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University of Minnesota Law School Legal Studies Research Paper Series Research Paper No. 07-38

Choice of Law and Legal Evolution: Rethinking the Market for Legal Rules Emanuela Carbonara Francesco Parisi This paper can be downloaded without charge from the Social Sciences Research Network Electronic Paper Collection at: http://ssrn.com/abstract=1011376

Choice of law and legal evolution: rethinking the market for legal rules Emanuela Carbonara and Francesco Parisi∗ Public Choice (2009), vol. 139, no. 3, pp. 461-492. Minnesota Legal Studies Research Paper No. 07-38.

Abstract We consider the impact of different choice-of-law regimes on the evolution of formal law. We follow an evolutionary approach to explain possible patterns of legal harmonization and competition. Some of them predict the universal diffusion of a single rule, even though not necessarily efficient. Permissive choice-of-law may lead countries to keep inefficient legal rules and firms to opt out of domestic law, leading to a dichotomy between the rules existing in the books and those utilized in commercial relationships. The emergence of such lex mercatoria may further undermine the legislative incentives to switch to more efficient rules. JEL Codes: K10, K33, D70 Keywords: Choice of Law, Transnational Business Law, Legal Harmonization, Legal Competition, Network Effects.

∗ Emanuela Carbonara: University of Bologna, Department of Economics, email: [email protected]. Francesco Parisi: University of Minnesota, School of Law, and University of Bologna, Department of Economics, email: [email protected]. A previous version of this paper was circulated under the title "Is the Evolution of Legal Systems Always Efficient?". We thank Masahiko Aoki, Giuseppe Dari Mattiacci, Peter Grajzl, Stefano Lombardo, Hans-Bernd Schaefer, Dieter Schmidtchen, Paul Stephan, Georg von Wangenheim, Chenggang Xu, two anonymous referees, and the editors Michael C. Munger and William F. Shughart II for their valuable suggestions and constructive criticisms. We are also grateful to the participants to the CEU Workshop on Comparative Institutional Economics, Budapest, May 2006, the 2006 EALE Conference in Madrid, the 3rd French German Talks in Law and Economics, Kassel, the 2007 ALEA Conference in Harvard and to seminars at ACLE, University of Amsterdam and BETA (CNRS, Université de Nancy 2) for their insightful comments and suggestions.

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Introduction

According to conventional wisdom, competition among legal rules can significantly affect the evolution of law. The literature, both theoretical and empirical, has examined what we could term the "efficiency hypothesis": freedom of choice and competition in the supply of law should favor the evolution and spread of efficient rules. The literature on legal competition has formulated market-for-rules metaphors, where freedom of choice for applicable law leads to an expansion of the “size of the market” for legal rules, as forum shopping and choice-of-law-rules enlarge the set of rules that could be used in any given transaction. In areas where parties have homogeneous preferences, these competitive forces should then lead to the convergence of legal systems, as states should then transplant the rules that are chosen most often (Kobayashi and Ribstein 1997, Mattei 1997, Ogus 1999 and 2002, Romano 2005.) In this paper we use choice-of-law regimes as a proxy for legal competition, as choice-of-law rules design the institutional setting which determines the specific functioning of the market for rules. We study how different choice-of-law rules affect the evolution of substantive law and evaluate their effectiveness in promoting the evolution of efficient law. We show that “victory” in rule competition is often unrelated to strict efficiency, where a rule is (strictly) efficient for a given transaction if it maximizes the parties’ joint payoffs absent third-party externalities. Inefficient rules may persist and even become universally adopted and diffused. We argue that rule competition is characterized by strategic externalities and economies of scale: a rule is more likely to be selected the more widespread it is. The presence of externalities and economies of scale in the choice of legal rules is explained by the existence of legal barriers to trade and transaction costs.1 As a result, the incentives for individuals and firms to choose a rule depends upon the rule’s diffusion as much as on its efficiency. The presence of strategic (network) externalities thus causes a coordination failure. If countries and firms could decide respectively on the rule to transplant and to choose for their contracts simultaneously, they would certainly coordinate on the rule that is intrinsically efficient, since that maximizes welfare for both. Given that they take decisions at different times, when they choose they have to take into account what other countries and firms have done before and they don’t internalize the externality they impose 1

The traditional view was that national borders matter in determining the volume of trade only to the extent to which there are discriminatory policies, geographical distance, or different consumer tastes. Recent empirical literature has challenged this hypothesis, showing that national borders have a substantial negative impact on trade even between countries like Canada and the United States, that have almost completely liberalized trade and are quite homogeneous culturally (Turrini and van Ypersele 2006, and references therein.)

