) > 0 (which is the case, for instance, if the total cost of setting up guilds includes a fixed cost per family), the economy may stay permanently in the clan equilibrium. The case displayed in the picture is where the economy that starts out in the clan equilibrium reaches the threshold at some later date t2. Proposition 7 (Clan as an Absorbing State). If  \begin{eqnarray*} \lim _{N \rightarrow \infty }\mu (N) &>& \gamma n^{{\bf C}}\left(y_1^{{\bf G}}-y^{{\bf C}}\right)+\kappa \left(a^{{\bf G}}_1-\left(n^{{\bf C}}\right)^{o+1}\right)-\delta \left(a^{{\bf G}}_1\right)\nonumber\\ &&+\,\delta ((n^{{\bf C}})^{o+1}), \end{eqnarray*} the economy in the clan equilibrium never adopts the guild. Here the values of nC and yC are defined in Proposition 3, and $$y_1^{{\bf G}}$$, $$a^{{\bf G}}_1$$ are values from the guild equilibrium after one period, starting from the clan balanced growth path as the initial condition. The proposition holds because, in a Malthusian context, income per person yC and $$y_1^{{\bf G}}$$ remains bounded. V.C. Complementary Mechanisms In reality, complementary mechanisms are likely to have also contributed to the failure of clan-based economies to adopt more efficient apprenticeship institutions. The clan-based organization had many advantages over the family other than faster knowledge growth; indeed, most economic and social life was organized around the clan. One specific aspect was that the clan adhered to what Greif and Tabellini call “limited morality”—a loyalty to kin but not to others. Such institutions have obvious attractions, such as an advantage in intra-group cooperation, the supply of public goods, and mutual insurance. But they have a comparative disadvantage in sustaining broader intergroup cooperation. In terms of economic efficiency, the two arrangements of family and clan therefore have clear trade-offs. The clan economizes on enforcement costs, but at the cost of economies of scale and pluralism. The bottom line is that for a successful clan-based economy, the cost of giving up the existing system of social organization (in favor of the guild system) is likely to have been much higher than what our stylized model suggests. Another dimension is that the dominance of the nuclear family in Europe created a need early on for organizations that cut across family lines. Guilds were independent of families, but they had many antecedents that had a similar legal status (such as monasteries, universities, or independent cities). Hence, earlier institutional developments may have made the adoption of guilds in Europe much cheaper compared to clan-based societies. Still other factors also may have been at work in specific regions. A striking difference between China and Europe before the Industrial Revolution is in settlement patterns. China was, as Greif and Tabellini point out, a land of clans, but much less than Europe a land of cities. As Rosenthal and Wong (2011, 113) stress, Chinese manufacturing was much less concentrated in cities than it was in Europe—a difference they attribute to the dissimilar warfare patterns. In China the main threat came not from one’s neighbors but from invading nomads from the steppe; hence the need for a Great Wall. Cities were walled to some extent, but walled cities were far fewer than in Europe, and the walls served more as symbols than as protection from attack. As much as 97% of the Chinese population lived outside the walled cities. This difference in urbanization is an important clue to why European institutions evolved in a different way. If the cost of adopting guilds depends on population density, the “effective” population density would have been much higher in Europe, because craftsmen were concentrated in small urban areas. In the model above, that difference would be represented as a lower level of the cost function μ(N) for a given overall population. In our analysis of institutional transitions, we focus on the introduction of apprenticeships and guilds in Western Europe. An important topic for future research is to consider also the ensuing transition from guild to market, which results in even more rapid growth. If we are comparing Europe with the world of clans, we must note that all-powerful guilds were not ubiquitous in Europe, and that by the middle of the seventeenth century craft guilds were declining in many areas. In the Netherlands, in England, and even to some extent in France, the power of guilds to impose restrictions on entry and to control product markets faded in the eighteenth century. It was then that “free trade” regions (i.e., exempted from guild control) emerged, such as the famous one in the Faubourg St. Antoine near Paris (Horn 2015, 1–3). In other words, not only did Europe adopt guilds, a superior set of institutions for transmitting skills relative to clans, but also, Europe was in transit to a market system which was even better at it. In nineteenth-century Britain, apprenticeship persisted despite the abolition of the 1563 Statute of Artificers in 1814. It did so because even in an age of mass schooling, the transmission of tacit technical knowledge through personal contact remained a critical part of skills transmission. In the United States, however, the absence of a tradition and high mobility made third party enforcement of apprenticeship contracts impracticable and the “market for apprenticeship” virtually disappeared (Elbaum 1989; Elbaum and Singh 1995). Notice that the explanation for the earlier adoption of guilds in Europe formulated in Proposition 6, namely, that for a given cost of adopting the new institution the benefits are higher if the initial condition is worse, cannot explain why Europe was also first to adopt the market system. Indeed, once Europe adopts the guild it has a better initial condition compared to clan-based economies, which based solely on this argument should lead to a slower adoption of an even better institution. Instead, this transition can be understood in terms of a lower cost of adopting the market once the guild is already in place. The market is closely related to the guild; both systems are based on impersonal institutions such as the corporations discussed above, so that once the guild system is established, moving to the market is a small step compared to jumping all the way from clan to market. More generally, the market system (and the guild, albeit to a lesser extent) relies on well defined and enforced property rights, and hence sufficient state capacity. The rise of the market equilibrium for apprenticeship therefore depends on, and is complementary to, wider changes in the economic and political organization of society that occurred at the same time. Conversely, the benefits that the clan system conferred beyond its narrow economic implications also may have contributed to a relatively higher cost of adopting the market. VI. Conclusion In this article, we have examined sources of productivity growth in preindustrial societies, in order to explain the economic ascendency of Western Europe in the centuries leading up to industrialization. We developed a model of person-to-person exchanges of ideas, and argued that apprenticeship institutions that regulate the transmission of tacit knowledge between generations are key for understanding the performance of preindustrial economies. In our analysis, we have put the spotlight on differences across institutions in the dissemination of knowledge. Of course, a second channel of productivity growth is innovation, that is, the creation of entirely new knowledge. Our analysis does allow for innovation in the form of new ideas, but we have held this aspect of productivity growth constant across institutions. A natural extension of our work would be to examine how the institutional differences we identify here as driving differences in the dissemination of knowledge may affect incentives for original innovation. The importance of highly skilled craftsmen for the innovative activities that led to the Industrial Revolution has become an important theme in the industrialization literature. Indeed, some scholars such as Hilaire-Pérez (2007) and Epstein (2013) have argued that rising artisanal skill levels and the high level of innovation among the most sophisticated craftsmen alone could have fostered the Industrial Revolution. While such an extreme view slights the contribution of codifiable knowledge and formal science, there is no question that high-ability artisans were a pivotal element in the rise of modern technology, and that Britain’s leadership rested to a great extent on the advantage it had in skilled workers (Kelly, Mokyr, and Ó Gráda 2014). Advances were made by a literate and educated elite, the classic example of upper-tail human capital (de la Croix and Licandro 2015; Squicciarini and Voigtländer 2015). Increasing longevity, moreover, in the mid-seventeenth century may have stimulated further investment in the human capital of this elite and facilitated the diffusion of their knowledge. Yet just as importantly, these highly educated people interacted with the most skilled and dexterous craftsmen (Meisenzahl and Mokyr 2012). A powerful example of this complementarity is the British watch industry in the eighteenth century. Watchmaking was a high-level skill, originally regulated by a guild (the Worshipful Company of Clockmakers, one of the original livery companies of the City of London) but by 1700 more or less free of guild restrictions. Training occurred exclusively through master-apprentice relations. In the seventeenth century, the industry experienced a major technological shock by the invention of the spiral-spring balance in watches by two of the best minds of the seventeenth century, Christiaan Huygens and Robert Hooke (ca. 1675). No similar macro-invention occurred over the subsequent century, yet the real price of watches fell by an average of 1.3% a year between 1685 and 1810 (Kelly and Ó Gráda 2016). As Kelly and Ó Gráda note, “Once this conceptual breakthrough occurred, England’s extensive tradition of metal working and the relative absence of restrictions on hiring apprentices, along with an extensive market of affluent consumers, allowed its watch industry to expand rapidly” (2016, 5). An eighteenth-century observer noted that for watchmaking an apprentice needed at least 14 years (or fewer if he was “tolerably acute”) and that to be truly skilled he needed to learn a “smattering of mechanics and mathematics”—presumably skills that were taught by the master (Campbell 1747, 252). Another issue is the interaction of the acquisition of tacit knowledge through apprenticeship with formal education after the rise of mass schooling in the nineteenth and early twentieth centuries. A key question here is whether apprenticeship and formal schooling should be viewed as complements or substitutes. One may conjecture that the more general knowledge provided by formal schooling was more appropriate and flexible in a time when technological change made entire crafts and occupations obsolete, and workers had to be prepared to move across multiple fields and occupations over their careers. If this factor was important, widespread apprenticeship could be viewed as a handicap that slowed down the transition to mass schooling necessary for modern growth. But it is also possible that tacit and formal knowledge complemented each other. To the present day, Germany has a system of “dual education” that combines apprenticeship with formal education in state schools. The system is generally viewed as an important contributor to German economic success, resulting (among other things) in much lower youth unemployment than other European countries. At the same time, Germany also has substantially lower participation in tertiary education than the United States. There may be some role for forms of apprenticeship even at the highest level of education. Graduate school in economics, for example, combines formal education with forms of apprenticeship (i.e., graduate students working as research assistants). We leave for future research an exploration of the various complementarities between the creation and dissemination of tacit and formal knowledge within a model of person-to-person exchanges of ideas. Supplementary Material An Online Appendix for this article can be found at The Quarterly Journal of Economics online. Data and code replicating the tables and figures in this paper can be found in de la Croix, Doepke, and Mokyr (2017), in the Harvard Dataverse, doi:10.7910/DVN/67KTKX. Footnotes * We thank Robert Barro and Larry Katz (the editors), four anonymous referees, Francisca Antman, Hal Cole, Alice Fabre, Cecilia García-Peñalosa, Murat Iyigun, Pete Klenow, Georgi Kocharkov, Lars Lønstrup, Guido Lorenzoni, Kiminori Matsuyama, Ben Moll, Ezra Oberfield, Michèle Tertilt, Chris Tonetti, Joachim Voth, Simone Wegge, and participants at many conference and seminar presentations for comments that helped substantially improve the article. Financial support from the National Science Foundation (grant SES-0820409) and from the French-speaking community of Belgium (grant ARC 15/19-063) is gratefully acknowledged. 1. Our emphasis on the role of clans in organizing economic life for comparative development is shared with Greif and Tabellini (2010), although the mechanisms considered are entirely different. 2. Specifically, the underlying engine of growth in our model is closely related to Lucas (2009), who in turn builds on earlier seminal contributions by Jovanovic and Rob (1989), Kortum (1997), and Eaton and Kortum (1999). Earlier explicit models of endogenous technological progress build on R&D efforts by firms, following the seminal papers of Romer (1990) and Aghion and Howitt (1992). While such models are useful for analyzing innovation in modern times, their applicability to preindustrial growth is doubtful, partly because legal protections for intellectual property became widespread only recently. 3. Recent growth models that build on a process of this kind (in addition to Lucas 2009) include Luttmer (2007, 2015); Alvarez, Buera, and Lucas (2008, 2013); Lucas and Moll (2014); Perla and Tonetti (2014); and König, Lorenz, and Zilibotti (2016). Among these papers, Luttmer (2015) also considers a market environment where students are matched to teachers, although without allowing for different institutions. Particularly relevant to our work is also Fogli and Veldkamp (2012), where the structure of a network has important ramifications for the rate of productivity growth. The research is also related to models of productivity growth over the very long run such as Kremer (1993) and Jones (2001). 4. Additional innovations relative to the recent literature on growth based on the exchange of ideas are that we examine endogenous institutional change, and that we allow for endogenous population growth. 5. We consider an era that is characterized by a sharp division of labor by gender, and where formal apprenticeship generally was open only to boys. Hence, we will refer to master and apprentice as “he” throughout the article, and our model does not distinguish two genders. 6. Of course, printed material became increasingly widespread after Gutenberg, but played a limited role in the training of craftsmen. The printing press was relatively more important for providing access to science and and similar “top end” knowledge; see Dittmar (2011) for an analysis of the overall impact of printing on early economic growth. 