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E X P L A I N I N G T H E S TA G N AT I O N O F C O M M E R C I A L I N S T I T U T I O N A L I N N O VAT I O N I N T H E I S L A M I C M I D D L E E A S T A Computational Exploration into the Unintended Consequences of Qur’anic Inheritance Law May 11, 2007 Shameel Ahmad [email protected] Advisor: Professor Avner Greif Department of Economics, Stanford University

ABSTRACT Timur Kuran’s explanation of the decline of commercial institutional innovation in the Islamic Middle East posits Qur’anic inheritance law as a potential obstacle to larger and longer-lasting commercial arrangements, which create pressure for such innovation. In this paper, I explore the logic of this theory by creating and analyzing a simple agent-based model of a mercantile society in agents choose contracts each round to maximize their utility. I use the model primarily to enumerate certain minimal parametric conditions on which Kuran’s argument could be predicated, and to suggest avenues for further empirical research that could support the theory’s claims.

Acknowledgements: I would like to thank Prof. Greif and Prof. Kuran for their early support and encouragement, and Prof. Rothwell for his patience and flexibility during the writing process. Any deficiencies remain, of course, entirely my own.



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I am astonished that commentators old and new have not attributed to the laws of inheritance a greater influence on the progress of human affairs.… Through the impact of these laws, man exerts an almost godlike power over the futre of his fellow men. Alexis de Tocqueville Democracy in America, p. 61

1.

Introduction The acceleration of economic progress in Western Europe in the Middle Ages is, by all accounts, an historical anomaly. An omniscient observer would certainly have bet against Western Europe if asked in 1000 A.D. to pick the region most likely to dominate the world a millennium later. She would likely have chosen China: the undisputed world-leader in contemporary scientific innovation, it had the most modern weaponry, transport, material production and medical technology of the time (Elvin 1973). If China was the safe bet, the new Middle East might have been the dark horse: Islam’s rise after the 7th century, particularly its expansion under the Umayyad caliphate (661-750), swept it into the Iberian peninsula in the west and the Indian subcontinent in the east with astonishing speed. By the close of the 10th century, advances by the Abbasids and then the Fatimids ensured Islam a trade network that stretched from the Mediterranean to the Indian Ocean. In comparison, Europe was but an uninteresting backwater. When the Umayyad al-Walid was turned back at Poitiers in 733, it was not perceived as a huge loss (Armstrong 2002). Incursions into medieval Central Europe were rarely followed up by a sustained attempt to maintain a colony or outpost (Wenner 1980). By several modern historians’ accounts, Lewis (2003) foremost among them, medieval Muslims did not find themselves concerned with the practices of these barbarians. Indeed, this lack of curiosity is symptomatic of the decline of the Islamic world relative to Western Christendom, and especially central for Lewis’ narrative.

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Rosenberg and Birdzell (1986) present a typical solution to this problem of premodern economic history, seeking to explain the sources and dynamics of Europe’s rise to dominance by identifying the unique features of Europe’s economic and political institutional evolution. This is very important but provides us, at best, with a partial answer: to fully understand why the societies of the world stand as they do today, we must also explain why other regions of the world took the institutional trajectories that they did, and why they were unable to compete with, and defend themselves from, an ascendant Europe. One explanation of the relative commercial decline of the Islamic Middle East 1 lies in the ability of Western European merchants to form ever-larger enterprises that lasted longer, and to capitalize on the advantages of scale and experience. Timur Kuran (2003) seeks to partially explain the lack of such innovations in the Islamic Middle East by arguing that the inheritance law prescribed in the Qu’ran, as enforced by Islamic courts, set firm limits on the maximum size of contracting groups, as well as the duration of these contracts, creating no pressure to create new institutional forms. In this paper, I explore the logic of this theory by simulating a society of independent utility-maximizing agents forming such contracts each round, using the NetLogo programming language (Wilensky 1999). I analyze the dynamics of this society and, in particular, interrogate the model to (a) specify the environmental conditions upon which the existence of such detrimental effects are predicated, and (b) propose hypotheses, reasoning about the necessary environmental conditions as well as individual and societal responses to them, about the historical record to help test and potentially corroborate Kuran’s argument.

1 I follow Kuran (2003) in defining the Middle East as encompassing the entire Arab world, Turkey, and Iran, as well as Andalusia and the Balkans when they were controlled by Muslims.



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Specifically, this paper examines two dependent variables as they vary in relation to the probability of dissolution (which serves here as a proxy for the difference in inheritance customs): the first is a single number constructed from the pair of preferences expressed by agents on average for enterprise size and longevity, and the second is the generational age of surviving lineages after a given number of periods. The first is important as a source of pressure for new legal, financial, commercial and organizational institutions; the second allows us to look into the accumulated experience of surviving agents, proxying for the tacit knowledge that is preserved and passed down in a single lineage. This model does not take into account directly the effects of multigeniture (as compared to primogeniture) on capital accumulation or wealth distribution; these have been documented in the literature. Doing so is not computationally difficult, since inequality indices like Gini and Theil are simple to implement algorithmically, but would complicate the model by requiring the specification of variables to deal with the growth of capital outside of the commercial enterprises under the scope of this study.

Section 2 contains a brief literature review, surveying accounts of inheritance law, comparative economic development, and the links between the two, as well as briefly examining the literature on agent-based modelling as justification for the use of this paradigm in this study. Section 3 lays out the model briefly, detailing the properties of agents, the sequence of events in a simulation run and the configuration of relevant parameters. Section 4 analyzes the results of particular simulation runs, with the aim of identifying what combination of parameters allows the probability of dissolution (that is, a difference of inheritance law) to play a major role in



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distinguishing enterprise sizes and durations between two otherwise groups of agents. Finally, Section 5 draws some conclusions from these results, proposes extensions to the model, and sets forth basic hypotheses about the historical record that would help corroborate the model, and hence, Kuran’s (2003) argument. Section 6 contains a pseudo-code summary of the model’s code, for the reader’s reference, as well as instructions on accessing an online version of the model (encoded as a Java applet).

2.

Literature Review This paper draws most heavily on Timur Kuran’s research on the potential ramifications of Islamic inheritance law for commercial innovation; it is his hypothesis on the negative effect of increased probability of dissolution on enterprise size and longevity that is being operationalized here (Kuran 2003). This hypothesis is outlined in the introduction above: during the description of the model, support is again drawn from his paper, which relies primarily on Udovitch (1970) for details of Middle Eastern partnership in practice and in law. The inheritance customs of the Islamic Middle East are surveyed most broadly in Powers (1986). Crone (1987) focuses on the legal system more generally, finding antecedents for Islamic inheritance law as far back as Roman and provincial law. Pre-Islamic inheritance practices, interestingly, often also tended towards multigeniture - Powers (1986) discusses this, arguing that the Qur’anic inheritance law was not as major a change from pre-Islamic Arab practices as has been thought. Morony (1981) discusses late Sasanian society, in which the problems of estate division saw the development of joint family trusts not unlike the later Islamic waqf, but which also featured the Persian and Nestorian practice of estate division only in case of intestacy.

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Kuran (2003) mentions also the use of multigeniture among pre-Islamic Turks and Mongols. Mundy (1988) surveys the literature and debates on this question more generally. As for the inheritance law under Islam proper, perhaps the rigidity with which it ultimately came to be enforced can best be demonstrated by the discussion of a 9th scholar of the Mudawanna (the branch of Maliki law dealing with personal and family law): Question: When a small plot of land is involved, belonging in common to several persons, and if the part which is due to each of these people, once the plot is divided, is so small that it is of no use, should one, in Malik’s opinion, proceed to the division or not? Malik said: one must proceed to the division, even if some people are opposed to it. As soon as a division is asked for, even if the demand is formulated by only one person, one must proceed with it. (Talbi 1981, p. 234) The recognition that inheritance institutions play a role in economic (as opposed to purely social or political) development is not especially new: the epigram from Tocqueville (1835) at the beginning of this paper suggests that it is not very old either. The earliest scholarly account I was able to find was Josiah Wedgwood’s (1929), which holds forth on the relationship between laws of succession and the economy (historical and contemporary) in the early 20th century. However, both Tocqueville and Wedgwood, along with early historians making parenthetical remarks in more general histories of inheritance customs (such as Lloyd (1877) and Cecil (1895)), focus on the relatively obvious role that inheritance structures play in long-term capital accumulation, particularly in terms of land estate, and on the historical relationship between feudalism and primogeniture. Generally, that primogeniture comes to be adopted as a standard is explained by reference to the rise of feudalism and the attendant decentralization of power. As for historians of the Middle East, the fragmentation of estates necessitated by Qur’anic multigeniture has been remarked upon (Kuran 2003 cites Baer 1962, pp. 79-83; Marcus 1989,