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on those deciding after them. Not only we prove that enhanced rule competition may lead to a situation where inefficient rules win the competition, but competition itself may also lead to a paradoxical situation where all agents choose the efficient rules whereas states adopt inefficient ones. Contrary to what has been suggested in the literature, open choice-of-law regimes may not be sufficient to lead to the “victory” of efficient rules, in the sense that legislators might still adopt inefficient rules in equilibrium. Although such outcome may seem efficient in itself (why should we worry about inefficient rules being written in the books when firms and individuals can opt out of them?), this outcome is shown to be inefficient. In fact, the use of foreign rules and litigation in foreign jurisdictions imply substantial costs for firms. Even if they may not be enough to guarantee “victory” of efficient rules, our model shows that choice-of-law regimes allowing some freedom of choice to economic actors can foster legal unification, at least in practice. Even if states initially keep their original rule, firms have the possibility to act on the market for rules, choosing the one that, given intrinsic efficiency and network effects, yields the highest expected payoff. This behavior can both improve the positive impact of the network effects and lower switching costs, inducing states to change their legal rule. In the process of spontaneous evolution of legal systems, choice of law rules are therefore crucial. Leaving firms free to opt out of domestic law can affect the speed and the cost of the harmonization process, as well as the direction of change and, ultimately, the efficiency of the equilibrium reached. This analysis allows us to discuss the effect of different choice-oflaw regimes and their optimality. Countries with less efficient rules prefer more permissive choice-of-law regimes, whereas countries with efficient rules are indifferent as long as some freedom of choice is left to firms. These results shed some interesting light on the important ongoing debate on the attributes of competitive choice-of-law regimes (Guzman 2002.) The scholarly consensus, reflected by the general trend adopted in practice seems to suggest an intrinsic superiority of a liberal market for legal rules.2 Our results identify some additional institutional conditions that need to be satisfied to ensure the “superiority” of open choice of law regimes. Our paper is also related to the literature making the point that the common law is more efficient than statute law because individuals who do not wish to be bound by a particular (inefficient) rule can in general contract around it (Posner 2003, De Alessi and Staaf 1991). Seen in this framework, our paper should be considered a paper about civil law systems, where everyone is bound by the rule enacted by the legislator and contracting 2

See Reimann (1999) and Ruhl (2006). Also, the Rome II regulation in the process of being approved by the European Commission increases substaintially the freedom of parties to choose the law governing their disputes.

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around inefficiencies is much more difficult in practice. We believe that the results in our paper pertain to both common and civil law. First of all, even if contracting around is allowed, it is likely to bring about substantial transaction costs. If transaction costs outweigh efficiency gains, individuals may stay with the inefficient rule. Secondly, our model shows that network externalities may lead countries to keep inefficient rules even if all agents opt out of them. Finally, in recent years, the ability of parties to contract around inefficient rules has been substantially reduced in common law countries.3 Differently from the literature in the “law and finance” tradition (La Porta et al. 1998), in this paper we are not trying to state the efficiency of any existing legal systems. We take the existence of efficient and inefficient rules as given and investigate their diffusion under different choice-of-law regimes. Finally, this model explains the observed prolonged coexistence of different legal rules. States face switching and adaptation costs when changing their law. These costs can be driven by several factors, including financial, social, cultural, and political factors. The presence of switching costs can delay or possibly prevent legal unification, perpetuating the existence of different legal families.4 In this paper we analyze the effects of rule competition within contract and commercial law. Our model can be extended to all areas of the law that admit ex ante choice of law to the parties involved. This model also would be suitable to analyze the issue of regulatory competition, with its related areas of bankruptcy, securities and antitrust law. The main difference with our setting would be that the choice of incorporation would be unilateral rather than multilateral. In that case too, however, network externalities and legal barriers would play a major role.5 The paper is organized as follows. Section 2 introduces the model. Section 3 analyzes the evolutionary game between countries and firms, characterizing the equilibria. Section 4 considers the effects of different choiceof-law regimes. Section 5 discusses the possibility of strategic adoption of choice-of-law rules by countries. Section 6 concludes. The Appendices contain the proofs of the propositions and some additional technical material. 3

This has happened with the expansion of tort law at the expenses of contract law. The consequence has been the substitution of many of the rules that govern contracts, typically default rules, with mandatory rules. One such example has been the introduction of strict product liability (Epstein 1989, Zywicki 2003). 4 In a recent paper, Carbonara and Parisi (2007) show that the presence of switching costs can hinder the process of legal harmonization. If countries are given the possibility to change their switching costs to facilitate the reduction of legal distance, they might actually choose to increase them thus reaching the paradoxical result that countries engaging in cooperative harmonization (e.g. by treaties) may end up with less harmonization than countries proceeding through unilateral, non-cooperative transplants. 5 Such areas are the ones on which the literature has focused most in recent years (see Guzman 2002, Reinmann 1999, Romano 2005).