7. Steffens (2001, 124–25) observes on the basis of nineteenth-century Belgian apprentices that little explicit teaching was carried out and that learning was occurring mainly through the performance of tasks. 8. The suggestion by Epstein (2008, 61) that the contract could be rewritten to prevent either side from defaulting is not persuasive. For instance, he suggests that by backloading some of the payments from master to apprentice, the latter would be deterred from defecting early—but that of course just shifts the opportunity to cheat from the apprentice to the master. 9. For a more nuanced view, see Davies (1956) who argues that enforcement was a function of the economic circumstances, but agrees that there is little evidence of apprentices being sued or denied the right to exercise their occupation for having served fewer than seven years. 10. Wallis (2008, 849) compares the process with what happens in more modern days amongst minaret builder apprentices in Yemen: “instruction is implicit and fragmented, questions are rarely posed, and reprimands rather than corrections form the majority of feedback.” De Munck makes a similar point when he writes that “masters were merely expected to point out what had gone wrong and what might be improved” (cited in De Munck and Soly 2007, 16, 79). 11. The transition away from a kinship-based training system occurred in China much later and slower than in Europe. The clan-based economy worked well for China, and there was little need for reform until European progress began to be a threat. Yet the differences were of degree, not of essence. The existence of some guilds in China from the late Ming period on is established fact, and by the late nineteenth century they had become quite powerful and operated as rent-seeking cartels (Brown 1979). Much more than in Europe, however, these guilds were based on common ancestry. There is some evidence that they may have made provisions about apprenticeship, though formal evidence of that is lacking before the twentieth century (Morse 1909, 31–34; Moll-Murata 2013, 234). There is no evidence, however, that these guilds did much to enforce the contract between master and apprentice. Guild regulations often restricted the number of apprentices that a master could take (as a measure to restrict entry, no doubt). In some cases guilds specifically postulated that only family members could learn the trade (Morse 1909, 33). However, it is clear that, in contrast with Europe, the ancient tradition of a close association between kinship (common origin) and training remained intact (Macgowan 1888–89, 181). In twentieth-century southern China it was reported that “not only were the elders of the town the heads of the clan but the entire industry was organized and monopolized by the clan” (Burgess 1928, 71). Even in modern China, “crucial skills are often kept within the family. The craftsman-owner and other experienced craftsmen intentionally inhibit the acquisition of knowledge by new workers who are not biologically related” (Zhu, Chen, and Dai 2016; see also Gowlland 2012). The practice of training within kinship units was especially prevalent in high-skilled crafts such as medicine (Islam 2016). 12. The cases of Japan and the Ottoman Empire are less clear cut; guilds clearly played some role here (see Nagata 2007, 2008; Yildirim 2008), but less is known about their role for organizing apprenticeship and the importance of family ties in the selection of apprentices. 13. The reputation and trust that sustained market equilibria depended to some extent on some level of third-party enforcement, in that contracts were signed in “the shadow of the law” in which both parties knew that in the last resort both could turn to the courts as a grim strategy, and hence it sustained voluntary cooperation. In such a world the surviving documents (most of them from court records) would reflect off the equilibrium path behavior and thus be biased in not reflecting the basic effectiveness of the system. 14. Our main results would be identical if a separate class of landowners were introduced. The model abstracts from an explicit farming sector; however, it would be straightforward to include farm labor as an additional factor of production (see Online Appendix A), or alternatively we can interpret some of the adults who we refer to as craftsmen as farmers. 15. This point is made explicit in Online Appendix A, where we extend the model to allow for a farming sector. 16. This implies that more productive masters cannot hire other masters to increase production, gain market share, and force less efficient masters to close down their workshop. 17. The Fréchet distribution also implies that growth in knowledge k shifts up productivity proportionally without changing the shape of the distribution; all quantiles of the knowledge distribution are proportional to the mean kθ, and standard measures of inequality and dispersion (such as the Gini coefficient) are independent of k. 18. Empirical work has found both a fertility and a mortality link to income per capita in medieval England, but gradually weakening over time (Kelly and Ó Gráda 2012, 2014). Our results for institutional comparisons would be similar in a framework that allows for growing income per capita even in the long term. 19. Fertility preferences can be motivated through parental altruism (Barro and Becker 1989 and applied in a Malthusian context by Doepke 2004, among others) or through direct preferences over the quantity and quality of children (e.g., Galor and Weil 2000; de la Croix and Doepke 2003). 20. This result follows from the min stability property of the exponential distribution. In particular, if ha and hb are independent exponentially distributed random variables with rates ka and kb, then min [ha, hb] is exponentially distributed with rate ka + kb. 21. Historically, the cost of training apprentices probably involved other components that may have varied with the quality of the master, such as his opportunity costs and the materials and equipment used by apprentices while learning. If opportunity costs were a major component of these costs, this would be one reason why the most skilled masters might have charged a higher price for taking on apprentices. 22. See Jovanovic (2014) for a study where a signal of skill is available, and assortative matching of young and old workers is an important driver of growth. 23. Luttmer (2015) provides an alternative approach for modeling the assignment of students to teachers. Luttmer’s model has the advantage of allowing for observability and not relying on an unbounded support of existing knowledge, albeit at the cost of a considerably more complex analysis. 24. The existence of two-sided moral hazard might in practice have made the problem better. The master might have an incentive to invest in teaching his apprentice and create loyalty if some of the compensation to masters came in the form of labor that the apprentice carried out for the master in the later stages of his apprenticeship. 25. If candidates are different from one another and the differences in talent are observable, one might expect assortative matching in that the most talented apprentices would be allocated to the most productive masters. We actually see this kind of matching in the data: the great London machine-tool maker Joseph Bramah trained the equally famous Henry Maudslay, who in turned trained some of the best mechanics and engineers of the nineteenth century. Such heterogeneity in the talent of the apprentices themselves would be an interesting extension of our model but again at the cost of greater complexity. 26. We should note that in reality, the distinction between centralized and decentralized institutions is less sharp than in our theory. Even where centralized enforcement institutions existed, they were often complemented by a self-enforcing mechanism based on trust and reputation (Humphries 2003; Mokyr 2008). 27. The cost can be interpreted as physical punishment, as destruction of property, or as spreading rumors that induce others not to buy from the individual in question. 28. Given that there are subsequent generations, one could also define a dynamic game involving all generations. However, given that preferences are of the warm-glow type, decisions of future generations do not affect the payoffs of the current generation, so that dynamic considerations do not change the strategic trade-offs faced by the players. 29. For any communication structure, the family equilibrium always exists, because in the expectation that no one else will punish shirking masters it is optimal to (i) never punish shirking masters either and (ii) not send one’s own children to be apprenticed outside the family. 30. The required assumptions can be made precise; what is key is that maximum population growth is larger than the maximum rate of effective productivity growth. 31. The curve is concave if θ(1 − α) < α, but results do not depend on this condition. 32. In reality, it may not be necessary to receive full training from all clan members. Instead, one could assume that apprentices initially search over the entire group, sample the masters’ knowledge, but then spend most of their time learning from the clan member identified to have the lowest h. We adopt the simpler notion of learning equally from all masters to preserve the symmetry that makes the problem tractable. 33. Another possibility is that altruism is at a level sufficient for parents to want to send their children to some, but not all, available masters. Characterizing the balanced growth path in this case is more complicated, because the selection of which masters to train with is nontrivial. Nevertheless, the basic shortcoming of the clan-based institution, namely, that different masters have similar knowledge and so less new knowledge can be gained by getting trained by more of them, would still apply in this type of equilibrium. 34. We assume that even though the knowledge of the master is unobservable, the act of teaching is not, and the only choice for the master is to either transmit the actual skill or not to teach at all. Hence, being able to observe whether the master teaches is sufficient to allow contract enforcement. 35. The contrast between clan and market equilibrium is an example of social structure being important for economic outcomes; a similar application to technology diffusion is provided in the recent work of Fogli and Veldkamp (2012). 36. We focus on the role of guilds in limiting entry because this is what matters for growth in our setting. Another anticompetitive role of guilds is to limit competition in product markets (Ogilvie 2014, 2016). In our model, this feature does not arise because we abstract from an intensive margin of labor supply. We also abstract from the introduction of new goods (as in increasing-variety models of growth); if a new good were a close substitute to wares of an existing guild, the guild would have an additional anticompetitive motive of hindering the introduction of the good. 37. This feature provides a contrast between our work and other recent research on the economic role of guilds, such as Desmet and Parente (2014). 38. To simplify notation, we assume that the children of masters in trade j will look for apprenticeship in other trades. This can be rationalized by a small role for “talent” in choosing trades. Our results do not depend on this assumption, because in equilibrium the returns of entering each trade are equalized. 39. In reality, of course, the European economy in the preindustrial era had examples of all four equilibria occurring simultaneously, since family equilibria were still common everywhere in Europe both in farming and in some high-end occupations. In France, for instance, there is strong evidence of kinship-related apprentice relations in the baker’s trade (Kaplan 1996, 193). Conversely, guilds of some kind were found in much of Eurasia including the Sreni of ancient India. But the fact remains that only (Western) Europe was characterized by the widespread adoption of a system build on exchange of knowledge outside of family lines. 40. Our theoretical analysis implicitly allows for such wide diffusion by assuming that guilds comprise all masters in a given trade, rather than being limited to specific cities or regions. 41. That is, a different choice of s would result in a proportionally different level of income per capita in the balanced growth path, but implications for growth and apprenticeships would be identical. 42. In the model, we treat m as a continuous variable. A value of m of, say, 1.1 should be interpreted to correspond to a situation in the data where most apprentices learn from a single master, and only about 1 in 10 apprentices benefit from multiple learning opportunities. 43. See, for example, Voigtländer and Voth (2013a, 2013b) on demographic changes in Europe after the Black Death. 44. To match the data for both income and population, it would be necessary to include a more flexible income-population link in the model and let this vary over time. This is in principle straightforward to do but also orthogonal to our focus on the implications of apprenticeship institutions for productivity growth, and hence we do not include such an extension here. Notice that productivity growth in the model is pinned down by the number of masters per apprentice m, and for given m does not depend on the assumed income-population link. 45. The numbers for productivity growth in Table II are based on the balanced growth rate for each apprenticeship institution. However, the model displays little transitional dynamics in terms of productivity growth, so that computations based on dynamic transition paths lead to virtually the same results. 46. Regarding the role of agricultural productivity, we argue in Online Appendix J that even though reliable measures of sector-level differences in productivity growth between Western Europe and other regions do not exist, the evidence suggests that improvements in artisanal productivity are likely to account for the largest portion of gap. 47. In his recent summary, Von Glahn (2016) remarks that “the salient place of social networks and kinship institutions such as lineage trusts in Chinese business often has been regarded as favoring a ‘patronage economy’ that hindered the development of impersonal, professional management” (396). Similarly, in her recent study of the clan records as a source of historical information, Shiue (2016) notes that Chinese lineage organization was quite different from Western forms of social organization and stresses the Confucian principle of kinship as the organizing principle of human relationships (462). The importance of kinship and lineage in the enforcement of other contracts is illustrated in Zelin and Gardella (2004). 48. The dominance of the nuclear family went together with the enforcement of strict monogamy, when it became infeasible for men to simultaneously father children from multiple women, and remarriage was only possible after widowhood; see de la Croix and Mariani (2015). 49. 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Clans, Guilds, and Markets: Apprenticeship Institutions and Growth in the Preindustrial Economy