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pp. 209-210; Doumani 1995, pp. 70-71; Meriwether 1999, Chap. 4). Even contemporary rulers appear to have been aware of the efficiency and tax revenue losses entailed by this fragmentation (Kuran 2003 cites Cohen 1993; Inalcik 1995; Cuno 1992, Chap. 4). That a relatively recent paper surveying medieval Islamic credit and banking should think it novel to suggest the Qur’anic law of inheritance as an obstacle to capital accumulation indicates perhaps that the focus of historians has tended to fall on land estates rather on more fungible fortunes (Ray 1997). In any case, what sets Kuran apart from the previous literature on the subject of Qur’anic inheritance law and economic history is his focus on the complexity of commercial institutions as opposed to capital accumulation. The lower complexity of Islamic commercial institutions, in comparison to the rapid evolution of European ones in medieval times, has been noted before. Issawi (1980), for example, sketching an answer to the question of how the European and Middle Eastern economies differed, notes two broad features: the first is the superiority of European accounting and insurance methods and the second is “the capacity among Europeans to build larger, more complex and more durable economic structures than the Middle Easterners built.” (Issawi 1980, p. 497). He cites numerous examples to make his case, even noting that the sufficiency of existing Middle Eastern commercial institutions for reaching larger sizes and longer durations, but he fails to provide a reason that this clear difference should exist. De Roover (1965) and Rosenberg and Birdzell (1986) both credit the superiority of 12th and 13th century Italian organizational innovations for their domination of Mediterranean commerce. Explanations for the rise of such complex in the northern Mediterranean and their absence in the southern Mediterranean abound: Greif (1994; 1996) discusses received explanations in greater detail, and uses game-theoretic equilibrium analysis to propose that differences in punishment



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strategies between the Maghribi and Genoese merchants (collectivist and individualist, respectively), with regard to agency relationships, explain the incentive for new institutions (the Italian family firm, the compagnia) in the latter and not the former. Kuran’s novel contribution to this literature is the link between inheritance law and lower institutional complexity. Kuran’s (2003) specific argument draws its logic from Greif’s notion of endogenous institutional change, and, in particular, the distinction between self-reinforcing and self-undermining institutions: both are game-theoretic equilibria, but self-reinforcing equilibria exhibit positive feedback such that, in the long-term, they hold for a wider range of parameters (situations) and self-destroying equilibria, as a result of their very nature, function in a parameter space that shrinks over time (Greif 2005, Chap. 6). On Kuran’s account, the Western partnership form, the commenda, was self-destroying in that it became decreasingly adequate for managing larger groups of partners for longer durations, and its Middle Eastern counterpart, the mudaraba, was self-reinforcing in that such pressures never arose (due to the inhibiting effects of Islamic inheritance law). More generally, this paper fits into the recent trend of institutional economic history that finds received explanations for the relative decline of the non-European world, and the Middle East in particular, unsatisfactory (Kuran 1997; Wong 1997). One set of critiques, perhaps represented most vociferously by Bernard Lewis (2003), credits a slowdown of intellectual innovation (in science, commerce, and political organization, among other fields) for the general economic decline of the region, but fails to specify why this should have happened. Another fairly common argument, often made by those with a leftist and/or anti-Western bias and of which Rodinson (1974) is typical, credits the Middle East’s decline entirely to the predation and



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peculation of an ascendant Europe, failing to note that the signs of commercial decline were visible in much of the Middle East before Suleman the Magnificent’s 1535 capitulations to the French, even if its rulers were militarily and politically potent. The new research agenda falls into the broader category of historical and comparative institutional analysis (North 1990; David 1994; Greif 2005).

METHODOLOGY What is the purpose of a computational agent-based simulation in this investigation? To begin with, we start with Hayek’s (1948b) distinction between the natural sciences and the social sciences, in his observation that the latter must explain complex phenomena where there are no deterministic laws to be adduced and experimentation is impossible. The rise of experimental economics as a discipline has not dulled Hayek’s point: economics still has no universal constants, nor iron-clad laws. The goal of social scientists, then, is to construct “hypothetical models in an attempt to reproduce the patterns of social relationships in the world around us” (Hayek 1948a, p. 68, emphasis added). A computational simulation is as valid an approach to behavioral reproduction as a formal mathematical model when viewed in this light; in fact, simulations often make it easier to reproduce certain kinds of complex patterns. Another way to justify the use of computation simulation is through the logic of theory formalization. Kuran has put forth the mechanics of a compelling argument that the Islamic law of inheritance played a role in retarding innovation in the structure of business enterprises. A computer simulation provides an avenue into the kernel of the problem by operationalizing the argument, forcing us to ask on what premises we can legitimately draw the conclusions that we



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do, and clarifying how the variables involved might interact with one another. We can observe and delineate the pathways through which shifting one exogenous variable has effects throughout the social system we’re observing. To summarize the thrust of Gilbert (1994) , simulation is hard to do: taking a verbal argument and creating a model from it requires the reification of tacit assumptions. A key problem, of course, as with any theoretical model, is ascertaining whether the model we have built has any representational validity. Given historical data, robustness and sensitivity testing are possible, but in the absence of such data, the best we can do is to identify trends and compare the model’s behavior to our qualitative, sometimes merely anecdotal, understanding of history, somewhat like the use of game-theoretic insights in economic history (Greif 2005, Chap. 5). Returning to Hayek: We may not be able to directly confirm the causal mechanism determining the phenomenon in question is the same as that of our model. But we know that, if the mechanism is the same, the observed structures must be capable of showing some kinds of action and unable to show others; and if, and so long as, the observed phenomena keep within the range of possibilities indicated as possible, that is so long as our expectations derived from the model are not contradicted, there is good reason to regard the model as exhibiting the principle at work in the more complex phenomenon. . . . Our conclusions and predictions will also refer only to some properties of the resulting phenomenon, in other words, to a kind of phenomenon rather than to a particular event. (Hayek 1967, p. 15) This model takes advantage of historical stylized facts to put together an argument for the conditions under which we ought to observe the phenomenon in question; the model itself is not a perfect depiction of reality, but an abstraction (as all models are) that may allow us some insight into the causal mechanisms at work in the real world.



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The expressivity of programming languages is somewhat different from the pure simplicity of mathematical proofs, but no less comprehensible for its additional flexibility. Leombruni and Richiardi (2005) compare and contrast traditional and computational modelling paradigms within the field of economics. Several important characteristics of computer simulation set it apart from traditional economic models: representing subtly multidimensionally heterogeneous agents is easier computationally, for example, as is dealing with parallel and unordered processes and complex interactions between agents. The nature of programming languages allow for a high degree of modularity that makes changes and extensions more tractable. For example, endowing agents with complex risk-attitudes is a trivial matter of adding a single function that takes a raw value (say, $100) as an input and returns a utility-adjusted value (say, 10 utils) according to some given formula. As simple as this is, the true power of the object-oriented paradigm is that this function is treated as a black-box by other parts of the model, giving the modeler great flexibility in modifying it (even while the model is running) without having to overhaul the rest of the code. Secondarily, the use of a GUI interface makes the model more immediately accessible to readers, who can play with it and observe the model’s dynamics in real-time on a series of graphs and monitors. The code is freely available to be remixed, extended, stripped down or examined, as with any kind of model, but there is also power in the simplicity of its interface with end-users. Section 6 has information on getting access to an interactive version of the model and to its source-code (a high-level pseudo-code summary is provided as well).



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3.

Model In this section, the model (program) is described. I begin by first providing a static description of merchants, listing the variables that they possess, and describing the basic set-up of the model and its visual interface. Since the program is essentially dynamic in nature, I focus on timelines that explain the sequence of events (first in summary form, and then in greater detail). I then treat the major assumptions of the model, upon which its results necessarily depend, as well as all the parameter variables, dealt with on an individual basis. At its most basic, this model features individual agents that choose to engage in partnerships once a round, choosing the size and duration that maximizes their utility. Each round is identical; agents may die, but unless succeeded by an heir, are not replaced. Thus, a single simulation run is theoretically infinite, terminating only if all agents die and their heirs choose to dissolve their estates.