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2

The model

We analyze legal competition and harmonization in an evolutionary setting. We have two types of players: countries (legislators) and firms. Countries choose the legal system to adopt domestically.6 Firms choose the rule yielding the highest payoff for their commercial transactions, conditional on the choice-of-law regime in use in their countries of origin. We assume that countries choose legal rules in order to maximize the total welfare of domestic firms.7 Time is continuous and extends from zero to infinity. The world consists of a continuum of countries with mass N . There are two legal rules, A and B. Countries are divided in two groups. The first consists of countries adopting legal rule A and the second is the group of those adopting B. Let n ∈ [0, 1] be the share of countries with rule A, whereas 1 − n is the share of countries with B. Legal rule A is more efficient, i.e., it allows higher gains when applied in transactions. Specifically, we normalize the gross revenue for a firm from a contract written using rule A to 1, whereas a contract stipulated according to B yields ϕ < 1. In each country a given number of economic agents (firms) operate. Countries are symmetric in the number of firms they have, and each country has m ≥ 1 firms. Initially, we assume that all firms are identical. Firms trade both with domestic and foreign partners. Conditional on the existing choice-of-law regime, when trading with foreign partners, firms may be able to choose the legal rules that apply to the contracts regulating their transactions.

2.1

Choice of law regimes

We consider three different choice-of-law regimes: 1) a restrictive regime; 2) a semi-restrictive regime and 3) a liberal regime. In a restrictive regime, firms have no freedom to choose a rule different from the one adopted in their country of origin. As a result of such rule, 6 When applied to firms, the term “domestic” indicates firms with the same legal background. When applied to legal systems, the term “domestic” indicates the legal system that would apply absent an express choice of law by the parties. 7 We are aware that our use of a benevolent lawmaker is at odds with public choice theory, which suggests different objective functions for governments. However, we have chosen this modeling strategy since our goal is to prove that, even in the presence of a benevolent lawmaker, rule competition could lead to the selection of inefficient rules, inducing countries to transplant them. If we had assumed a self-interested or biased planner, this result would have been much easier to obtain. But the assumption would have driven the result, undermining its novelty and significance. Furthermore, the existing literature on rule competition is based on the assumption of a benevolent planner, and we think it methodologically wise to confute the existing results, without departing too drastically from the assumptions used in the existing literature.

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firms basically are not allowed to write contracts using foreign rules and the rule they use plus their probability of trading are determined fully by their country’s legislative decisions. This amounts to the assumption that firms can trade only with other firms that adopt the same legal rules. This regime can approximate a regime based on the lois suppletive test when the rules considered are all mandatory rules.8 In a semi-restrictive regime, the chosen rule has to bear a close relationship with the parties or with the object of their contract. Hence firms with the same legal background have to use their common rules, whereas they can choose a foreign rule if they write contracts with foreign firms. This implies that, when a firm is matched with another firm from the same legal system they use the legal rules they share. Freedom of choice becomes available only when a firm trades with a foreign party. This second regime resembles a regime based on a substantial relationship test.9 Finally, in a liberal regime, firms are free to choose the legal rule they prefer, even when trading with partners within the same legal area. Given a rule yielding higher returns when used in a contract, firms will always try to use that rule. This latter regime is modeled on the basis of a ordre public test.10

2.2

Choice of law — Decisions by firms

When choice-of-law rules allow the use of foreign legal rules, firms can include choice-of-law clauses in their contracts. When firms adopt a foreign rule in their contract, they face a cost λ > 0. This cost represents the likely legal fees necessary to acquire information and expertise on the foreign legal rules.11 By allowing their contracts to be subjected to foreign law firms increase their chances of trading with foreign entities around the world. When a firm that has the expertise to use foreign law interacts with a firm that possesses only domestic legal expertise (either A or B), the rule applied in 8

According to this test, the parties are not allowed to select a governing law which deviates from mandatory provisions of the domestic legal system. According to such a regime, only suppletive rules of the domestic system can be substituted through choice of foreign law (Parisi and Ribstein 1998.) 9 A regime operating through a “substantial relationship test” requires the chosen legal rule to have a relevant connection to the contracting parties or to their legal relationship. Generally this grants much discretion to the courts in validating the contractual choice of law. 10 According to an ordre public test, the parties’ choice of law is validated so long as essential, non-derogable principles of the domestic legal system are not undermined. 11 A key component of the cost of using a foreign rule are the agency costs arising in the relationship between the firm and the legal practitioners advising the firm in the application of foreign legal rules. A moral-hazard problem with hidden information is likely to exist, given that the firm is not able to tell whether the domestic lawyers it relies upon are suggesting the rules actually minimizing the firm’s transaction costs and the firm’s and the lawyer’s objectives typically diverge.