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Oxford University Press
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© The Author(s) 2017. Published by Oxford University Press on behalf of the President and Fellows of Harvard College. All rights reserved. For Permissions, please email: journals.permissions@oup.com
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Abstract

Abstract In the centuries leading up to the Industrial Revolution, Western Europe gradually pulled ahead of other world regions in terms of technological creativity, population growth, and income per capita. We argue that superior institutions for the creation and dissemination of productive knowledge help explain the European advantage. We build a model of technological progress in a preindustrial economy that emphasizes the person-to-person transmission of tacit knowledge. The young learn as apprentices from the old. Institutions such as the family, the clan, the guild, and the market organize who learns from whom. We argue that medieval European institutions such as guilds, and specific features such as journeymanship, can explain the rise of Europe relative to regions that relied on the transmission of knowledge within closed kinship systems (extended families or clans). JEL Codes: E02, J24, N10, N30, O33, O43. I. Introduction The intergenerational transmission of skills and more generally of “knowledge how” has been central to the functioning of all economies since the emergence of agriculture. Historically, this knowledge was almost entirely “tacit” knowledge, in the standard sense used today in the economics of knowledge literature (Cowan and Foray 1997, 71–73; Foray 2004, 96–98). Although economic historians have long recognized its importance for the functioning of the economy (Dunlop 1911, 1912), it is only more recently that tacit knowledge has been explicitly connected with the literature on human capital and its role in the Industrial Revolution and the emergence of modern economic growth (Humphries 2003, 2010; Kelly, Mokyr, and Ó Gráda 2014). The main mechanism through which tacit skills were transmitted across individuals was apprenticeship, a relation linking a skilled adult to a youngster whom he taught the trade. The literature on the economics of apprenticeship has focused on a number of topics we shall discuss in some detail below. Yet little has been done to analyze apprenticeship as a global phenomenon, organized in different modes. In this article, we examine the role of apprenticeship institutions in explaining economic growth in the preindustrial era. We build a model of technological progress that emphasizes the person-to-person transmission of tacit knowledge from the old to the young (as in Lucas 2009; Lucas and Moll 2014). Doing so allows us to go beyond the simplified representations of technological progress used in existing models of preindustrial growth, such as Galor (2011). In our setup, a key part is played by institutions—the family, the clan, the guild, and the market—that organize who learns from whom. We argue that the archetypes of modes of apprenticeship that we consider in the model, while abstract, can be mapped into actual institutions that were prevalent throughout history in different world regions. We use the theory to address a central question about preindustrial growth, namely, why Western Europe surpassed other regions in technological progress and growth in the centuries leading up to industrialization. What is at stake here is that while on the whole medieval Europe was not more advanced than China, India, or the Middle East, at some point before 1700 the seeds of Europe’s primacy were planted, even if they were not to come to full fruition until the Industrial Revolution after 1750. These seeds were of many kinds, and here we will concentrate on one kind only, namely, artisanal skills. In particular, we claim that late medieval and early modern European institutions such as guilds, with specific regulatory features such as apprenticeship and journeymanship, were critical in speeding up the dissemination of new productive knowledge in Europe, compared to regions that relied on the transmission of knowledge within extended families or clans.1 After 1500, many decades before the Industrial Revolution, we can readily observe major advances in European craft production in products as diverse as shipbuilding, textiles, lensgrinding, metalworking, printing, mining, clockmaking, millwrighting, carpentry, ceramics, painting, and so on. Before 1700, few if any of those improvements had much to do with formal codified knowledge; they derived first and foremost from improved artisanal skills—which historians have called “mindful hands” (Roberts and Schaffer 2007)—that disseminated rapidly. Before developing a theory of the modes of institutional organization of apprenticeship and their implications for knowledge dissemination, we address three key issues one should address in modeling. First, the main issue is the extent to which the mode of organizing the transmission of skills was consistent with technological progress. We take the view from the outset that all systems of apprenticeship are consistent with at least some degree of progress. Even when the system has strong conservative elements that administer rigid tests on the existing procedures and techniques, learning by doing generates a certain cumulative drift over time that can raise productivity, even in the most conservative systems. That said, the rates at which innovation occurred within artisanal systems have differed dramatically over time, over different societies and even between different products. Differences in rates of technological progress may in principle have two different sources, namely, the rate of original innovation and the speed of the dissemination of existing ideas. While we discuss implications for original innovation, our theoretical analysis focuses on the second channel. Specifically, we ask how conducive the intergenerational transmission mechanism was to the dissemination of best-practice techniques, and how conducive an apprenticeship system based on personal contacts and mostly local networks was to closing gaps between best-practice and average-practice techniques. Second, the training contract between master and apprentice (whether formal or implicit), for obvious reasons, represents a complicated transaction. For one thing, unless that transmission occurs within the nuclear family (in a father-son line), the person negotiating the transaction is not the subject of the contract himself but his parents, raising inevitable agency problems. Moreover, the contract written with the “master” by its very nature is largely incomplete. The details of what is to be taught, how well, how fast, what tools and materials the pupil would be allowed to use, as well as other aspects such as room and board, are impossible to specify fully in advance. Equally, apart from a flat fee that many apprentices paid up front, the other services rendered by the apprentice, such as labor, were hard to enumerate. This was, in a word, an archetypical incomplete contract. As a consequence, in our theoretical analysis moral hazard in the master-apprentice relationship is the central element that creates a need for institutions to organize the transmission of knowledge. Third, as a result of the contractual problems in writing an apprenticeship agreement, a variety of institutional setups for supervising and arbitrating the apprentice-master relations can be found in the past. In all cases except direct parent-child relationships, some kind of enforcement mechanism was required. Basically three types of institutions can be discerned that enforced contracts and, as a result, ended up regulating the industry in some form. They were (i) informal institutions, based on reputation and trust; (ii) nonstate semiformal institutions (guilds, local authorities such as the Dutch neringen); and (iii) third-party (state) enforcement, usually by local authorities and courts. In many places all three worked simultaneously and should be regarded as complements, but their relative importance varied quite a bit. In our theoretical analysis, we map the wide variety of historical institutions into four archetypes, namely the (nuclear) family, the clan (i.e., a trust-based institution comprising an extended family), the guild (a semiformal institution), and the market (which constitutes formal contract enforcement by a third party). Our theoretical model builds on a recent literature in the theory of economic growth that puts the spotlight on the dissemination of knowledge through the interpersonal exchange of ideas.2 Given our focus on preindustrial growth, the analysis is carried out in a Malthusian setting with endogenous population growth in which the factors of production are the fixed factor land and the supply of effective labor by workers (“craftsmen”) in a variety of trades. Knowledge is represented as the efficiency with which craftsmen perform tasks. While there is some scope for new innovation, the main engine of technological progress is the transmission of productive knowledge from old to young workers. Young workers learn from elders through a form of apprenticeship. There is a distribution of knowledge (or productivity) across workers, and when young workers learn from multiple old workers, they can adopt the best technique to which they have been exposed. Through this process, average productivity in the economy increases over time.3 The central features of our analysis are that the transmission of knowledge (teaching) requires effort on the part of the master; that this leads to a moral hazard problem in the master-apprentice relationship; and that, as a consequence, institutions that mitigate or eliminate the moral hazard problem are key determinants of the dissemination of knowledge and economic growth.4 The “family” in our analysis is the polar case where no enforcement mechanism is available that reaches beyond the nuclear family, and hence children learn only from their own parents. In the family equilibrium, there is still some technological progress due to experimentation with new ideas and innovation within the family, but there is no dissemination of knowledge, and hence the rate of technological progress is low. The “clan” is an extended family where reputation and trust provide an informal enforcement mechanism. Hence, children can become apprentices of members of the clan other than their own parent (such as uncles). The clan equilibrium leads to faster technological progress compared to the family equilibrium, because productive new ideas disseminate within each clan. The “guild” in our model is a coalition of all the masters in a given trade that provides a semiformal enforcement mechanism, but also regulates (monopolizes) apprenticeship within the trade. Finally, the “market” is a formal enforcement institution where an outside authority (such as the state) enforces contracts, and in addition, rules are in place that prevent anticompetitive behavior (such as limitations on the supply of apprenticeship imposed by guilds). In terms of mapping the model into historical institutions, we regard most world regions (in particular, China, India, and the Middle East) as being characterized by the clan equilibrium throughout the preindustrial era. Here extended families organized most aspects of economic life, including the transmission of skills between generations. The distinctive features of Western Europe are a much larger role of the nuclear family from the first centuries of the Common Era; little significance of extended families; and an increasing relevance of institutions that do not rely on family ties (such as cities and indeed guilds) starting in the Middle Ages. Hence, in the language of the model, we view Western Europe as undergoing a transition from the family to the guild equilibrium during the Middle Ages, and onward to the market equilibrium in the centuries leading up to the Industrial Revolution. To explain the emerging primacy of Western Europe over other world regions, we look to the comparative growth performance of the clan and guild institutions. Both the clan and the guild provided for apprenticeship outside the nuclear family, and a count against the guild is the anticompetitive nature of guilds, that is, the possibility that guilds limited access to apprenticeship to raise prices. However, our analysis identifies a much more important force that explains why the Western European system of knowledge acquisition came to dominate. Namely, apprenticeship within guilds was independent of family ties, and thus allowed for dissemination of knowledge in the entire economy, whereas in a clan-based system the dissemination of knowledge was impaired. A different side of the same coin is that in a clan-based system, relatively little is gained by learning from multiple elders, because given that these elders belong to the same clan, they are likely to have received the same training and thus to have very similar knowledge. In contrast, in a guild (and also in the market) family ties do not limit apprenticeship, and hence the young can sample from a much wider variety of knowledge, implying that apprenticeship is more productive and knowledge disseminates more quickly. The historical evidence shows that, indeed, in Europe master and apprentice were far less likely to be related to each other than elsewhere. Moreover, the guild system sometimes included specific features, in particular journeymanship, that had the effect of providing access to a broader range of knowledge and fostering the spread of new techniques and ideas. In a narrower system based on blood relationships, such a wide exchange of ideas was not feasible. Our framework can also be used to explore why institutional change (i.e., the adoption of guilds and, later on, the market) took place in Europe, but not elsewhere. If adopting new institutions is costly, the incentive to adopt will be lower when the initial economic system is relatively more successful, that is, in a clan-based economy compared to a family-based economy. If the cost of adopting new institutions declines with population density, it is possible that new institutions will only be adopted if the economy starts out in the family equilibrium, but not if the clan equilibrium is the initial condition. We also discuss complementary mechanisms (going beyond the formal model) that are likely to have contributed to faster institutional change in Europe. The article engages three recent literatures in economic history that have received considerable attention. One is the debate over whether craft guilds were on balance a hindrance to technological progress, or whether they stimulated it by supporting apprenticeship relations (for a recent summary, see van Zanden and Prak 2013b and Ogilvie 2004). The second new literature is the one emphasizing the ingenuity of artisans and skilled workers in generating knowledge, and minimizing the classic distinction between formal science and practical knowledge. Roberts and Schaffer stress the importance of “local technological projects” carried out by the “tacit genius of on-the-spot practitioners”; here they clearly refer to thoughtful and well-trained