STATIC DESCRIPTION Each merchant possess the following variables: VARIABLE who wealth share age heirs generation my_choices my_group



DESCRIPTION Unique identifier for each merchant, integer Amount of capital possessed, real number Percentage of capital contributed to a contract (and hence, percentage of revenue to be received), real number Age of merchant, integer

INITIAL VALUE Set sequentially (from 0), fixed 500 (updated after each round) No initial setting, changed each round Set stochastically, from U[0,20], and raised by 1 each round Number of heirs, integer Set stochastically, from U[1,5], and raised stochastically each round Generation of merchant, identifying how many direct 1, raised when heir succeeds ancestors he has succeeded, integer merchant (reconstitution) List of all possible partnership choices, array of 17 triplets No initial setting, changed and (profit, size, duration) re-sorted each round Identifies which group merchant belongs to, integer (named No initial setting, set to -1 before after who of arbitrarily-chosen “founder”) each round (indicating ungrouped)

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VARIABLE top_size top_dur dead dissolved

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DESCRIPTION Size of top-ranked partnership choice pulled from my_choices, integer (used for graphing purposes only) Duration of top-ranked partnership choice pulled from my_choices, integer (used for graphing purposes only) 1 if merchant is dead, Boolean 1 if dead merchant’s estate is dissolved, Boolean

INITIAL VALUE No initial setting, set each round No initial setting, set each round 0 0

Table 1

For the purposes of visual and computational tractability, I use a 4x4 symmetrical matrix with only even numbers, [2,4,6,8]x[2,4,6,8], though the result can be shown more generally, for any [0,a]x[0,b], a,b∈Z, by identical methods. The size choices are easily interpreted as the number of individuals in a contracting group; the duration choices may be thought of as an analogue to the number of months in a year (a caveat: in the model, each round is assumed to consist of 8 periods, or, more generally, a number of periods equal to the maximum duration-choice available). In Figure 1 below, the box to the left corresponds to this grid, oriented as a graph with the origin to the bottom-left; the gradations of gray mark the ascent up and rightwards towards longer and larger partnerships (respectively). The agents are represented by colored dots (the colors do not signify anything, serving only to differentiate agents and useful for simulation runs with small numbers of them). The light blue oblong boxes are all user-selectable parameters, within the ranges set by the program: both the parameters and the ranges are discussed on a case-by-case basis below. The light-yellow boxes contain graphs: the three on the right are updated automatically each round, and the two on the left must be manually refreshed to display the shape of the cumulative survival function and the utility function, respectively.



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Figure 1

SUMMARY TIMELINE OF A SINGLE ROUND 1. Merchants rank all possible outcomes (s,d) by expected utility 2. Merchants queue up at optimal (s*,d*) and look for partners (If unable to find partners, they switch queue to next-best until they are able to form a contract) 3. Partners form a group and pool their capital 4. Program calculates revenue, checks merchants to see if any of them have died while in contract and (if so) if their heirs have chosen to dissolve the contract 5. Revenue is distributed back to the merchants according to their shares, less any costs arising from reconstitution or dissolution



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6. Merchants age, have children (stochastically) and may die during the period of time in which they are not in contract 7. Dead merchants are replaced by an heir (if their shares were reconstituted) or are removed from the game (if their shares were dissolved).

DETAILED TIMELINE OF A SINGLE ROUND Each round, a merchant calculates his mean return from a variety of contracts, chosen from the matrix of [size choices] x [duration choices]. The mean returns are compared from a risk-neutral perspective or from a risk-averse perspective, the choice and degree of the latter depending on the user’s setting. The merchant ranks all of his 17 choices (the 16 possible contracts in this four-by-four space, plus the option not to participate in a contract at all, assumed to provide no return at all2 ), and then proceeds to queue up on the grid in the square corresponding to his two-dimensional top choice. If he finds enough partners willing to contract with him, he commits to a contract; if not, he moves on to his second choice, queuing up again. He has no information about other individual merchants: he only knows that they are standing in the same queue. If there are more merchants n in the queue than available spots s in a contract (e.g. 10 merchants in a group for a (4,6) contract), then (n – (n % s))/s groups (i.e. (10 – (10 mod 4)/4 = 2 groups) are formed by picking randomly among the n merchants and the remaining (n % s) merchants (i.e. (10 mod 4) = 2 merchants) must move on to their next choices. This recursive procedure ends either when the

2 This assumption can be rather critical: it implies that agents will engage in contracts under clearly suboptimal conditions (e.g. 99% mortality rate) because an infinitesmally positive expected utility outranks zero.



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merchant forms a contract or he ends up having failed to find any set of partners with similar preferences. In each separate group, then, s merchants have come together for d periods in a (s,d) contract, forming a temporary and separate grouping apart from all other merchants. They each contribute some amount of capital, equivalent to share% of their total worth, to a common pool: their final profit-shares are determined by the percentage of their capital in this pool. Thus, richer merchants invest more and receive a proportionately greater share of the profit than poorer merchants. The actual profit is not determined randomly: it is a fixed function of s, d and pooled partnership capital K. The inclusion of s and d here encapsulates some basic assumptions about the relation between contract size, contract duration and profit outcomes: thus, the functional form of this relationship is critical to the model, and to any results we draw from it. The section on assumptions below goes into greater detail. Once this profit has been determined, randomness plays a role: will all the partners survive d periods? If so, everything comes off successfully, and the profit is distributed to the partners in accordance to their shares; if not, however, the contract must be reconstituted by the heirs of the dead partner(s). Again, this is determined randomly: if the contract is reconstituted, then the partners receive their profit share, minus percentage reconstitution_costs (a user-defined variable between 0% and 20%). If any heir insists on dissolving the contract the surviving partners receive their profit share back, minus percentage dissolution_costs (a user-defined variable between 0% and 100%). After receiving their returns, the contracting merchants part ways.



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The contracts having been concluded, the merchants return “home” (to the origin, (0,0)). They age a single round, and have children (produce more heirs) according to given probability distribution that varies with wealth. They may also die during the (8 - d) periods in which they were not in contracct. If a merchant has died and is succeeded by an heir (either by voluntary reconstitution of his estate by all heirs, or by primogeniture), his generation increases by 1. A merchant who is not succeeded by anyone disappears from the board (technically, he is converted into a different type of agent called ghost instead of merchant; this allows the characteristics of dead merchants to be analyzed and compared to those of living ones, though such analysis is not possible in this study due to lack of space.)

ASSUMPTIONS This section details the major structural assumptions that underpin this model, and upon which all results are necessarily predicated.

The Z Score: Condensing the Number of Partners and Contract Length to a Single Figure This assumption is made primarily to facilitate the presentation of results. I combine the two preference variables, size and duration, into a single number (let us call it the Z score), corresponding to the distance from the origin in the two-dimensional space of size and duration. (To be more accurate, this space must be strictly positive with the inclusion of {0}, since it is not a valid option to pair a non-zero size with a zero duration, and vice versa). In algebraic terms, we can define Z partwise as follows:



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17 Z = (s2 + d2)1/2 if s > 0, d > 0 Z=0

otherwise

This is somewhat arbitrary, though not so much in the case of weighting the two variables: any relative multiplicative weighting can be thought of as just a change in the choice-variables’ value-ranges: for instance, doubling the weighting on size is the same as giving merchants choices from [0,4,8,12,16] instead of [0,2,4,6,8] and using equal weighting. The model allows increasing or decreasing output returns to both size and duration separately, with fractional exponents and exponents greater than one. A great variety of shapes are then possible for Z-curves. The discussion below assumes the simplest case, where the exponents on size and duration are 1.

Figure 2: Z-Curves



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This formulation immediately presents an obvious analogy: the Z-function corresponds to a concave utility function in a two-good space (see figure 2 above). An isomorphic Z-curve (i.e. a curve along which Z remains constant) then traces out indifference curves. At the risk of being overly metaphorical, one could call these innovation-induction invariant curves; the higher the level the Z-level sustained by a society over the long-term, the greater the “quantitative” pressure that arises for new forms of commercial organization to manage the larger scale. Of course, this is a gross oversimplification: a single curve combines different “qualitative” forms of pressure that cannot be meaningfully compared, so (s,d) = (8,4) may create pressure to increase formal division of labor, whereas (s,d) = (4,8) may lead to the rise of more complex accounting techniques, though both lie on Z = 8.9443. (An appropriate weighting would help matters somewhat, but carries the risk of making an overly arbitrary assumption; equal weighting is used simply as a default, and since we use Z more as a unit of presentation than a unit of analysis). Still, this crude metaphor allows us to condense the difference between European and Islamic inheritance law to variation in a simple (though not necessarily fixed or linear) constraint, determined by the parameter variables of this model. Kuran’s (2003) argument, in essence, is that Qur’anic inheritance law, as enforced by courts in practice, provided for a stable, low constraint, whereas Europe was more fortunate in having the freedom to experiment with inheritance standards (and thus shift the constraint outwards as more favorable systems were standardized). Thinking about the problem this way emphasizes the importance of properly specifying the shape of these Z-curves and the shape of the constraint curve. The concept of Z-scores (the distance from the origin to a given Z-curve) will be used during the analysis of the model, but



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always with an eye on decomposing it into its constituent factors, when doing so is interesting. This idea as a whole is returned to in the concluding section of this paper, as a means of recapping its objective and conclusions.