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their contract will be the one used by the latter firm. So, for instance, if a firm familiar with both legal rules trades with a firm using only rule B, their contract will be written using B. On the other hand, the rule chosen when both firms have acquired legal expertise in both systems depends on the applicable choice-of-law regime. In the population of firms there is a probability x that one is able to use rules from A, whereas with probability 1 − x it uses rules from B. This means that a fraction x of firms belonging to countries with legal system A uses rules only from A whereas the remaining 1 − x chooses to bear the cost λ and also to use rules from B. Similarly, a fraction x of firms belonging to countries adopting B undertakes investments that allow them to use also legal rule A.

2.3

The matching process

In order to trade, firms are matched randomly in pairs. For example, a firm from a country adopting A will be matched with another firm from the same legal background with probability n and with a firm from legal system B with probability β(1 − n), where β ∈ (0, 1) . This random matching implies that firms with different legal backgrounds meet less frequently and β represents the relative frequency. This is a non-uniform matching procedure and allows for an immediate definition of a two-region legal environment, where each region may correspond to a specific legal family.12 The parameter β represents an economic loss which firms (hence countries) bear because of the lack of legal harmonization and is therefore a cost of the international differences in legal systems.13 A firm is not matched with any other firm with probability (1 − β)(1 − n). In that case no trade occurs and the loss to the firms and to their countries of origin is equal to the surplus they would have obtained from the contract minus transaction costs. When two firms are matched, trade takes place if and only if they are able to write a contract, i.e., if they agree on common legal rules. Foregone transactions of this type constitute another cost from the lack of harmonization. For example, if a firm from a country with legal system A is matched with a firm from a country with B, they are able to trade if and only if one has invested in legal expertise that allows it to contract using foreign law. A related cost from lack of harmonization is therefore given by λ. The matching process and the rules chosen for the contract are represented in Tables 1 and 2, respectively for the semi-restrictive and for the 12

A similar non-uniform matching process is used in Matsuyama et al. (1993). The parameter β can represent the so called "border effect". This may be due, in a first instance, to higher transaction costs firms with different legal systems face when writing a contract. A second explanation might be that firms have to pay higher legal costs to sue a foreign partner that behaves opportunistically. See Turrini and van Ypersele (2006). 13

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liberal choice-of-law regimes.

2.4

Choice of law — Decisions by countries

Initially, countries have either rule A or B in their legal systems. Define n0 as the proportion of countries adopting regime A at some initial time t = 0 with n0 ≤ 1. Countries adopting a given legal rule may wish to switch to the other regime (e.g., some or all the n0 countries adopting A could switch to regime B and vice-versa). However, switching is costly. We assume that switching costs consist of two parts: a fixed cost c > 0 and a variable cost that is proportional to the percentage of firms that has to learn the transplanted legal rules. The fixed component c represents the direct costs of legal change, such as the legislative costs of adopting new law and the need to adapt the new rules to preexisting legal regimes.14 The variable component is given by learning costs for firms. Variable costs are therefore proportional to the share of firms that has never invested in legal expertise on the foreign legal rule. We assume a linear specification, such that the variable cost becomes sxm for countries switching from A to B and s(1 − x)m for countries switching from B to A. Total switching costs therefore are SCA→B (x) = c + sxm

(1)

for a country transplanting legal rule B. Similarly SCB→A (x) = c + s(1 − x)m

(2)

is the switching cost for a country transplanting legal rule A.

2.5

Payoffs

Payoff functions for firms depend on the choice-of-law rule. In the restrictive regime, no choice of law is allowed to firms. Their payoff is fully determined by the rule adopted by their country of origin π ˆA = n

(3)

π ˆ B = ϕ (1 − n) Payoffs for countries choosing regimes A or B are defined as VˆA = mˆ πA πB VˆB = mˆ 14

(4)

Furthermore, as a consequence of legislative change, jurisprudence becomes obsolete and the creation of new case law is required. Finally, the enactment of a new law raises learning costs for judges and legal practitioners and is likely to create legal uncertainty. The parameter c might also represent the political and social costs of transplantation.