artisans who advance the frontiers of useful knowledge (Roberts and Schaffer 2007; see also Long 2011). Little in this literature, however, has focused on the intergenerational transmission of the knowledge embedded in such “mindful hands” through the institutions of apprenticeship. The third literature is concerned with understanding economic, institutional, and cultural differences between Europe and other world regions as a source of the relative rise of Europe and decline of other regions in the centuries leading up to the Industrial Revolution (e.g., Voigtländer and Voth 2013a, 2013b; Broadberry 2015). We build in particular on the work by Greif and Tabellini (2017) on the role of clans in China versus “corporations” in Europe (i.e., formal organizations that exist independently of family ties) for sustaining cooperation (see also Greif 2006; Greif, Iyigun, and Sasson 2012). However, Greif and Tabellini do not consider the implications of such institutions for the generation and dissemination of productive knowledge. The article is organized as follows. Section II describes key historical aspects of apprenticeship systems on which we base our theory. Our formal model of knowledge growth is described in Section III. Section IV analyzes the different apprenticeship institutions and derives their implications for economic growth. Section V quantifies the ability of the theory to account for the rise of European technological primacy, and considers endogenous adoption of institutions. Section VI concludes. Proofs for formal propositions, theoretical extensions, and a growth accounting exercise are provided in the Online Appendix. II. Historical Background II.A. Learning on the Shop Floor Through most of history, the acquisition of human capital took the form, in the felicitous phrase of De Munck and Soly (2007), of “learning on the shop floor.” One should not take this too literally: some skills had to be learned on board ships or at the bottom of coal mines. Yet it remains true that learning took place through personal contact between a designated “master” and his apprentice.5 As they point out (2007, 6), before the middle of the nineteenth century there were few alternative routes for acquiring useful productive skills. Some of the better schools, such as Britain’s dissenting academies or the drawing schools that emerged on the European continent around 1600, taught, in addition to the three Rs, some useful skills such as draftmanship, chemistry, and geography. But on the whole, the one-on-one learning process was the one experienced by most.6 The economics of apprenticeship in the premodern world is based on the insight that each master artisan basically produced a set of two connected outputs: a commodity or service, and new craftsmen. In other words, he sold “human capital.” The economics of such a setup explains many of the historical features of the system. The best known, of course, is that the apprentice had to supply labor services to the master in partial payment for his training and his room and board. In some instances, this component became so large that the apprentice contract was more of a labor contract than a training arrangement.7 Such provisions underline the basic idea of joint production, in which the two activities—production and training—were strongly complementary. As Humphries (2003) has pointed out, the contract between the master and the apprentice in any institutional setting is problematic in two ways. First, the flows of the services transacted for is nonsynchronic (although the exact timing differed from occupation to occupation). Second, these flows cannot be fully specified ex ante or observed ex post. The apprentice, by the very nature of the teaching process, is not in a position to assess adequately whether he has received what he has paid for until the contract is terminated. Even if the apprentice himself could observe the implementation of the contract, the details would be unverifiable for third parties and adjudicators. Because the transaction is not repeated, the party who receives the services or payment first has an incentive to shirk. This is known ex ante, and therefore it is possible that the transaction does not take place and that the economy would suffer from serious underproduction of training.8 However, since that would mean that intergenerational transmission of knowledge would take place exclusively within families, some societies have come up with institutions that allowed the contracts to be enforced between unrelated parties. These institutions curbed opportunistic behavior in different ways, but they all required some kind of credible punishment. As we will see in our theoretical analysis below, the more sophisticated and effective institutions led to better quality of training (in a precise manner we will define) and thus led to faster technological progress. II.B. Apprenticeship in Western Europe The evidence suggests that at least in early modern Europe the market for apprenticeship functioned reasonably well, despite the obvious dangers of market failure. A good indicator of the working of the market for human capital, at least in Britain, was the premium that parents paid to a master. Occupations that demanded more skill and promised higher lifetime earnings commanded higher premiums. The differences in premiums meant that this market worked, in the sense that the apprenticeship premium seems to have varied positively with the expected profitability and prestige of the chosen occupation (Brooks 1994, 60). As noted by Minns and Wallis (2013), the premium paid was not a full payment equal to the present value of the training plus room and board, which usually were much higher than the upfront premium. The rest normally was paid in kind with the labor provided by the apprentice. The premium served more than one purpose. In part, it was to insure the master against the risk of an early departure of the apprentice. But in part it reflected also the quality of the training and the cost to the master, as well as its scarcity value (Minns and Wallis 2013, 340). More recently, it has been shown that the premium worked as a market price reflecting rising and falling demand for certain occupations resulting from technological shocks (Ben Zeev, Mokyr, and Van Der Beek 2017). It is telling that not all apprentices paid the premiums: whereas 74% of engravers in London paid a premium in London, only 17% of blacksmiths did (Minns and Wallis 2013, 344). If an impecunious apprentice could not pay, he had the option of committing to a longer indenture, as was the case in seventeenth-century Vienna (Steidl 2007, 143). In eighteenth-century Augsburg a telling example is that a “big strong man was often taken on without having to pay any apprenticeship premium, whereas a small weak man would have to pay more.” It is also recorded that apprentices with poor parents who could not afford the premium would end up being trained by a master who did inferior work (Reith 2007, 183). This market worked in sophisticated ways, and it is clear that human capital was recognized to be a valuable commodity. The formal contract signed by the apprentice in the seventeenth century included a commitment to protect the master’s secrets and not to abscond, as well as not to commit fornication (Smith 1973, 150). The precise operation of apprenticeship varied a great deal. The duration of the contract depended above all on the complexity of the trade to be learned, but also on the age at which youngsters started their apprenticeship. On the continent three to four years seems to have been the norm (De Munck and Soly 2007, 18). As would perhaps be expected, there is evidence that the duration of contracts grew over the centuries as techniques became more complex and the division of labor more specialized as a result of technological progress (Reith 2007, 183). To what extent was the master-apprentice contract actually enforced? Historians have found that often contracts were not completed (De Munck and Soly 2007, 10). Wallis (2008, 839–40) has shown that in late seventeenth-century London a substantial number of apprentices left their original master before completing the seven mandated years of their apprenticeship. The main reason was that the rigid seven-year duration stipulated by the 1562 Statute of Artificers (which regulated apprenticeship) was rarely enforced, as were most other stipulations contained in that law (Dunlop 1911, 1912).9 As Wallis (2008, 854) remarks, “like many other areas of premodern regulation, the tidy hierarchy of the seven-year apprenticeship leading to mastery was more ideal than reality.” Rather than an indication of contractual failure, the large number of apprentices that did not “complete” their terms indicates a greater flexibility in Britain. The number of lawsuits filed against such apprentices was not large (Rushton 1991, 94), and London court records indicate that apprentices wishing to be released from their masters could do so fairly easily in the Lord Mayor’s Court (Wallis 2012). Wallis notes that about 5% of all indentures ended up in this court (2012, 816). It seems that many of the early departures were by mutual consent (see also Wallis 2008, 844). To protect themselves against an early departure, many masters in England demanded and received a lump-sum upfront tuition payment from the parents or guardian of the youngster (Minns and Wallis 2013; Ben Zeev et al. 2017). The flexibility of the contracts in preindustrial England limited the risk each contracting party faced from the opportunistic behavior of the other. This institution, then, would be more successful in terms of transmitting existing skills between generations in an efficient manner. Once an apprentice had mastered a skill, there would be little point in staying on. Moreover, in many documented cases apprentices were “turned over” to another master—by some calculation this was true of 22% of all apprentices who did not complete their term (Wallis 2008, 842–43). There could be many reasons for this, of course, including the master falling sick or being otherwise indisposed. But also, at least some apprentices might have found that their master did not teach them best practice techniques or that the trade they were learning was not as remunerative as some other. The exact mechanics of the skill transmission process are hard to nail down. After all, the knowledge being taught was tacit, and mostly consisted of imitation and learning-by-doing. It surely differed a great deal from occupation to occupation. Moreover, our own knowledge is biased to some extent by the better availability of more recent sources. All the same, Steffens (2001) has suggested that much of the learning occurred through apprentices “stealing with their eyes” (131)—meaning that they learned mostly through observation, imitation, and experimentation. The tasks to which apprentices were put at first, insofar that they can be documented at all, seem to have consisted of rather menial assignments such as making deliveries, cleaning, and guarding the shop. Only at a later stage would an apprentice be trusted with more sensitive tasks involving valued customers and expensive raw materials (Lane 1996, 77). Yet they spent most of their waking hours in the presence of the master and possibly more experienced apprentices and journeymen, and as they aged they gradually would be trusted with more advanced tasks.10 One of the most interesting findings of the new research on apprenticeship, which is central to the theory developed below, is that in Europe family ties were relatively less important than elsewhere in the world, such as India (Roy 2013, 71, 77). In China, guilds existed11 but were organized along clan lines, and it is within those boundaries that apprenticeship took place (Moll-Murata 2013, 234). In contrast, Europeans came to organize themselves along professional lines without the dependence on kinship (Lucassen, de Moor, and van Zanden 2008, 16). Comparing China and Europe, van Zanden and Prak (2013a) write: “In China, training was provided by relatives, and hence a narrow group of experts, instead of the much wider training opportunities provided by many European guilds.” The contrast between Asia and Europe in systems of knowledge transmission is also emphasized by van Zanden (2009): We can distinguish two different ways to organize such training: in large parts of the world the family or the clan played a central role, and skills were transferred from fathers to sons or other members of the (extended) family. In fact, in parts of Asia, being a craftsman was largely hereditary ... In contrast to the relatively closed systems in which the family played a central role, Western Europe had a formal system of apprenticeship—organized by guilds or similar institutions—and in principle open to all. In China, young men were specifically selected and ordered by their families to apprentice with another lineage member. Such apprenticeship relations were routinely formed across patrilines and even branches (Rowe 1990, 75). In Western Europe, despite the fact that within the guilds the sons of masters received preferential treatment and that training with a relative resolved to a large extent the contractual problems, following in the footsteps of the parents gradually fell out of favor (Epstein and Prak 2008, 10). The examples of Johann Sebastian Bach and Leopold Mozart notwithstanding, fewer and fewer boys were trained by their fathers. By the seventeenth century, apprentices who were trained by relatives were a distinct minority, estimated in London to be somewhere between 7% and 28% (Leunig, Minns, and Wallis 2011, 42). Prak (2013, 153) has calculated that in the bricklaying industry, less than 10% continued their fathers’ trades. This may have been a decisive factor in the evolution of apprenticeship as a market phenomenon in Europe but not elsewhere.12 II.C. Mobility and the Diffusion of Knowledge In premodern Europe, as early as fifteenth-century Flanders, artisans were mobile. In England, such mobility was particularly pronounced (Leunig, Minns, and Wallis 2011), with lads from all over Britain seeking to apprentice in London, not least of all the young James Watt and Joseph Whitworth, two heroes of the Industrial Revolution. But as Stabel (2007, 159) notes, towns and their guilds had to accept and acknowledge skills acquired elsewhere, even if they insisted that newcomers adapt to local economic standards set by the guilds. Constraints were more pronounced on the continent, but even here apprentices came to urban centers from smaller towns or rural regions (De Munck and Soly 2007, 17), and mobility of artisans and the skills they carried with them extended to all of Europe. The idea of the “journeyman” or “traveling companion” was that after completing their training, new artisans would travel to another city to acquire additional skills before they would qualify as masters—much like postdoctoral students today (Leeson 1979; Lis, Soly, and Mitzman 1994). As such, journeymanship was traditionally the “intermediate stage” between completing an apprenticeship and starting off as a full-fledged master. Journeymen and apprentices are known to have traveled extensively as early as the fourteenth century, often on a seasonal basis, a practice known as “tramping.” By