The Relationship between Partnership Size, Contract Length and Profitability In this model, the profitability of any partnership is modelled deterministically: π(K,s,d) = (K/10)sadb where K is the capital pooled by s merchants in a partnership lasting d periods, and a and b are exponents in [0,∞) denoting increasing, constant, or decreasing returns to additional members and additional time. K is in fact itself a linear function of s; since pooled capital is the sum of contributions ki (a fixed share of merchant i’s wealth) from s merchants, K = s*avg(ki). When attempting to maximize their expected profit, then, the optimization problem is reduced to maximizing sa+1db, discounted appropriately using the probabilities of mortality and dissolution. Note that the variable size_exp, as implemented, corresponds to (a+1), not a. An equivalent stochastic model could draw profitability from a Normal distribution with mean π (as defined above) and some fixed variance σ; merchants would still attempt to maximize π by maximizing sadb, though now some randomness is achieved. If σ were instead a function (of K, s, d, a, b, or any subset thereof), then the optimization problem could be solved using a mean-variance utility function as typical in basic finance theory. For instance: u(π) = E(π) - (σ(π) + π2) / A



for A∈R sufficiently large

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This is not implemented in this paper, as doing so would require the specification of how partnership size and duration affect the variance of profit outcomes. Are larger groups more likely to play it safe than smaller ones? Are longer contracts (that is, enterprises which extend over multiple trade missions) inherently more risky than short ones? These questions are not clearly answerable, and leaving them open as parameters runs the risk of cluttering our parameter space. The general interpretation of size_exp corresponds to the returns on additional partners purely in terms of profit. The structure of the mudaraba or its European equivalent, the commenda, tended to divide partners into two types: investors, who contributed financing, and agents, who carried out the actual missions without necessarily contributing to the capital. An additional investor contributes additional capital and perhaps some intangible knowledge, connections abroad or experience in a particular market. An additional agent, on the other hand, could bring as little as the latter, but potentially much more, if he could assist in opening up a new market, for instance; in any case, the structure of the mudaraba in general suggests that large groups tended to be formed by having more investors and not more actual agents (although investors were likely to have separate partnerships with many different sets of agents). The returns to additional partners then, in the sense in which we are interested in it, boils down returns to scale in investment. Although a single rich merchant could, in theory, invest a very large sum in a single mission, the fragmentary effects of Qur’anic inheritance law on estates and the necessity to diversify as a means of avoiding risk make it more likely that a number of investors would contribute towards a large sum.



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Our interpretation of dur_exp is slightly more complicated: it does not refer to longer missions per se, but to contracts that extend over multiple trade missions. What might the advantages of such a contract be? It could offer stability, lower renegotation (transaction) costs between partners, and efficiency in organization, all of which might lead to greater profitability. On the other hand, it locks the merchants into groups for longer periods of time, increasing the risk of being exposed to a mortality while in contract (which in turn carries a risk of dissolution), and reduces their flexibility in choosing partners according to the specific parameters of a particular mission.

MODEL PARAMETERS This section details the independent variables that the user may set exogenously, as well as their ranges and descriptions of their interpretations and computational implementations.

Number of Merchants Range: 0-100 merchants (in increments of 1) The number of merchants is not an immediately obvious variable of importance, but this implementation of the algorithm that matches merchants with each other to form groups highlights an important aspect of this problem: the ability of merchants to realize their optimal contracts depends on the existence of enough other merchants that share their goal. Consider that a group of five merchants, no matter how much they would like to be in a group of eight, must settle for either a group of size four or two groups of size two (with one merchant left out in each case). The granularity of this model aside, the best they can do is a group of five. It is a sufficient



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deterrent to the formation of larger groups, then, to consistently inhibit a minority from forming such groups. Thus, even if there existed, say, several young rich risk-seeking merchants with no heirs, any contract they form is limited by their number. Furthermore, to effect institutional change would require the long-term and widespread persistence of large group sizes and long durations; a small group of iconoclasts is unlikely to achieve this without some support from fellow merchants.

Mortality Two methods of modelling mortality are used in this model, a simple binomial probability function and the more complex Gompertz-Makeham formula: Range: 0-100% (in increments of 1%) The binomial function takes the user input prob_mort to be the probability that a single merchant dies during the course of a single round (eight periods). All forecasts are then carried out according to highly tractable binomial formulae: a merchant attempting to calculate the expected utility of an s-person d-period contract would use the following to calculate the probability that j of the (s - 1) other merchants will die. C(s,j)(prob_mort)jd(1 - prob_mort)(s-j)d The final step of evaluating any potential contract (s,d) is discounting the entire by the probability that the merchant himself will survive the round. The special case of prob_mort = 1, in which every course of action is equally optimal, is dealt with by convention, choosing (s,d) =



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(0,0). There are largest disadvantage of the binomial function is its insensitivity to merchants’ ages: an old merchant is as likely to die over any given period as a young one.

Cumulative Survival Curve (Binomial), varying with probability of mortality 1 0.9 probability of survival

0.8

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Figure 3

Range: α: 0-0.2, β: 0-0.2, γ: 0.01-0.2 (in increments of 0.01) The Gompertz-Makeham function is a useful alternative to implement, since it models the probability of death in two components, one age-independent and one age-dependent (Gavrilov and Gavrilova 1991). The probability of death at age t is thus: h(t) = α + βeγt α (alpha) is the age-insensitive component of the mortality function: one might model the introduction of new sanitation methods or workplace safety regulations in an adult population by a decrease in α. β (beta), on the other hand, is age-specific: the higher it is, the greater the role age plays in determining an individual’s survival. It makes sense for it to be positive: all else held

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equal, older people are more likely to die over a given period than young ones. α and β could be used together to model the outbreak of a disease to which the old are particularly susceptible. γ (gamma) effectively controls the maximum age that is possible for agents. The three of these can be used to yield cumulative survival curves with a larger variety of shapes than the one-parameter binomial alternative, as the graphs below (Figure 4, 5 and 6) show (the non-varying parameters are held at 0.05).

Cumulative Survival Function (Gompertz-Makeham), for varying levels of 1 0.9 probability of survival

0.8 0.7 0 0.01 0.05 0.1

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Figure 4



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Cumulative Survival Function (Gompertz-Makeham), for varying levels of 1 0.9

probability of survival

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Figure 5

Cumulative Survival Function (Gompertz-Makeham), for varying levels of 1 0.9 probability of survival

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Figure 6



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Range: 0-100% (in increments of 5%) This is the key exogenous variable in this study: the probability of dissolution represents the chance that the death of a partner (while in contract) results in the dissolution of the entire contract. The difference between Islamic multigeniture and European primogeniture is reduced to a difference in the probability of dissolution: the former, since it mandates a large portion of the estate for division into pre-defined shares for various heirs (wives, sons, daughters, and more distant relatives) and requires the express consent of all heirs to reconstitute a suspended partnership, clearly represents a much greater chance of dissolution than the latter, in which such an event is unlikely with only one heir, and almost impossible given the incentives to involve a single son in the business and groom him to succeed his father. The probability of reconstitution is the complement of the probability of dissolution.

Reconstitution Costs Range: 0-20% (in increments of 10%) Reconstitution costs represent the costs to the surviving contracting partners of having the contract held up by a death but not dissolved, represented as a percentage of contract revenue. These may include transaction costs and the costs of waiting for the heirs agree to reconstitution (since the law requires heirs to agree positively and unanimously on reconstitution, and suspends the partnership’s assets until such agreement). The range for this is relatively small, but it could potentially be quite important: primogeniture lowers reconstitution costs to zero, effectively,



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since the system puts in place incentives to groom the eldest son for immediate succession as well as to involve him in the running of the enterprise, whereas reconstitution costs may rise with the number of heirs under multigeniture. (The implementation here does not increase reconstitution_costs for merchants with more heirs, but such costs to a partnership rise when more than one member dies).

Dissolution Costs Range: 0-100% (in increments of 10%) Dissolution costs represent the costs to the surviving contracting partners of having the partnership’s assets liquidated by the heirs of a deceased partner, as a percentage of revenue. Defining the range of this is important: the user can set values from 0 to 100%, meaning that, at worst, merchants could lose their entire initial investment, but no more than this.

Coefficient of Constant Risk Aversion Range: 0-0.5 (in increments of 0.01) Risk aversion is modelled using the standard utility transformation for constant risk aversion, where the coefficient of constant risk aversion (CCRA) is user-defined. u(x) = 1–e-(CCRA)(x) The following graph (Figure 7) shows the utility transformation function as CCRA is varied.



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Utility Function for Varying Levels of CCRA 1 0.9 0.8

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Figure 7

Returns to Additional Partners and Additional Time in Contract Range: 0-2 (in increments of 0.25) The returns on additional partners (represented by the exponent size_exp in the partnership profit function) and additional time in contract (represented by the exponent dur_exp in the partnership profit function) are both critical to the model. Imagine, as an extreme case, that bringing in additional partners brought absolutely no material advantage: then any increased risk of dissolution, no matter how small, would be sufficient incentive to keep partnership sizes low in general. The fact that Islamic partnerships so often consisted of sedentary investors and mobile merchants, particularly for long-distance trade, suggests that bringing in additional partners as investors would not necessarily be smart: they would contribute some capital, and perhaps share

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some experience, but their impact beyond this could easily be marginal. Similarly, if the advantages to sticking to a single group for multiple trade missions were small, then multiple shorter contracts customized to each mission could be optimal.

A NOTE ON INFORMATION The agents are endowed with perfect foresight: that is, they can uniquely determine the (s*, d*) that maximizes their expected utility because they know the function that translates any group’s pooled capital into revenue, and all its associated variables (most importantly, the structure of mortality rates, either pmort or the parameters of the Gompertz-Makeham function, and the probability of dissolution, pdiss.). The outcomes could be randomized (for example, they could be given access to the parameters of some probability distribution that determines an enterprise’s earnings randomly), but our interest here is primarily in their behavior, and thus their forecasts, and only secondarily the cumulative effects of contract outcomes. Noise could be easily added to forecasts (using classical measurement error, for instance) but such a modification simply makes the scatter of the merchants’ choices more “realistic” without providing additional analytical insight. However, the fact the merchants be able to make forecasts with some minimal level of accuracy is critical to the model’s functioning: if the merchants were totally blind (if our noise drowns out the signal), they would enter contracts at random and without regard for their true relative worth, and hence be unable to maximize their utility in any meaningful way. This isn’t necessarily fatal to the society as a whole if the merchants are capable of learning: merchants could learn from their own histories and improvise their own rules that



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would, given time, approximate accurate foresight. This kind of inductive reasoning could be modeled algorithmically, as could a type of evolutionary genetic learning in which merchants that figure out the rules quicker do better, survive longer and breed more than slower ones, eventually wiping them out; these would form interesting simulation experiments in the evolution of a large group’s awareness of rules governing their games (institutions, in the most rudimentary Northian definition of the term), but are not germane to the problem at hand. For our purposes, we assume that such learning has already happened and that the relevant functions and variables are known to all merchants.

ASSESSING THE MODEL Agent-based modelling simulations generally should be held up to two types of scrutiny: verification and validation (Manson 2003). Briefly, to verify a computational model is to ensure the transformational correctness of the code (essentially, to debug it) and to validate a model is to assess the representational accuracy of the model (i.e. how does the model’s behavior compare to target behavior as empirically observed?).

Verification For this model, verification is partially accomplished during the construction of the model (following appropriate guidelines in the construction of a object-oriented program makes the isolation and testing of modules relatively easy). At the end, it makes sense to check summarily the model’s behavior in boundary cases, such as:



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• For prob_diss = 0, adjustments to dissolution_costs and reconstitution_costs should not affect agent decisions • For prob_mort = 0 or 1, adjustments to prob_diss should not affect agent decision • For dur_exp = 0, the optimal duration is always 2 (since this means that additional time spent in contract leads to no increase in partnership profitability), and similarly for size_exp • When reconstitution_costs are positive but dissolution_costs are 0, some increase in prob_diss should raise optimal size/duration More generally, merchants can be traced through the game individually: doing so makes it possible to ensure that wealth is being subtracted and added correctly, that ages are being updated correctly and so on. Furthermore, the same method allows one to ensure that any single contract runs appropriately, by simultaneously watching all merchants involved in the group. The matching mechanism that groups merchants with like-minded peers can be checked by watching the behavior of odd-numbered groups of merchants under different parametric conditions: for example, watch 10 merchants attempt to form groups under parameters that would make (8,8) optimal (e.g. low prob_mort, low prob_diss etc.), and make sure that 8 of them (but not the same 8 from round to round) form a group, and that the other two cycle through their choices until they arrive together at a 2-person partnership. Any odd-numbered group of merchants should see a single merchant end up forming no contract at all each round. That the survival and utility functions are being implemented properly in general can be checked simply from their respective output plots, since the plotting functions use the same functional machinery as the agents do. The model allows the programmer (but not the user who

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accesses it online, unfortunately) to add temporary monitors or plots for further model variables: the median number of heirs, the wealth of the poorest merchant, the age of the oldest merchant can all be tracked live, updated each round, to ensure that the population as an aggregate is behaving appropriately.

Validation The empirical validation of this model would require more data than is currently available. The model corresponds, to the extent possible, to soft data, to historical and reliable descriptions of organizational structure. By and large, this is not a problem: risk aversion and mortality are specified according to well-established precedents, and there is nothing greatly arbitrary in assigning the ranges [0,1] to the probability of dissolution and to the percentage costs of dissolution, since the entire range is explored for both cases. Where the lack of validation weakens the model most critically is in the specification of the partnership profit function; the model allows for some variation (in the respective exponents of size and duration), but it would benefit greatly from a large dataset that included figures on partnership size, contract length, and outcome. The model may need to be changed to accommodate the peculiarities of different modalities of commerce (long-distance vs. short-distance trade, maritime vs. land-based, by commodity or region) - if it were to focus on just one of these due to the specificity of the data (say, the maritime spice-trade in the Indian Ocean), a more robust result would be possible, though potentially at the cost of a less universal one. Boere and Squazzoni (2005) discuss this trade-off in greater detail.



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4.

Results This model has several parameter variables, as described in Section 3 above. Here, I analyze what combinations of parameter values are necessary to make the probability of dissolution an important factor in determining partnership size and contract duration. There are four potential ways that we can make agents respond to increases in the probability of dissolution by lowering their choice-variables for size and/or duration: 1. Increasing the probability of mortality 2. Decreasing the costs of reconstitution 3. Increasing the costs of dissolution 4. Decreasing the returns on additional merchants and additional time in contract 5. Increasing the risk aversion of merchants The lack of clarity and unwieldiness of three-dimensional graphs force me to focus on these one at a time. (Note that the first four variables are dealt with under the assumption of risk neutrality.) For a given factor X, I hold the others fixed (at values that make the action of X interesting, discovered simply by exploring the model’s parameter space) and observe the outcome (Z-scores) of a single agent’s optimization strategy as we vary the probability of dissolution for selected values of X. The first example of the probability of mortality should make this approach clear. In addition, I examine the generational age of merchants over time at different levels of probability of dissolution: as mentioned earlier, this is a proxy for the tacit knowledge accumulated within a single lineage of merchants. The importance of large family companies

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like the Bardis and Peruzzis in the early commercial history of Europe, and the coastal Italian cities in particular, is critical to the divergence in commercial institutional complexity (Hunt and Murray 1995, Chap. 5); does the probability of dissolution significantly lower the average generational age of surviving merchants? How many merchants alive at any point can trace back their genealogy to ancestors that were playing the same game, and how far back can they do so?