the early modern period, this practice was fully institutionalized in Central Europe (Epstein 2013, 59). Itinerant journeymen, Epstein argues, learned a variety of techniques practiced in different regions and were instrumental in spreading best-practice techniques. Towns that believed themselves to enjoy technological superiority forbade the practice of tramping and made apprentices swear not to practice their trades anywhere else, as with Nuremberg metal workers and Venetian glassmakers (Epstein 2013, 60–61). Such prohibitions were ineffective at best and counterproductive at worst. Not every apprentice had to go through journeymanship, and relatively little is known about how long it lasted and how it was contracted for. Journeymen have been regarded by much of the literature as employees of masters, and were often organized in compagnonnages, which frequently clashed with employers. Journeymen in many cases were highly skilled workers, but more mobile than masters. Known as “travelers” or “tramps,” they often chose to bypass the formal status of master but prided themselves on their skills, considering themselves “equal partners” to masters (Lis, Soly, and Mitzman 1994, 19). In Elizabethan England, the “number of surplus though fully apprenticed men forced to take the road clearly grew ... the custom of quizzing, registering and entertaining the stranger became more regularized” (Leeson 1979, 56). The letter of the 1562 Statute of Artificers was clearly intended to curtain mobility, but in practice these aspects of the statute were widely disregarded (Leeson 1979, 63–65). The mobility of journeymen lent itself to the creation of networks in the same lines of work, and it stands to reason that technical information flowed fairly freely along those channels of communication. Journeymen are relevant to our story for two reasons: first, because when working in a shop different from the one they were trained in, they were exposed to other skills after they completed their apprenticeship; and second, because the apprentices in the workshops in which they worked after completing their training could learn from them (and thus indirectly from the journeymen’s masters) in addition to their own masters (e.g., Unger 2013, 186). In this way they were an important component of how the European system of apprenticeship allowed learning from more than just one source. But skilled masters, too, traveled across Europe, often deliberately attracted by mercantilist states or local governments keen to promote their manufacturing industries through the recruitment of high-quality artisans. Technology diffusion occurred largely through the migration of skilled workers, or through apprentices traveling to learn from the most renowned masters (and then returning home). Interestingly, such migration seems to have focused mostly on towns in which the industry already existed and which were ready to upgrade their production techniques (Belfanti 2004, 581). II.D. Apprenticeship and Guilds In medieval and early modern Europe, where in most areas third-party enforcement of contracts was still quite weak, the guilds played a crucial role in making apprenticeship relations effective. As late as the eighteenth century, for French bakers, “the guild made the rules for apprenticeship and mediated relations between masters and apprentices ... it sought to impose a common discipline and code of conduct on masters as well as apprentices to ensure good order” (Kaplan 1996, 199). Where third-party enforcement was stronger, or where apprenticeship contracts could be enforced through informal institutions, this role of the guilds became less essential, and consequently market equilibria became more common. There has been a lively debate in the past two decades about the role of the guilds in premodern European economies. Traditionally relegated by an earlier literature to be a set of conservative, rent-seeking clubs, a revisionist literature has tried to rehabilitate craft guilds as agents of progress and technological innovation. Part of that storyline has been that guilds were instrumental in the smooth functioning of apprenticeships. As noted, given the potential for market failure due to incomplete contracts, incentive incompatibility, and poor information, agreements on intergenerational transmission of skills needed enforcement, regulation, and supervision. In a setting of weak political systems, the guilds stepped in and created a governance system that was functional and productive (Epstein and Prak 2008; Lucassen, de Moor, and van Zanden 2008; van Zanden and Prak 2013b). In a posthumously published essay, Epstein stated that the details of the apprenticeship contract had to be enforced through the craft guilds, which “overcame the externalities in human capital formation” by punishing both masters and apprentices who violated their contracts (Epstein 2013, 31–32). The argument has been criticized by Ogilvie (2014, 2016). Others, too, have found cases in which the nexus between guilds and apprenticeships proposed by Epstein and his followers does not quite hold up (Davids 2003, 2007). The reality is that some studies support Epstein’s view to some extent, and others do not. The heated polemics have made the more committed advocates of both positions state their arguments in more extreme terms than they can defend. Guilds were institutions that existed through many centuries, in hundreds of towns, and for many occupations. This three-dimensional matrix had a huge number of elements, and it stands to reason that things differed over time, place, and occupation. Most scholars find themselves somewhere in between. Guilds were at times hostile to innovation, especially in the seventeenth and eighteenth centuries, and under the pretext of protecting quality they collected exclusionary rents by longer apprenticeships and limited membership. But in some cases, such as the Venetian glass and silk industries, guilds encouraged innovation (Belfanti 2004, 576). Their attitude to training, similarly, differed a great deal over space and time. Davids (2013, 217), for instance, finds that in the Netherlands, “guilds normally did not intervene in the conditions, registration, or supervision of [apprenticeship] contracts.” Unger (2013, 203), after a meticulous survey, must conclude that the “precise role of guilds in the long term evolution of shipbuilding technology remains unclear.” Moll-Murata (2013, 256), in comparing the porcelain industries in the Netherlands and China, retreats to a position that “contrasting the guild rehabilitationist [Epstein’s] and the guild-critical positions is difficult to defend ... we find arguments supporting both propositions.” Guilds and apprenticeship overlapped, but they did not strictly require each other, especially not after 1600. Apprenticeship contracts could find alternative enforcement mechanisms to guilds. In the Netherlands local organizations named neringen were established by local government to regulate and supervise certain industries independently of the guilds. They set many of the terms of the apprenticeship contract, often the length of contract and other details (Davids 2007, 71). Even more strikingly, in Britain, most guilds gradually declined after 1600 and exercised little control over training procedures (Berlin 2008). Moreover, informal institutions and reputation mechanisms in many places helped make apprenticeship work even in the absence of guilds. As Humphries (2003) argues, apprenticeship contracts in England may have been, to a large extent, self-enforcing in that opportunistic behavior in fairly well-integrated local societies would be punished severely by an erosion of reputation. Market relationships were linked to social relationships, and such linkages are a strong incentive toward cooperative behavior (Spagnolo 1999). For example, a master found to treat apprentices badly might not only lose future apprentices but also damage relations with his customers and suppliers. The same was true for the apprentices, whose future careers would be damaged if they were known to have reneged on contracts. If both master and apprentice expected this in advance, in equilibrium they would not engage in opportunistic behavior and would try to make their relationship as harmonious as possible.13 The limits to such self-enforcing contracts are obvious. Mobility of apprentices after training would mean that the the reach of reputation was limited, and in larger communities the reputation mechanism would be ineffective. Substantial opportunistic behavior could cause the cooperative equilibrium to unravel. All the same, it has been stressed that despite the convincing evidence that guilds in some cases helped in the formation of human capital and supported innovation, the two economies in which technological progress was the fastest after 1600 were the Netherlands and Britain, the two countries in which guilds were relatively weak (Ogilvie 2016). That such a correlation does not establish causation goes without saying, but it does serve to warn us against embracing the revisionist view of guilds too rashly. In the theory articulated below, the growth implications of the guild system can be assessed according to their next best alternative. If the state is sufficiently strong to enforce contracts and enable apprenticeship without guilds being involved, the anticompetitive aspect of guilds dominates, and thus guilds hinder growth (consistent with faster growth in the Netherlands and Britain after 1600, when the state increasingly took over functions once served by guilds and cities). But when the state is weak, and the choice is between apprenticeship provided via guilds or via clans, the faster dissemination of knowledge associated with guilds dominates. We now turn to the theory that spells out these results in a formal model of knowledge transmission. III. A Model of Preindustrial Knowledge Growth In this section, we develop an explicit model of knowledge creation and transmission in a preindustrial setting. By ``preindustrial,'' we mean that aggregate production relies on a land-based technology that exhibits decreasing returns to the size of the population. In addition, there is a positive feedback from income per capita to population growth, implying that the economy is subject to Malthusian constraints. We do not mean to imply a commitment to a fundamentalist “iron wage” version of this model in which all gains from productivity growth are relentlessly translated into population growth; the assumption is made only for modeling convenience. Compared to existing Malthusian models, the main novelty here is that we explicitly model the transmission of knowledge from generation to generation and the resulting technological progress. This allows us to to analyze how institutions affect the transmission of knowledge, and how this interacts with the usual forces present in a Malthusian economy. III.A. Preferences, Production, and the Productivity of Craftsmen The model economy is populated by overlapping generations of people who live two periods, childhood and adulthood. All decisions are made by adults, whose preferences are given by the utility function:   \begin{equation} u(c, I^{\prime })=c+\gamma \,I^\prime , \end{equation} (1)where c is the adult’s consumption and I΄ is the total future labor income of this adult’s children. The parameter γ > 0 captures altruism toward children. The role of altruism is to motivate parents’ investment in their children’s knowledge. The adults work as craftsmen in a variety of trades. At the beginning of a period, the aggregate economy is characterized by two state variables: the number of craftsmen N, and the amount of knowledge k in the economy. Craftsmen are heterogeneous in productivity, and knowledge k determines the average productivity of craftsmen in a way that we make precise below. We start by describing how aggregate output in our economy depends on the state variables N and k. The single consumption good (which we interpret as a composite of food and manufactured goods) is produced with a Cobb-Douglas production function with constant return to scale that uses land X and effective craftsmen’s labor L as inputs:   \begin{equation} Y = L^{1-\alpha } X^\alpha , \end{equation} (2)with α ∈ (0, 1). The total amount of land is normalized to 1, X = 1. Land is owned by craftsmen.14 At first sight, including land (and hence allowing for decreasing returns) in the technology may appear surprising, because land is usually not an important input for artisans and craftsmen. However, land is still a scarce factor because raw materials used in manufacturing such as wool, leather, timber, grains, grapes, and bricks had a substantial land component. Alternatively, we would get similar results in an economy where there are constant returns for the craftsmen’s technology, but people also consume food, which is subject to the land constraint. In such a setting, aggregate decreasing returns would be reflected in a gradually declining relative price of manufactured output along a balanced growth path.15 The effective labor supply by craftsmen L is a CES aggregate of effective labor supplied in different trades j:   \begin{equation} L=\left(\int _0^1 (L_j)^\frac{1}{\lambda } dj \right)^\lambda , \end{equation} (3)with λ > 1. The elasticity of substitution between the different trades is $$\frac{\lambda }{\lambda -1}$$. The distinction among different trades of craftsmen (watchmaker, wheelwright, blacksmith, etc.) is important for our analysis of guilds below, which we model as coalitions of the craftsmen in a given trade. However, the equilibrium supply of effective labor will turn out to be the same in all trades, so that Lj = L for all j. For most of our analysis, we can therefore suppress the distinction between trades from the notation. We now relate the supply of effective labor by craftsmen L in efficiency units to the number of craftsmen N and the state of knowledge k. Manufacturing is carried out by a set of independent master craftsmen, each one working on their own.16 Craftsmen are heterogeneous in knowledge. The productive knowledge of a craftsman i is measured by a cost parameter hi, where a lower hi implies that the master can produce at lower cost and hence has more productive knowledge. Intuitively, different craftsmen may apply different methods and techniques in their production, which vary in productivity. Specifically, the output qi of a craftsman with cost parameter hi is given by:   \begin{equation} {q}_{i}=h_{i}^{-\theta }. \end{equation} (4) The final-goods technology equation (2) is operated by a competitive industry. Given the Cobb-Douglas production function, this implies that craftsmen receive share 1 − α of total output as compensation for their labor, and consequently the labor income of a craftsman supplying qi efficiency units of craftsmen’s labor is:   \begin{equation} I_{i}=q_{i} \,{(1-\alpha )}\, \frac{Y}{L}. \end{equation} (5)The heterogeneity in the cost parameter hi among craftsmen takes the specific form of an exponential distribution with distribution parameter k:   \begin{equation*} h_{i}\sim \mbox{Exp}(k). \end{equation*} Given the exponential distribution, the expectation of hi is given by $$\mathbb {E}\,[h_{i}]=k^{-1}$$. Hence, higher knowledge k corresponds to a lower average cost hi and