PROBABILITY OF MORTALITY Since the model revolves around what happens when merchants die, it is not surprising that the probability of mortality plays a central role. If there was no chance of dying, (prob_mort = 0 under the binomial model, alpha = beta = 0 under Gompertz-Makeham), then (8,8) is universally optimal, no matter how risk-averse merchants are, how small the benefit of additional partners/time in contract or how probable and how expensive dissolution is. The case of certain death is dealt with by convention: merchants choose (0,0), though every choice leads to the same outcome. Z-Score against Probability of Dissolution, for Varying Levels of Probability of Mortality (size_exp = dur_exp = 0.25, dissolution_costs = 0.2, reconstitution_costs = 0) 12

Duration (number of periods)

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Figure 8



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Figure 8 above shows the salient features of the interaction between the probability of mortality and the probability of dissolution. First, for a low enough probability of dying, increasing the probability of dissolution has no effect on outcomes. This readily suggests a first empirical test for this hypothetical model: do there exist places/times where/when, for whatever reason, residents tended to live significantly longer and/or were healthier and, if so, are there any marked differences in their enterprise sizes or durations? There is the obvious objection that medieval mortality rates, whether European or Middle Eastern, were generally fairly stable and fairly high, given the incidence of plague (Hirst 1953; Dols 1977). Even if there was a decline in mortality rates over time, it seems unlikely that it would cross this threshold, which would have to be a fairly low number by necessity. However, since the graph shows us that changing the probability of mortality at all has a significant effect on outcomes, we can generalize the question,and ask if there were ever any major difference in mortality rates over time or space. The medieval era, fortunately for us, provides us with at least one such natural experiment: the Black Death, the most severe epidemic of the pneumonic plague on record. Hunt and Murray (1999, p. 154) observe that the Black Death, which ravaged Europe’s population (as well as the Middle East’s) in the mid-14th century, significantly lowered Tuscan partnership sizes, since “high mortality from the recurring plagues made long-term commercial associations very tenuous, especially when many heirs had become more interested in spending their inheritance than in perpetuating the business.” That the issue of succession is highlighted is worthy of note: with multiple heirs, as required under Qur’anic law, the problem of insufficiently patient heirs is compounded.



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Epidemiological histories of the medieval era indicate that Europe rarely suffered from an outbreak of the pneumonic plague after the Black Death, rather suffering sporadically from localized instances of the relatively less deadly bubonic plague, with the exception of Russia (Hirst 1953, p. 34). The Middle East, up until 1516, at least, witnessed repeated outbreaks of the pneumonic plague: detailed evidence is not available for every part of the region, but Dols concludes that “repeated and substantial population reductions in population” are the likeliest scenario for the Middle East up until that time, compared with a strong argument that no secular demographic decline is evident in Western Europe (Dols 1979, p. 175; Bean 1962-63). We might then expect this to be an additional handicap for Middle Eastern merchants, particularly in light of the facts that plague outbreaks were most common in major seaports and that the Middle East’s centrality in major land and sea trade-routes intensified the spread of the disease. Dols (1979, p. 178-9) cites Constantinople, Alexandria, Smyrna and Rosetta as endemic centres of both types of plague. The model suggests that these higher mortality rates would significantly magnify the effects of an institutional increase in the probability of dissolution. Secondly, the upper limit at which the probability of dissolution has a marginal effect on outcomes it fairly low: 0.1 at lower levels of mortality (prob_mort = 0.05 and 0.1) and higher ones (prob_mort = 0.8) and 0.4 at medium levels (prob_mort = 0.2). Although the link between the number of heirs and probability of dissolution is not explicit here, such a result would indicate that beyond a certain threshold number of heirs, there would not be a great distinction among merchants in their choices; that is, having to negotiate among five heirs for reconstitution may be more detrimental than having to negotiate among two, but merchants expecting to deal



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with a societal average of five heirs will not choose contracts much differently than if they were expected ten, fifteen or twenty heirs (though they might if they only expected two). The Z-score, as was mentioned when the concept was introduced, is somewhat artificial, and obscures something that may be quite important: when do agents respond to an increase in the probability of dissolution by choosing to contract with fewer merchants versus by choosing to contract for fewer months? Under these parameters, the graphs below show that this depends on the level of mortality: at anything but low levels, agents optimize by minimizing duration. Agents maximize their size preferences at these low levels, dropping them only at fairly high (0.2) levels of mortality.

Dur against Probability of Dissolution, for Varying Levels of Probability of Mortality (size_exp = dur_exp = 0.25, dissolution_costs = 0.2, reconstitution_costs = 0) 9

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Figure 9



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Size against Probability of Dissolution, for Varying Levels of Probability of Mortality (size_exp = dur_exp = 0.25, dissolution_costs = 0.2, reconstitution_costs = 0) 9

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Figure 10

These conclusions are very sensitive, understandably, to how we set size_exp and dur_exp (i.e. to the nature of returns on additional partners and time in contract). Still, we learn from this that merchants have two ways of dealing with a higher probability of dissolution, and do not always employ them simultaneously: a large data-set on partnership sizes and longevity may allow us to draw some tentative bounds on the relative sizes of size_exp and dur_exp. Gompertz-Makeham is more difficult to explore graphically, due to its three shape parameters: however, it is available to users to experiment with online. One interesting result is that a mortality rule that emphasizes senescence over accidents (that is, privileges β and γ over α) can create equilibria in which merchants choose larger or longer contracts when younger but grow progressively more cautious as they age. A society of merchants that was younger on average would have an advantage over one that was older, under the same levels of probability of



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dissolution. Figure 11 below illustrates the average size and duration preferences of one such run: note that the fact that size is what changes here is arbitrary, due to the settings of size_exp and dur_exp. It is equally possible to create conditions in which neither size nor duration preferences vary, only duration varies or both vary with age. Sample Run, Showing Fluctuations in Size Preferences over Time (alpha=gamma=0.01, beta = 0.08, reconstitution_costs = 0, dissolution_costs = 0.4, prob_diss = 0.3, ccra = 0.01, dur_exp=size_exp=0.25)

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Figure 11

COSTS OF RECONSTITUTION As long as the costs of reconstitution are low (in the 0-20% range set in the model’s configuration), they have no observable effect on agent behavior, excepting the special circumstance in which dissolution is relatively cheaper than reconstitution, in which case Z-scores increase slightly with the probability of dissolution. If we assume that reconstitution_costs < dissolution_costs, however, reconstitution costs play no role in deterring merchants from forming larger groups or longer contracts.



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COSTS OF DISSOLUTION Intuitively, the costlier dissolution is, the more we should expect merchants to go out of their way to avoid it. The graphs below show Z-scores plotted against probability of dissolution, for different levels of dissolution costs (between 20% and 80%). Each graph has a different level of mortality: we require a non-negligible chance of death (5%) to see real variation between the different cost levels. In the real world, of course, such cost-levels would not be fixed, but randomized (depending, say, on which partner died and during what phase of the trade mission). Here, we take them as representing average figures perceived by individual agents. Even when dissolution is relatively costless, agents adjust to smaller durations (again, this is an artifact of the chosen size_exp and dur_exp; see discussion below for more). We see that don’t require that dissolution to be overwhelmingly costly to find significant deviations in behavior - if the additional benefit of more partners/more time in contract grows more slowly than the additional (probabilistic) cost of death/dissolution from more partners/more time in contract, then any positive dissolution cost is sufficient to shift optimal size/duration choice variables. Z-Score Against Probability of Dissolution, for Varying Levels of Dissolution Costs (size_exp = dur_exp = 0.25, reconstitution_costs = 0, prob_mort = 0.01, heirs = 5) 12 10

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Figure 12



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Z-Score Against Probability of Dissolution, for Varying Levels of Dissolution Costs (size_exp = dur_exp = 0.25, reconstitution_costs = 0, prob_mort = 0.05, heirs = 5) 12 10

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Figure 13

Z-Score Against Probability of Dissolution, for Varying Levels of Dissolution Costs (size_exp = dur_exp = 0.25, reconstitution_costs = 0, prob_mort = 0.1, heirs = 5) 12 10

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Figure 14

RETURNS TO ADDITIONAL PARTNERS / TIME IN CONTRACT The graphs below, Figures 15 and 16, show the effect of varying probability of dissolution for different levels of size_exp and dur_exp. Notice that a significant effect requires

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decreasing returns to additional partners and time spent in contract and that, under such an assumption, a small shift a relatively low positive probability of dissolution forces the Z-score down. The decomposition of the Z-score here is fairly obvious: agents tend to maximize (subject to other constraints) the factor (number of partners or time in contract) that gives relatively higher returns. The decomposed graphs are not shown here. Z-Score against Probability of Dissolution, for Varying Levels of dur_exp (prob_mort - 0.1, dissolution_costs = 0.4, reconstitution_costs = 0, size_exp = 0.25) 12 10

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Figure 15 Z-Score against Probability of Dissolutiion, for Varying Levels of size_exp (prob_mort = 0.1, dissolution_costs = 0.4, reconstitution_costs = 0, dur_exp = 0.25) 12 10 8

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Figure 16



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RISK AVERSION It should be no surprise that risk aversion substantially lowers the critical level of dissolution probability necessary to impact Z-scores, but it is especially important because it allows this mechanism to work at lower mortality levels (compared to those necessary when risk-neutrality is assumed) and enhances its effect dramatically at higher mortality levels. More generally, it can be thought of as a factor that lowers the barriers of other variables necessary to produce our desired result: even if dissolution were less costly, or additional partners more useful in increasing returns, a corresponding increase in risk aversion can dampen such effects. Z-Score against Probability Dissolution, for Varying Levels of CCRA (size_exp = dur_exp = 0.25, dissolution_costs = 0.4, reconstitution_costs = 0, prob_mort = 0.05) 12 10

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Figure 17

GENERATIONAL AGE In the following graphs, a group of 100 merchants is spawned (with random ages, random initial numbers of heirs, and reproduction according to a random function positively correlated



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with wealth) and the average generational age of the society is followed for 50 rounds. This is repeated for 11 possible values of probability of dissolution (0, 0.1, ... 1.0). Even small shifts in the probability of dissolution produce distinct changes in generational age, ones that compound over time. The first of the graphs (Figure 18) below illustrates this quite well: at fairly minimal assumptions (low risk aversion, low mortality rate, and low dissolution costs), we see a growing gap between the no-dissolution case and any case where dissolution has a positive probability. The second (Figure 19) shows that, at higher levels of other independent variables, the spread grows even further.