therefore higher productivity. We assume that the same k applies to all trades. Given the exponential distribution for hi and equation (4), output qi follows a Fréchet distribution with scale parameter kθ and shape parameter $$\frac{1}{\theta }$$.17 We can now express the total supply of effective labor by craftsmen as a function of state variables. The average output across craftsmen is given by:   \begin{equation} {q}= \mathbb {E}\,(q_{i})=\int _0^\infty h_{i}^{-\theta } (k \exp (-k h_{i})) dh_{i} = k^\theta \Gamma (1-\theta ), \end{equation} (6)where $$\Gamma (t)=\int _0^\infty x^{t-1}\exp (-x)dx$$ is the Euler gamma function. The total supply of effective craftsmen’s labor L is then given by the expected output per craftsman $$\mathbb {E}\,(q_{i})$$ multiplied by the number of craftsmen N:   \begin{equation} L=N \,k^\theta \, \Gamma (1-\theta ). \end{equation} (7)Income per capita can be computed from equation (2) and (7) as:   \begin{equation} y=\frac{Y}{N}= \frac{L^{1-\alpha }}{N} = \Gamma (1-\theta )^{1-\alpha } \,k^{(1-\alpha )\theta }\,N^{-\alpha }. \end{equation} (8) III.B. Population Growth and the Malthusian Constraint So far, we have described how total output (and hence output per adult) depends on the aggregate state variables N and k. Next, we specify how these state variables evolve over time. We start with population growth. Consistent with evidence from preindustrial economies (see Ashraf and Galor 2011), the model allows for Malthusian dynamics.18 The presence of land in the aggregate production function implies decreasing returns for the remaining factor L, which gives rise to a Malthusian trade-off between the size of the population and income per capita. The second ingredient for generating Malthusian dynamics is a positive feedback from income per capita to population growth. While often this relationship is modeled through optimal fertility choice,19 we opt for a simpler mechanism of an aggregate feedback from income per capita to mortality rates. Every adult gives birth to a fixed number $$\bar{n}>1$$ of children. The fraction of children that survives to adulthood depends on aggregate output per adult y, namely:   \begin{equation} n=\bar{n} \, \min [1, s \,y]. \end{equation} (9)Here min [1, s y] is the fraction of surviving children, and n is the number of surviving children per adult. This function captures that low living standards (e.g., malnutrition) make people (and in particular children) more susceptible to transmitted diseases, so that low income per capita is associated with more frequent deadly epidemics. In recent times, we can also envision s to depend on medical technology (i.e., the invention of antibiotics would raise s). However, given that we analyze preindustrial growth, we will assume that s is fixed. We will also focus attention on a phase of development where the mortality trade-off is still operative, so that survival is less than certain and $$n=\bar{n} s \,y$$. The law of motion for population then is:   \begin{equation*} N^\prime = n \, N= \bar{n} \, s \,y \,N=\bar{n} \, s\,\, Y . \end{equation*} Consider a balanced growth path in which the stock of knowledge k grows according to a constant growth factor g:   \begin{equation*} g=\frac{k^{\prime }}{k}. \end{equation*} In such a balanced growth path, the Malthusian features of the model economy impose a relationship between growth in knowledge g and population growth n, as shown in Proposition 1. Proposition 1 (The Malthusian Constraint). Along a balanced growth path, the growth factor of technology g and the growth factor of population n satisfy:  \begin{equation} g^{\theta (1-\alpha )}=n^{\alpha }. \end{equation} (10) Proof. Income per capita y is given by equation (8). Along a balanced growth path, y is constant, and hence equation (10) has to hold in order to keep the right-hand side of equation (8) constant, too. The Malthusian constraint states that faster technological progress is linked to higher population growth. Given equation (10), a faster rate of technological progress is also associated with a higher level of income per capita. Income per capita is constant in any balanced growth path: Malthusian dynamics rule out sustained growth in living standards, because accelerating population growth ultimately would overwhelm productivity growth. Instead, economies with faster accumulation of knowledge will be characterized by faster population growth and hence, over time, increasing population density. III.C. Apprenticeship, Innovation, and the Evolution of Knowledge We now turn to the accumulation of knowledge in our model economy. In a given period, all productive knowledge is embodied in the adult workers. During childhood, people have to acquire the productive knowledge of the previous generation. There are two sources of increasing knowledge across generations. First, craftsmen are heterogeneous in their productive knowledge. Young craftsmen can learn from multiple adult craftsmen and then apply the best of what they have learned. This knowledge dissemination process results in endogenous technological progress. In addition, after having acquired knowledge from the elders, young craftsmen can innovate, that is, generate an idea that may improve on what they have learned, resulting in a second source of technological progress. In order to model the idea that apprentices (or their parents) are subject to imperfect information on the efficiency of the different masters, we assume that the young can observe the efficiency of masters only by working with them as apprentices. Consider an apprentice who learns from m masters indexed from 1 to m (the choice of m will be discussed below). The efficiency hL learned during the apprenticeship process is:   \begin{equation} h_L=\min \left\lbrace h_{1},h_{2},\ldots ,h_{m}\right\rbrace . \end{equation} (11)Hence, apprentices acquire the cost parameter of the most efficient (i.e., lowest cost) master they have learned from. After learning from masters, craftsmen attempt to innovate by generating a new idea characterized by cost parameter hN. The quality of the idea is random, and it may be better or worse than what they already know. As adult craftsmen, they use the highest efficiency they have attained either through learning from elders or through innovation, so that the final cost parameter h΄ is given by:   \begin{equation} h^\prime =\min \left\lbrace h_L,h_N\right\rbrace . \end{equation} (12)As will become clear below, the model can generate sustained growth even if the rate of innovation is 0 (i.e., own ideas are always inferior to acquired knowledge). In that case, the dissemination process of existing ideas is solely responsible for growth. However, allowing for innovation allows for a positive rate of productivity growth even if each child learns only from a single master. Recall that the distribution of the hi among adult craftsmen is exponential with distribution parameter k. The distribution of new ideas is also exponential, and the quality of new ideas depends on existing average knowledge:   \begin{equation*} h_{N}\sim \mbox{Exp}(\nu k). \end{equation*} That is, the more craftsmen already know, the better the quality of the new ideas generated. The parameter ν measures the relative importance of transmitted knowledge and new ideas. If ν is close to zero, most craftsmen rely on existing knowledge, and if ν is large, innovation rather than the dissemination of existing ideas through apprenticeship is the key driver of knowledge. The exponential distributions for ideas imply that, given the knowledge accumulation process described by equations (11) and (12), the knowledge distribution preserves its shape over time (as in Lucas 2009). Specifically, if each young craftsman learns from m masters that are drawn at random we have:20  \begin{eqnarray*} h_L= \min \left\lbrace h_{1},h_2,\ldots ,h_{m}\right\rbrace &\sim\, \mbox{Exp}(m k),\\ h^\prime = \min \left\lbrace h_L,h_N\right\rbrace &\quad \sim \mbox{Exp}(m k+\nu k). \end{eqnarray*} Hence, with m randomly chosen masters per apprentice, aggregate knowledge k evolves according to:   \begin{equation} k^\prime =(m+\nu ) k. \end{equation} (13)The market for apprenticeship interacts with population growth. In particular, if each master takes on a apprentices, and each apprentice learns from m masters, the condition for matching demand and supply of apprenticeships is:   \begin{equation} N^\prime \, m = N\, a. \end{equation} (14)We ignore integer constraints and treat m and a as continuous variables. Below, we will focus on equilibria where each apprentice chooses the same number of masters m, and each master has the same number of apprentices a. We now arrive at the core of our analysis, namely, the question of how the number and identity of masters for each apprentice are determined. Apprenticeship is associated with costs and benefits. While working as an apprentice with a master, each apprentice produces κ > 0 units of the consumption good (this is in addition to the output generated by the aggregate production function). This output is controlled by the master. In turn, a master who teaches a apprentices incurs a utility cost δ(a), where δ(0) = 0, δ΄(a) > 0, and δ″(a) > 0 (i.e., the cost is increasing and convex in a). Incurring this cost is necessary for transmitting knowledge to the apprentices. We assume for simplicity that the function δ(·) is quadratic, that is, $$\delta (a)=\tfrac{\bar{\delta }}{2} a^2$$ and that it is the same for all masters.21 If a master takes on a apprentices but then puts no effort into teaching, the apprentices still generate output κa by assisting the master in production. Thus, there is a moral hazard problem: masters may be tempted to take on apprentices, appropriate production κa, but not actually teach, saving the cost δ(a). Dealing with this moral hazard problem is a key challenge for an effective system of knowledge transmission. The danger of moral hazard is especially severe here because the very nature of apprenticeship defines it as the quintessential incomplete contract (see Section II). In a modern market economy, we envision that such problems are dealt with by a centralized system of contract enforcement. In such a system, a parent would write contracts with masters to take on the children as apprentices. A price would be agreed on that is mutually agreeable given the cost of training apprentices and the parent’s desire, given altruistic preferences in equation (1), to provide the children with future income. Courts would ensure that both parties hold up their end of the bargain. In preindustrial societies lacking an effective system of contract enforcement, other institutions would have to ensure an effective transmission of knowledge from the elders to the young. Our view is that variation in these alternative institutions across countries and world regions plays a central role in shaping economic success and failure in the preindustrial era. After a brief discussion of model assumptions, we analyze specific, historically relevant institutions in the context of our model of knowledge-driven growth. III.D. Discussion of Model Assumptions Our model of growth in the preindustrial economy is stylized and relies on a set of specific assumptions that yield a tractable analysis. We conclude our description of the model with a discussion of the role and plausibility of the assumptions that are most central to our overall argument. Above all, apprenticeship institutions matter in our economy because the knowledge of masters is not publicly observable. This creates the incentive for apprentices to sample the knowledge of multiple masters to gain productive knowledge, and implies that institutions that determine how apprentices are matched to masters matter for growth. To maintain tractability, in the model the lack of information on productivity is severe: nothing at all is known about the productivity of different masters, even though there is wide variation in their actual productivity. Taken at face value, this assumption is clearly implausible. However, possible concerns about its role can be addressed in two ways. First, in our model all knowledge differences between masters are actual productivity differences, that is, masters who know more produce more. A realistic alternative possibility is that at least some variation in knowledge is in terms of “latent” productivity, that is, some masters may know techniques and methods that will turn out to be highly productive and important at a later time when combined with other knowledge but do not give a productivity advantage in the present. A well-known example are the inventions of Leonardo da Vinci, which could not be implemented given the knowledge of his age, but which turned into productive knowledge centuries later. Similarly, the success of the steam engine was based in large part on a set of gradual improvements in craftmen’s ability to work metal to precise specifications; for instance, steam engines work only if the piston can move easily in the cylinder but with a tight fit. Many improvements in techniques would have been of comparatively little value when first invented but then became critical later on. Along these lines, in Online Appendix B we describe an extension of our model where a craftsman’s output can be constrained by the state of aggregate knowledge. This version leads to exactly the same implications as the simpler setup described here, but actual variation in productivity is much smaller than variation in latent productivity, so that imperfect information on underlying productivity appears more plausible. The extended model is also useful for addressing another potential concern about the model, namely, that the support of latent knowledge is unbounded, with a fat-tailed distribution that allows, in principle, for sustained growth based entirely on knowledge diffusion. At face value, this assumption implies that all potential knowledge is already known to at least one person at the beginning of time, which may be regarded as implausible. However, the extended model makes clear that this setting can be regarded as a simple analytical approximation to a model with a finite support of knowledge. In particular, if the knowledge distribution is cut off at some upper bound and replaced with a point mass at the bound, we would get the same results for the growth implications of different apprenticeship institutions and overall similar equilibrium outcomes in the short and medium run. Second, it would be possible to relax the assumption of total lack of information about productivity, and instead assume that an informative, but imperfect, signal of each master’s productivity was available.22 In such a setting, more productive masters could command higher prices for apprenticeships, they would employ a larger number of apprentices, and the spread of productive knowledge would be faster. As we document in Section II, the historical evidence for Europe suggests that, indeed, more productive and knowledgeable masters were able to command higher prices and attract more apprentices. However, as long as information on productivity is less than perfect, the basic trade-offs articulated by our analysis and the comparative growth implications of the institutions analyzed below would be the same. Less-than-perfect information about productivity is highly plausible; even in today’s world of instant communication and online discussion boards, for example, graduate students do not have perfect information about which adviser will be the best match for them. We adopt the extreme case of complete lack of observability for tractability; without this assumption the distribution of knowledge would not preserve its shape over time, so that we would have to rely on numerical simulation for all results.23 It should also be noted that in a world of artisans and small workshops there were limits on the number of apprentices that each master could take on. Diseconomies of scale would set in fairly soon, even if there were no guild limitations on the number of apprentices (which often existed). This means that the standard mechanism through which technology diffuses (the more efficient firms expand and take over the industry) was not operative in this period. In addition, the master-apprentice relationship in the model is simplified compared to reality. We use a setting with one-sided moral hazard, that is, masters can cheat apprentices but not vice versa. In reality, moral hazard was a major concern on both sides of the master-apprentice relationship. This assumption is introduced merely to simplify the analysis. It would be straightforward to introduce two-sided moral hazard in our setting, and the role of institutions for mitigating moral hazard would be unchanged.24 We also assume that the only reason why apprentices get differential training is because they work with heterogeneous masters—we do not allow for the apprentices to differ in talent.25 Finally, in the model, apprentices interact in the same way with all of their masters, and they make a one-time choice of the number of masters to learn from. As ever, reality is substantially more complicated; choices of whom to learn from unfolded sequentially over time, and most apprentices generally did only one full apprenticeship (although changing masters was actually not uncommon; see Bellavitis, Cella, and Colavizza 2016; Crowston and Lemercier 2016; and Schalk 2016), followed by other shorter interactions during journeymanship. Once again, these assumptions are for simplicity and tractability but are not central to our main results regarding the role of institutions for knowledge transmission. The key point in the theoretical setup is that apprentices adopt the techniques of the most efficient master they learned from. It is not necessary that apprentices spend equal time with each master; in reality, an interaction may be brief and end once an apprentice ascertains that a given master has nothing new to offer. The model abstracts from such differentiated interactions and imposes symmetrical master-apprentice relations to improve tractability. Having said that, when matching the model to data, care should be taken to account for the fact that “apprenticeships” in the model correspond to a wider range of interactions in reality. Some of these real-world interactions may also consist of horizontal diffusion of techniques in which artisans learn from one another. While we abstract from such interactions in the theoretical model, the historical evidence about the mobility of artisans and journeymen suggests that such horizontal dissemination was an important element in the dissemination of technical knowledge. IV. Comparing Institutions for Knowledge Transmission The crucial question in our theory is how the moral hazard problem inherent in apprenticeship is resolved. If masters do not make an effort to teach their apprentices, parents will have no incentive to send children to learn from masters outside the family. Apprentices would not learn anything, whereas masters would gain the apprentices’ production κ. Parents would be better off keeping children at home, thereby keeping output κ in the family. Thus, for apprenticeship outside the immediate family to be feasible (and thus for knowledge to disseminate), an enforcement mechanism is required in order to provide incentives for masters to exert effort. IV.A. Centralized versus Decentralized Institutions We consider two types of institutions, characterized by centralized versus decentralized enforcement. Under centralized enforcement, people can write contracts specifying that the master must put in effort (and indicating the price of apprenticeship), and there is a centralized system (such as courts) that punishes anyone who breaks a contract. In contrast, in a decentralized system no such central authority exists, and instead people have to form coalitions to maintain a sufficient threat of punishment to resolve the moral hazard problem.26 To allow for the possibility of decentralized enforcement, we assume that each adult can inflict a utility cost (damage) on any other adult.27 However, the punishment that a single adult can mete out is not sufficient to induce a master to put in effort, that is, the punishment is lower than the cost of training a single apprentice. In contrast, coalitions of people can always make threats that are sufficient to guarantee compliance. An effective threat of punishment therefore requires coordination among parents. Coordination, in turn, requires communication: for a master’s shirking to have consequences, the fact of the shirking has to be communicated to all would-be punishers. Thus, the extent to which people are able to communicate with each other partly determines how much knowledge transmission is possible. Over time, societies have differed in the extent and manner in which individuals were connected in communication networks. We consider two different scenarios for decentralized enforcement, the “family” and the “clan,” which we consider particularly relevant for contrasting Europe during the Early Middle Ages with China, India, and the Middle East during the same period and beyond. The decentralized systems correspond to a period when centralized enforcement was not yet sufficiently effective. Even if courts existed, contract enforcement was often costly, slow, and uncertain. More important, for centuries the reach of the state and hence its courts was severely limited. Europe, for example, used to consist of hundreds of independent sovereign entities, and the enforcement of the law outside one’s immediate surroundings (say, the city of residence) was weak. With this in mind, the first centralized enforcement institution that we consider is organized not by the state but by a coalition of all the masters in a given trade: a “guild.” The guild monitors the behavior of its members and enforces the apprenticeship contracts between parents and masters. However, the guild also has anticompetitive features. It can set the price of apprenticeship, thereby exploiting its monopoly in a given trade. Guilds played a central role in European economic life during the Middle Ages, and our theory will allow us to assess their implications for knowledge creation and dissemination. The final institution that we consider is the “market,” where there is a centralized enforcement system for all trades as in a modern market economy. Importantly, under this institution the government not only enforces contracts but also prevents collusion; trades are no longer allowed to form guilds that limit entry and lower competition, and both parents and masters act as price takers. The market institution corresponds to the final stages of the preindustrial economy, when in Europe nation-states became powerful and increasingly abolished the traditional privileges of guilds. IV.B. The Family Decentralized institutions enforce apprenticeship agreements through the formation of coalitions of parents that coordinate on a sufficient threat of punishment for shirking masters. Different decentralized institutions are distinguished by the size of these coalitions and the identity of their members. For the formation of a coalition to be feasible, the members have to be able to communicate with each other about the behavior of masters. Hence, one polar case is where members of different families are unable to communicate with each other, so that no coalitions can be formed. The lack of communication rules out coordinating on punishing shirking masters. As a consequence, apprenticeship outside the immediate family is impossible, that is, each child learns only from the parent. In principle, the moral hazard problem is present even within the family. However, in utility (equation (1)) parents care about their own children, and we assume that the degree of altruism γ is sufficiently high for parents never to shirk when teaching their own children. The result is a “family equilibrium,” that is, an equilibrium where knowledge is transmitted only within dynasties, but there is no dissemination of knowledge across dynasties. Formally, under decentralized institutions we model the knowledge accumulation decisions as a game between the craftsmen of a given generation. The strategy of a given craftsman has three elements: Decide whether to send own children to others as apprentices for training, and if so, which compensation to pay the masters of one’s children. Decide whether to exploit one’s own apprentices (if any). Decide whom to punish (if anyone). We focus on Nash equilibria.28 The strategy profile for the family equilibrium is as follows: All craftsmen train their children on their own. If (off the equilibrium path) a master gets someone else’s child as an apprentice, the master exploits the apprentice. No one ever punishes anyone. If communication outside the immediate family is impossible, the family equilibrium is the only equilibrium. The family equilibrium can also occur as a “bad” equilibrium in an economy where more communication links are available, but people fail to coordinate on a more efficient punishment equilibrium.29 Now consider the balanced growth path under the family equilibrium. We assume that the Malthusian feedback, parameterized by the maximum number of children $$\bar{n}$$ and the survival parameter s, is sufficiently strong for dynamics to lead to a balanced growth path in which income per capita is constant.30 The following proposition summarizes the properties of the balanced growth path. Proposition 2 (Balanced Growth Path in Family Equilibrium). If altruism is sufficiently strong (i.e., γ is sufficiently large), there exists a unique balanced growth path under the family equilibrium with the following properties: Each child trains only with his own parent: mF = 1, and aF = nF. The growth factor gF of knowledge k is:  \begin{equation*} g^{{\bf F}}=1+\nu . \end{equation*} The growth factor nF of population N is:  \begin{equation*} n^{{\bf F}}=(1+\nu )^\frac{(1-\alpha ) \theta }{\alpha }. \end{equation*} Income per capita yF is constant and satisfies:  \begin{equation*} y^{{\bf F}}=\frac{(1+\nu )^\frac{{(1-\alpha )} \theta }{\alpha }}{\bar{n}\,s}. \end{equation*} Proof. See Online Appendix C. The condition for sufficient altruism reflects that parental altruism should be strong enough to overcome the disutility of teaching one’s children. The rate of technological progress is positive in the family equilibrium but small. In the absence of new ideas (ν = 0), there is stagnation (gF = nF = 1). This is because the only source of progress is the new ideas of craftsmen (recall that ν measures the quality of new ideas). New ideas are passed on to children, which makes children, on average, more productive than the parents. However, knowledge does not disseminate across dynasties. Given the growth rate of knowledge gF = 1 + ν, Malthusian dynamics ensure that population grows just fast enough to offset productivity growth and yield constant income per capita. Figure I represents the determination of the balanced growth path in the family equilibrium. The concave curve represents the Malthusian constraint given by equation (10).31 The intersection between this constraint and the line g = 1 + ν gives the balanced growth path under the family equilibrium F. Figure I View largeDownload slide Productivity and Population Growth in the Family (F) Equilibrium Figure I View largeDownload slide Productivity and Population Growth in the Family (F) Equilibrium IV.C. The Clan Next, we consider economies where there is communication within an extended family or clan. While many other structures could be considered, the clan has particular historical significance because of its importance for organizing economic exchange in the major world regions outside Europe. Formally, we consider a setting where all members of a dynasty who share an ancestor o generations back can communicate (here o = 0 corresponds to the family equilibrium, o = 1 means siblings are connected, and so on). Now consider a potential “clan equilibrium” with the following equilibrium strategy profiles: All craftsmen send their children to be trained by each master in the clan, and parents compensate masters for the apprenticeship by paying each δ΄(a) − κ (the marginal cost), where a is the number of apprentices per master. All masters put effort into teaching. If (off the equilibrium path) a master cheats an apprentice, all current members of the clan punish the master. For example, if o = 1, children are trained not only by their parent but also by their uncles. For o = 2, second-degree relatives serve as masters, and so on.32 Along a balanced growth path, the total number of adults (i.e., masters) belonging to the clan is (nC)o, where nC is the rate of population growth in the balanced growth path. For learning from all current masters to be feasible, we assume that all members of the clan work in the same trade. An alternative setup allows for large clans that engage in many trades, in which case a child would be trained only by those masters in the clan who work in the child’s chosen trade. In either case, we envision that in the clan equilibrium children obtain the knowledge of a handful of masters who belong to the same clan and to the same trade. The following proposition summarizes the properties of the balanced growth path in the clan equilibrium. Proposition 3 (Balanced Growth Path in Clan Equilibrium). There is a threshold omax  > 0 such that if o < omax  and if altruism is sufficiently strong (i.e., γ is sufficiently large), there exists a balanced growth path in the clan equilibrium with the following properties: The number of masters per child m is given by the numberof adults in the clan, mC = (nC)o, and the number ofapprentices per master is aC = (nC)o + 1. The growth factor gC of knowledge k is the solution to:  \begin{equation} g^{{\bf C}}=1+\frac{\nu \,{(n^{{\bf C}})}^o}{g^{{\bf C}}-\nu }. \end{equation} (15) The growth factor nC of population N is given by:  \begin{equation*} n^{{\bf C}}=(g^{{\bf C}})^\frac{{(1-\alpha )} \theta }{\alpha }. \end{equation*} Income per capita is constant and satisfies:  \begin{equation*} y^{{\bf C}}=\frac{(g^{{\bf C}})^\frac{{(1-\alpha )} \theta }{\alpha }}{\bar{n}s}. \end{equation*} For o = 0, the balanced growth path coincides with the family equilibrium, whereas for o > 0 knowledge growth, population growth, and income per capita are higher compared to the family equilibrium. The growth gC of knowledge k is increasing in the size of the clan o. Proof. See Online Appendix D. Parallel to the family equilibrium, the condition on sufficiently high altruism ensures that parents find it worthwhile to pay for