Generational Age against Time, for Varying Levels of Probability of Dissolution (size_exp = dur_exp = 0.25, dissolution_costs = 0.2, reconstitution_costs = 0 , prob_mort - 0.05, ccra = 0.01) 3.5 0

Generation Age (generations)

3

0.1 0.2 0.3 0.4 0.5

2.5 2 1.5

0.6 0.7

1

0.8 0.9 1

0.5 0 0

5

10

15

20

25 Time (rounds)

Figure 18



30

35

40

45

50

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45

Generational Age against Time, for Varying Levels of Probability of Dissolution (size_exp = dur_exp = 0.25, reconstitution_costs = 0, dissolution_costs = 0.4, prob_mort = 0.1, ccra = 0.1) 3.5

Generational age (generations)

3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

2.5 2 1.5 1 0.5 0 0

5

10

15

20

25

30

35

40

45

50

Time (rounds)

Figure 19

5.

Conclusions This paper has used a computer-simulated model to shed light on the dynamics of partnership size and contract duration as they relate to the probability of dissolution, which proxies for the differential role of inheritance law in the Middle East and in Western Europe. The model clarifies certain aspects of Kuran’s argument by operationalizing it, and provides insight into the nature of parameter conditions necessary for the relationship to hold consistently. In this final section, the results in Section 4 are used to generate several hypotheses about the historical record which could help corroborate or falsify this model and, by cautious extension, Kuran’s narrative on the role of Qur’anic inheritance law in Middle Eastern institutional stagnation. Some extensions to the model are suggested; I believe that the main features of the target have been sufficiently represented in the model as used here, but embellishments may reveal additional nuances and subtleties to the conclusions drawn and

Shameel Ahmad, May 11, 2007

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hypotheses suggested. Finally, I recap the objective of this research project, using a slightly different point of view and the terminology of marginal benefits and marginal costs to explain the model.

PREDICTIONS The model allows us to make some predictions about how merchants in the Middle East may have responded to the constraint imposed on them and where and when we ought to look to find exceptions (if they can be found at all). These aren’t predictions in the sense of making an educated guess about the future; rather, they represent educated (empirically verifiable) guesses about the partially-veiled historical record. They also serve quite well as a means of validating the model, taking Milton Friedman’s (1953) emphasis on predictive as opposed to structural accuracy as a starting point, as many agent-based modellers do (see, e.g., Hegselmann 1996). The results on mortality and the brief discussion about the plague are a good place to begin. Any large variability in mortality rates over time and space in the Middle East would serve as a good starting point for an empirical investigation. Dols (1979) cites Baltazard and Seydian (1960; 1963) on the relatively fortunate fate of medieval Persia and Kurdistan in the absence of rats: plague was only transmitted by of gerbils and fleas (the former restricted by their number and the latter by their nature as poor vectors), and thus appears to have had a relatively minor effect on that region’s demography. How did enterprise structure and longevity there vary from the norms of Maghribi and Levantine merchants, if at all? If the difference in mortality was significant enough, our model suggests that the negative effects of Islamic inheritance law could be all but negated by a lower likelihood of death.



Shameel Ahmad, May 11, 2007

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More generally, any data or anecdotal evidence on commercial activity during periods of plague visitation upon cities (whether in Europe or the Middle East) should corroborate the model’s account. Hunt and Murray’s (1999) report on Florence during the Black Death cited earlier is one such example, but we should expect to see this phenomenon practically universally. The results on the size of dissolution costs indicate that they do not have to be especially large to deter merchants from having more partners or longer-lasting contracts, even for relatively low levels of mortality: something on the order of 20% (of the sum of the original investment and expected profit) is sufficient when risk aversion and decreasing returns to partners/time in contract are assumed. This is a particularly good test case for the model, as court cases based on the dissolution of such contracts should enable us to put a rough figure on how much merchants stood to lose when this happened. Even a range of reasonable figures allows us to peg the variable to a smaller bracket of variability, and thus enable us to make better guesses about the other variables: if the costs were consistently very low, in the single figures, say, then we would have reason to either suspect the model’s hypothesis as a whole or to search for clues for a particularly high mortality rate, level of risk aversion, etc. The data on returns indicate that we require decreasing returns to additional merchants and/or time in contract to get the result we would like: under constant or increasing returns to either, our model’s optimizing agents have an incentive to contract in larger groups for longer despite increases in mortality or the probability of dissolution. However, we do not necessarily need both to be decreasing: the inheritance law could be equally damaging if it restricted Middle Eastern merchants to small groups or short contracts as opposed to both. Historical data could help us resolve this, if multiple micro-studies across the Middle East could show a bias towards



Shameel Ahmad, May 11, 2007

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one factor over the other. Additional corroboration of the model might be available, insofar as data is available on economies of scale in medieval trade, and perhaps written discussions from merchants themselves about the reasons behind their relatively short contracts. Risk aversion is an easy assumption to make about people, past and present. To be sure, however, risk aversion varies across populations: there may even be risk seekers. If innovation and risk-taking are be correlated, we would find ourselves looking for for a risk-taking Schumpeterian entrepreneur to break the organizational mould. However, that any group of merchants would have to be able to sustain partnership sizes and durations long enough under the prevailing system of inheritance law to truly effect institutional change. New organizational structures may appear and then disappear just as quickly, failing to become entrenched in standard practice or to evolve, as did European commercial innovations. Evidence of ephemeral innovations that fail to gain traction would thus be consistent with this theory: if they bring no great advantage to small groups of merchants organizing for single missions, there is no reason for them to catch on at large, even if they appear in specific places and over specific periods of time. Goitein’s (1966) research on the Cairo Geniza documents, for example, reveals examples of double-entry bookkeeping in the 11th century among the Jewish merchants of Qayrawān, much earlier than in Genoa or in Venice, where evidence dates its use to the early 14th century (Brown 1968). The most robust result is perhaps that of generational age: because of the tendency of these small differences to compound over time, the effect of probability of dissolution is observable under fairly weak conditions. A comparison of Western family enterprises, veritable



Shameel Ahmad, May 11, 2007

49

dynasties stretching for decades, with Middle Eastern ones, abruptly truncated, should provide a source of qualitative confirmation for this effect. And how would we expect individual merchants to respond to this barrier? To the extent that they can observe characteristics of their prospective partners, we should expect them to discriminate in favor of younger, healthier merchants with fewer heirs: given that the number of heirs may not be directly observable (particularly since they could stretch into the extended family), that health isn’t necessarily observable, and that older merchants may also be likelier to be wealthy, willing and able to invest, this doesn’t help us too much. But we may expect to see anecdotal evidence of bias against observably sick investors in mudaraba contracts, and against older investors who are not rich (wanting simply to buy a small share in some trade mission as investment). Another way for merchants to reduce their risk is to diversify their portfolio by investing in multiple contracts: however, this isn’t so clear-cut a strategy from the systemic point of view, since it is against any single merchant’s interest to have his fellow investors involved in multiple contracts (assuming that these investments overlap), and a single death then disrupts multiple contracts. Given a small group of investors with a choice of contracts as a strategy-set, then, we probably expect to see something like a coordination game where investors attempt to minimize their risk by maximizing the number of contracts they’re invested in while simultaneously minimizing the amount of overlap with other merchants. Perhaps the most obvious strategy is to avoid using the mudaraba contract altogether; the only real alternative, however, was the use of informal kinship-based structures, in which relatives and compatriots abroad served as agents on behalf of merchants. Goitein (1967) finds



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widespread evidence of this among the Cairo Geniza documents, though conclusions from these can only be drawn for the close-knit group of Jewish merchants from which they derive. (These merchants also contended with the same constraints as their Muslim counterparts; although they had their own communal court system, the superiority of Islamic courts, particularly with regard to enforcement, often meant that Jewish cases, including ones over inherited estates, could be settled under Qur’anic law.)