the training of their children.33 The upper bound omax  on the size of the clan limits productivity growth to a level where the Malthusian feedback is sufficiently strong to generate a balanced growth path with constant income per capita. The clan equilibrium leads to a higher growth rate compared to the family equilibrium because children learn from more masters. In particular, they benefit not just from the new ideas of their own parent but also from the new ideas of their uncles and other current members of the clan. Thus, new knowledge disseminates more widely compared to the family equilibrium. However, there is still no dissemination of knowledge across clans. Equation (15) implies that as long as ν > 0 (there is some innovation), a higher o (larger clans) leads to faster growth. However, if there are no new ideas, ν = 0, the growth rate in the clan equilibrium is 0. Intuitively, in a clan the masters of a given apprentice all trained with the same masters when they were apprentices, which implies that they all started out with the same knowledge. If the masters do not have new ideas of their own, studying with multiple masters does not provide any benefit over studying with only one of them. Hence, knowledge does not accumulate across generations. Another way of stating this key point is that learning opportunities in the clan are limited, because the knowledge of the available masters is correlated. This correlation arises from the fact that the available masters once learned from the same teachers, and hence acquired the same pooled knowledge present within the clan. As we will see, this issue of correlated knowledge across masters is the key distinction between the clan and institutions such as the guild and the market that extend beyond blood relatives. Figure II represents the determination of the balanced growth path in the clan equilibrium. In addition to the Malthusian constraint (10), we have drawn the function   \begin{equation} n=\left(\frac{(g-1)(g-\nu )}{\nu }\right)^\frac{1}{o}, \end{equation} (16)which is derived from equation (15). This function is equal to 1 when g = 1 + ν, increases monotonically with g for g > 1 + ν, and ultimately crosses the Malthusian constraint. The function (16) captures the relationship between population growth and the size of the clan. When n = 1, every person has one child, and hence there are no siblings and no uncles. Therefore, children can learn only from their own parent, who is the sole adult member of the clan. At higher rates of population growth, the clan is bigger, and hence there are more masters who generate ideas and whom the young can learn from, resulting in faster technological progress. Figure II View largeDownload slide Productivity and Population Growth in the Clan (C) Equilibrium Figure II View largeDownload slide Productivity and Population Growth in the Clan (C) Equilibrium IV.D. The Market At the opposite extreme (compared to the family) of enforcement institutions, we now consider outcomes in an economy with formal contract enforcement (as in the usual complete-markets model). All contracts are perfectly and costlessly enforced, so that masters who promise to train apprentices do not shirk.34 There is a competitive market for apprenticeship. Given market price p for training apprentices, masters decide how many apprentices to train, and parents decide how many masters to pay to train their children. In equilibrium, p adjusts to clear the apprenticeship market. A craftsman’s decision to take on apprentices is a straightforward profit maximization problem. In particular, given price p a master will choose the number of apprentices a to solve:   \begin{equation*} \max _a\lbrace p\, a +\kappa \,a -\delta (a) \rbrace . \end{equation*} The benefit of taking on apprentices derives from the price p as well as the apprentices’ production κ, and the cost is given by δ(a). Optimization implies that in equilibrium the price of apprenticeship equals the marginal cost of training an apprentice:   \begin{equation*} p=\delta ^\prime (a)-\kappa . \end{equation*} Now consider parents’ choice of the number of masters m that their children should learn from. Given p, parents will choose m to maximize their utility from equation (1):   \begin{equation*} \max _m \left\lbrace -p\, m\,n +\gamma \, \mathbb {E}\,I^\prime \right\rbrace , \end{equation*} where n is the number of children and I΄ is the income of the children, which is given by equation (5). Each child’s expected income depends on m, because learning from a larger number of masters increases the expected productivity (and hence income) of the child. The objective function is concave, because as m rises, the probability that an additional master will have the highest productivity declines. Lemma 1. The first-order condition for the parent’s problem implies:   \begin{equation} \delta ^\prime (a)-\kappa = \gamma \, \theta {(1-\alpha )} \frac{1}{m+\nu }\frac{Y^{\prime }}{N^{\prime }}. \end{equation} (17) Proof. See Online Appendix E. Notice that the decision problem implicitly assumes that the young apprentice gets m independent draws from the distribution of knowledge among the elders, as though the masters were drawn at random. The possibility of independent draws from the knowledge distribution is a key advantage of the market system over the clan system. In a clan, the potential masters have similar knowledge (because they learned from the same “grand” master), and hence the gain from studying with more of them is limited (there is still some gain because of the new ideas generated by masters). Of course, it would be even better to study only with masters known to have superior knowledge. We assume, however, that a master’s knowledge can be assessed only by studying with them; hence, choosing masters at random is the best one can do. The market equilibrium gives rise to a unique balanced growth path, which is characterized in the following proposition. Proposition 4 (Balanced Growth Path in Market Equilibrium). The unique balanced growth path in the market equilibrium has the following properties: The number of apprentices per master aM solves equation (17):  \begin{equation} \delta ^\prime (a^{{\bf M}})-\kappa = \gamma \, \theta {(1-\alpha )}y^{{\bf M}}\left(\frac{a^{{\bf M}}}{n^{{\bf M}}}+\nu \right)^{-1}, \end{equation} (18)and the number of masters per child mM is given by $$m^{{\bf M}}=\frac{a^{{\bf M}}}{ n^{{\bf M}}}$$. The growth factor gM of knowledge k is given by:  \begin{equation*} g^{{\bf M}}=m^{{\bf M}}+\nu . \end{equation*} The growth factor nM of population N is given by:  \begin{equation*} n^{{\bf M}}=(g^{{\bf M}})^\frac{{(1-\alpha )} \theta }{\alpha }. \end{equation*} Income per capita is constant and satisfies:  \begin{equation*} y^{{{\bf M}}} =\frac{(g^{{\bf M}})^\frac{{(1-\alpha )} \theta }{\alpha }}{\bar{n}\,s}. \end{equation*} The market equilibrium yields higher growth in productivity and population and higher income per capita than do the clan equilibrium and the family equilibrium. Proof. See Online Appendix F. To analyze the equilibrium, we can plug the expressions for aM, mM, and yM into equation (17) to get:   \begin{equation} \delta ^\prime ((g^{{\bf M}}-\nu )n^{{\bf M}})-\kappa = \gamma \theta {(1-\alpha )} \frac{1}{g^{{\bf M}}}\,\,\,\, \frac{n^{{\bf M}}}{\bar{n}\,s}. \end{equation} (19)This equation describes a relationship between gM and nM which we call the “apprenticeship market,” as it is derived from the demand for apprenticeship and the equilibrium condition on the apprenticeship market. Equation (19) can be rewritten as:   \begin{equation} n^{{\bf M}}=\frac{\kappa }{\bar{\delta }(g^{{\bf M}}-\nu )- \displaystyle \frac{\gamma \theta {(1-\alpha )}}{\bar{n}\,s\,g^{{\bf M}}}}. \end{equation} (20)This function of gM is plotted in Figure III. The negative relationship between population growth and the rate of technical progress in equation (19) can be interpreted as follows. When fertility is higher, the market for apprenticeships is tighter, the equilibrium price of apprenticeship is higher, and parents demand fewer masters. Hence faster population growth is associated with lower productivity growth. Notice that such a feedback does not arise in the family equilibrium, because there apprenticeship is limited by the fact that only parents can serve as masters, rather than being constrained by market forces. Figure III View largeDownload slide Productivity and Population Growth in the Market (M) Equilibrium Figure III View largeDownload slide Productivity and Population Growth in the Market (M) Equilibrium The market equilibrium leads to faster growth than the clan equilibrium does because knowledge is disseminated across ancestral boundaries throughout the entire economy. The masters teaching apprentices represent a wider range of knowledge, implying that more can be learned from them.35 All of this is made possible by having a different enforcement technology for apprenticeship contracts, namely courts rather than punishment by clan members. IV.E. The Guild Historically, economies did not transition directly from the family or clan equilibrium to the market equilibrium; rather, there were intermediate stages of semiformal enforcement through institutions other than the state. In Europe, the key intermediate institution was the guild system, which for centuries regulated apprenticeship and knowledge transmission, at a time when state power was still weak. Craft guild is a generic term for an organization of craftsmen and manufacturers who shared an occupation and hence a training. Yet while they can be found everywhere, their function and power varied enormously both over time and across different regions. In Europe, continental craft guilds in most areas were politically powerful and used this power not only to organize the industry but also to monitor its operations and enforce rules. In England, guilds were less powerful and their political influence was much more limited. In the Ottoman Empire, guilds emerged in the sixteenth century but seem to have acted mostly as trade cartels and lobbying bodies, which did little to enforce industry regulations (Faroqhi 2009, 30–40). In China guilds emerged fairly late, and as noted above, often coincided with people of common origin rather than people sharing an occupation. We now provide a formal characterization of a “guild equilibrium” as an intermediate step between the family equilibrium and the market equilibrium. We envision a guild as an association of all masters involved in the same trade. In the production function (3), the effective labor supply from many different trades is combined with limited substitutability across trades, so that market power can arise. Allowing for heterogeneous labor supply by different trades, the labor income of a craftsman i in trade j is:   \begin{equation*} I_{ij}=q_{ij} \,{(1-\alpha )}\, \frac{Y}{L}\left(\frac{L_j}{L}\right)^{\frac{1}{\lambda }-1}. \end{equation*} Apprentices choose the most attractive trade. In equilibrium, the net benefit of joining as an apprentice is equalized across trades, so that for all j we have:   \begin{equation} \mathbb {E}\,I^{\prime }_{ij} - p_j m_j = \mathbb {E}\,q^{\prime }_{ij} \,{(1-\alpha )}\, \frac{Y^{\prime }}{L^{\prime }} -p \, m. \end{equation} (21) Collusion among masters in a given guild leads to social costs and benefits compared to the clan equilibrium. The costs are the usual downsides from limited competition; the guild has an incentive to raise prices and limit entry. Guilds enforced labor market monopsonies, and as a result often limited the number of apprentices that each master was allowed to take on at one time, specified the number of years each apprentice had to spend with his master, or even stipulated time periods that had to elapse between taking on one apprentice and the next (Kaplan 1981, 283; Trivellato 2008, 212). The purpose of these constraints was to limit supply and increase exclusionary rents, which for our analysis means that technological progress is slowed down compared to a market equilibrium.36 However, guilds operated across different dynasties and thus represented the full range of knowledge in the given trade. If the guild also enforced apprenticeship contracts (in the same fashion as in the clan equilibrium above), there was more scope for knowledge accumulation. Thus, in the absence of strong centralized contract enforcement institutions (i.e., if the clan and not the market was the relevant alternative), the guild had a genuinely positive role to play.37 Consider the choice of a guild j of setting the price of apprenticeship pj within the trade, or equivalently, of choosing the number aj of apprentices per master. The guild maximizes the utility of the masters in the trade. If the guild lowers aj, the effective supply of craftsmen’s labor in trade j in the next generation goes down. Due to limited substitutability across trades, this increases future craftsmen’s income in the trade, and thus the price pj that today’s apprentices are willing to pay. Thus, as in a standard monopolistic problem, the guild will raise pj to a level above the marginal cost of training apprentices. The maximization problem of the guild can be expressed as:38  \begin{equation} \max _{ a_j}\lbrace p_j\, a_j-\delta (a_j)+\kappa \,a_j \rbrace \end{equation} (22)subject to:   \begin{eqnarray*} S_j N^{\prime } m_j &=& N \, a_j,\\ p_j &=&\gamma \frac{\partial \mathbb {E}\, I^{\prime }_{ij}}{\partial m_j},\\ \mathbb {E}\, I^{\prime }_{ij} -p_j m_j &=& (1-\alpha )\, \frac{Y^{\prime }}{N^{\prime }}- p\, m. \end{eqnarray*} Here Sj is the endogenous relative share of apprentices choosing to join trade j. We have Sj = 1 in equilibrium; however, the guild solves its maximization problem taking the behavior of all other trades as given, so that Sj varies with pj and aj in the maximization problem of the guild. The second constraint represents the optimal behavior of parents sending their children to trade j (equalizing pj to the marginal benefit of training with an additional master). The third constraint stems from the mobility of apprentices across trades (from equation (21)). These two equations represent the two market forces limiting the power of the guild. Notice that $$\frac{Y^{\prime }}{N^{\prime }}$$ is exogenous for the guild j, because each trade is of infinitesimal size. Lemma 2. In the symmetric equilibrium, the solution to the maximization problem (22) satisfies:   \begin{equation} \delta ^\prime (a)-\kappa =\Omega (m) \,\,\gamma \theta {(1-\alpha )}\frac{1}{m+\nu } \, \frac{Y^{\prime }}{N^{\prime }} \end{equation} (23)with Ω(m) < 1. Proof. See Online Appendix G. Thus, the condition determining equilibrium in the apprenticeship market is of the same form as in the market equilibrium (see Lemma 1), but with the benefit from apprenticeship scaled down by a factor strictly smaller than 1. Hence, the extent of apprenticeship (and productivity growth) will be lower compared to the market equilibrium. In the limit where trades become perfect substitutes, λ → 1, we have that Ω(m) → 1, that is, guilds have no market power and the problem of the guild leads to the same solution as the market (Lemma 1). We can now characterize the balanced growth path in the guild equilibrium. Proposition 5 (Balanced Growth Path in Guild Equilibrium). The unique balanced growth path in the guild equilibrium h