EXTENSIONS There are several fruitful ways that the model could be extended: given that gathering enough data to validate any of the model’s parameters is highly unlikely, we can continue to explore the complexities of the dynamics of enterprise size and longevity by modelling additional features of medieval commerce. Examples of this include: • Differentiation of mortality rates and risk aversion across the agent population • Having profitability vary with experience (a function of age and generational age) • Variable shares (correlating perhaps to perceived riskiness of the contract) • Dealing with risk by investing in multiple contracts simultaneously • Make the heirs play a more important role in dissolution, by tying the probability of the latter more directly to the number of the former (but only in the case of Islamic law, because only one heir counts under the strictest form of primogeniture). With this kind of study, it is always fruitful to study more individual cases to understand the qualitative nature of the problem we are trying to model. There may be additional historical,



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cultural, and legal dissimilarities across regions of the Middle East that need to be accounted for by new model parameters: these would also constitute useful extensions.

CONCLUDING REMARKS Before I conclude, I recap here the aim of this paper from a different point of view, only expressible now that certain concepts within the model have been described in detail: generally, if we expect the marginal benefit of partners/time in contract to be decreasing in partners/periods and the marginal probability of additional partners/time in contract to be constant (or increasing) in partners/periods (we exclude the case in which the marginal cost of an additional partner/period is always greater than the benefit), we can guarantee the existence of an intersection between the two curves that denotes an optimal set of contracts. A higher probability of dissolution, ceteris paribus, shifts the marginal cost curve up, and the intersection point moves towards the origin (i.e. towards smaller groups/shorter durations). A three-dimensional illustration of this is shown below: the x and y axes define the two-dimensional space (size, duration) and the z axis measures utility. The green manifold represents the benefits of additional partners/periods (assumed symmetrical here) and the red one represents the costs (again, assumed symmetrical). Their intersection draws out a curve whose projection on the xy-plane (excluding points on the x and y axes themselves) represents a set of optimal contracts (the graph on the left shows a top-down view of the intersection, which is convex under these assumptions). Clearly, the shape of the intersecting set is dependent on the shape parameters of the benefit and cost manifolds.



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Figure 20

This paper can then be interpreted as an attempt to parametrize the cost manifold in particular (rising out of the probability of mortality, probability of dissolution, the costs of various outcomes and levels of risk aversion) and the benefit manifold secondarily, as a matter of necessity (using only general numbers as returns to additional merchants and time in contract), with the aim of enumerating qualitatively the conditions under which the probability of dissolution (and, hence, inheritance law) plays a critical role in determining the shape of optimal contract sets (and, hence, the nature of societal pressure for institutional innovation), which were earlier dubbed Z-curves.



Shameel Ahmad, May 11, 2007

6. Model Pseudo-Code Summary An online, interactive version of the model, requiring a browser capable of displaying Java applets, is available from my website at http://www.stanford.edu/~shameel, as well as the source-code in the NetLogo language. The description in Section 3 should equip the user to set-up and run custom-runs. Below is a high-level pseudo-code summary that boils the program down to its most basic actions: the function main-loop constitutes a single round in any given simulation run. main-loop [

ask merchants [

order-choices

queue-up

]

while (any merchants ungrouped) [

ask all-ungrouped-merchants [get-in-groups]

]

run-contracts

ask merchants-in-contract [

if (died-in-contract) [become dead-merchant]

]



distribute-revenue



ask merchants [

if (died-out-of-contract) [become dead-merchant] ]



ask dead-merchants [

if (dissolution-of-estate) [become dead-lineage]

else [increase generation]

]

ask merchants [update]

53

Shameel Ahmad, May 11, 2007

order-choices [

foreach (16 ordered pairs from [2,4,6,8]) [

calculate expected utility of contract

]

add utility of abstaining from all contracts

sort 17 choices by expected utility

s.t. choices (1) is first choice

choices (2) is second choice .... ] queue-up [

go-to choices (1) ] get-in-groups [

look for ungrouped merchants in same queue

if (enough to form group with) [form-group]

else delete choices (1) ; shifting 2nd place to 1st place, etc.

queue-up ] run-contracts [

ask each-group-of-merchants [

pool-capital

calculate-revenue

calculate-profit-shares

] ] distribute-revenue [

ask each-group-of-merchants [

adjust-revenue for number of dead members, dissolved estates

assign profit-shares to each surviving merchant

] ] update

]



[ have-kids age-one-round leave-group return-to-origin

54

Shameel Ahmad, May 11, 2007

55

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Hunt, E. and Murray, J. 1999. A History of Business in Medieval Europe, 1200-1550. Cambridge, Cambridge University Press. İnalcık, H. 1955. “Land Problems in Turkish History.” Muslim World 45: pp. 221–28. Issawi, C. 1980. “Europe, the Middle East and the Shift in Power: Reflections on a Theme by Marshall Hodgson.” Comparative Studies in Society and History, 22(4): pp. 487-504. Kuran, T. 1997. “Islam and Underdevelopment: An Old Puzzle Revisited,” Journal of Institutional and Theoretical Economics, 153(1): pp. 41-71. Kuran, T. 2003. “The Islamic Commercial Crisis: Institutional Roots of Economic Underdevelopment in the Middle East,” Journal of Economic History, 63(2): pp. 414-446. Leombruni, R. & Richiardi, M. G. 2005. “Why are Economists Sceptical About Agent-Based Simulations?” Physica A. 355(1): pp. 103-109. Lewis, B. 2003. What Went Wrong? The Clash between Islam and Modernity in the Modern Middle East. New York, NY, Oxford University Press. Lloyd, E. 1877. The Succesion Laws of Christian Countries, with special reference to the law of primogeniture as it exists in England. London, Stevens and Haynes. Manson, S. M. 2003. “Validation and Verification of Multi-Agent Systems,” in M. A. Janssen ed., Complexity and Ecosystem Management: The Theory and the Practice of Multi-Agent Systems. Northampton, MA, Edward Elgar, pp. 58-69. Marcus, A. 1989. The Middle East on the Eve of Modernity: Aleppo in the Eighteenth Century. New York, NY, Columbia University Press. Meriwether, M. L. 1999. The Kin Who Count: Family and Society in Ottoman Aleppo, 1770– 1840. Austin, TX, University of Texas Press. Morony, M.G. 1981. “Landholding in Seventh-Century Iraq: Late Sasanian and Early Islamic Patterns,” in A.L. Udovitch ed., The Islamic Middle East: 700-1900. Princeton, NJ, Darwin Press, pp. 177-208. Mundy, M. 1988 “The Family, Inheritance, and Islam: A Re-examination of the Sociology of Far’id Law.” in Aziz Al-Azmeh ed., Islamic Law: Social and Historical Contexts. London: Routledge, pp. 1–123 North, D. C. 1990. Institutions, Institutional Change and Economic Performance. Cambridge, Cambridge University Press. Pomeranz, K. 2000. The Great Divergence : Europe, China, and the Making of the Modern World Economy. Princeton, NJ, Princeton University Press. Powers, D. S. 1986. Studies in the Qur’an and the Hadith: The Formation of the Islamic Law of Inheritance. Berkeley, CA ,University of California Press



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Ray, N. D. 1997. “The Medieval Islamic System of Credit and Banking: Legal and Historical Considerations,” Arab Law Quarterly, 12(1): pp. 43-90 Rodinson, M. 1974. Islam and Capitalism, trans. B. Pearce, New York, NY, Pantheon Books. Rosenberg, N. and Birdzell Jr., L.E. 1986. How the West Grew Rich: The Economic Transformation of the Industrial World. New York, NY, Basic Books. Talbi, M. 1981. “Law and Economy in Ifriqiya (Tunisia) in the Third Islamic Century: Agriculture and the Role of Slaves in the Country’s Economy,” in A. L. Udovitch ed., The Islamic Middle East: 700-1900. Princeton, NJ, Darwin Press, pp. 209-250. Tocqueville, A. 1835. Democracy in America, trans. G. Bevan (2003), London, Penguin Books. Udovitch, A. 1970. Partnership and Profit in Medieval Islam. Princeton, NJ, Princeton University Press Wedgwood, J. 1929. The Economics of Inheritance. London, George Routledge & Sons. Wenner, M. W. 1980. “The Arab/Muslim Presence in Medieval Central Europe,” International Journal of Middle East Studies, 12(1): pp. 59-79 . Wilensky, Uri. 1999. NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. Wong, R. Bin. 1997. China Transformed: Historical Change and the Limits of European Experience. Ithaca, NY, Cornell University Press.

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