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In the semi-restrictive regime, firms can choose a different rule when contracting with a foreign partner. Payoffs for firms are π AA = n + xβ(1 − n)

(5)

π AB = n + (1 − n)β [x + ϕ(1 − x)] − λ π BA = (1 − n)ϕ + βn − λ

π BB = ϕ [(1 − n) + βn(1 − x)] where π ij is the expected payoff from trade for a firm with legal background i that is also able to write contracts using rules different from its own, j (where i, j = A, B). For example, the expected payoff for a firm with legal background A which acquired expertise in using foreign law B is π AB as given in expression (5). This is because a firm with legal background A has two opportunities to use rule A in a contract: when it is matched with a domestic firm adopting A (with probability n) or when it is matched with a foreign firm (with probability β(1 − n)) that is willing to contract under rule A (with probability x). Notice that firms always prefer flexibility if the cost λ is not too large. As it can be seen, gains (or profit) from either rule depend also on the number of other countries and firms adopting it. These can be interpreted as the (positive) network effects in the adoption of legal rules. Given that a share n of countries adopts A, the expected payoffs from A and B for a firm are, respectively π A = nπ AA + (1 − n)π BA

π B = nπ AB + (1 − n)π BB

(6) (7)

Payoffs for countries, choosing A or B thus become VA = m(xπ AA + (1 − x)π AB )

(8)

VB = m(xπ BA + (1 − x)π BB ) Finally, in the liberal regime, firms can opt out of domestic law and adopt foreign law even when contracting with other domestic firms. Given that rule A always yields a higher revenue, firms will always choose to use rule A when their commercial partners are able to use that rule. This implies that all payoffs in expression (5) remain the same with the only exception of the payoff π BA , which becomes: π ˜ BA = (1 − n)ϕ(1 − x) + (1 − n)x + βn − λ

(9)

The expected payoffs for firms and countries can be determined as before.

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3

Evolution and coexistence of legal rules

In this section the dynamic evolution of rule competition and legal systems is analyzed under the various choice-of-law regimes described above. We will explore this dynamic dimension following an evolutionary approach. We begin by relaxing the assumption of common knowledge. Players learn to play by encountering similar situations repeatedly and looking at the results of their own past choices and of those of other players. When a strategy proves to be more profitable than the one they had previously undertaken, players start adopting the better strategy. This leads the majority of the population gradually to follow the new strategy, changing their past behavior. Therefore, players’ choices follow an adaptive logic that looks at past results and is strongly history and path dependent. A steady state equilibrium is simply a stationary point in this evolutionary, dynamic process. Given the institutional reality and the complexity of decisions in the problem at hand, we believe that this way of modeling legal evolution and competition between legal rules is particularly appropriate. In order to study legal evolution, we assume that countries and firms initially follow a given legal tradition, that they inherited from the past or that they learned from their immediate neighbors (Parisi 2001.) Define n(t) the share of countries that have legal rule A at time t. Similarly, x(t) is the share of firms that can use A in their contracts (i.e.,, firms from countries adopting system A and other firms that acquired expertise in using A in their contracts). Both n(t) and x(t) evolve through time. In particular, we assume that at any moment in time countries observe the payoff obtainable under each legal rule and decide to adopt the regime that yields the higher payoff, given the rules chosen by other countries and the choice of law made by firms in contracts. When a rule yields a higher payoff, the share of players choosing that strategy increases, whereas the share of players selecting a lower-payoff strategy decreases.15 We can now analyze the dynamic evolution for the three choice-of-law regimes introduced above.

3.1

Legal evolution under restrictive choice-of-law

In the restrictive regime, firms don’t have the possibility of choosing rules outside their domestic legal system. The only relevant choice therefore is that undertaken by countries, which will adopt a legal rule based on the payoff function in (4). Thus, only n evolves. A country prefers rule A to B if VA > VB . Given our assumption of symmetric countries, when VA > VB all countries prefer A to B. Countries already adopting A keep it, whereas those following B would like to change 15

This specification follows the evolutionary games literature, where agents choose the action that is the best response to the actions others followed in the past.

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to A. However, changing from B to A implies switching costs SCB→A (x) as given in expression (2). Hence, it can be seen that n˙ > 0 if VˆA − VˆB > SCB→A (x). Substituting the expressions for VˆA and VˆB in equation (4), n˙ > 0 if and only if c + sm ϕ + (10) n> 1 + ϕ m(1 + ϕ) Note that a country switches from B to A when the share of countries adopting A is sufficiently large. The critical mass of countries required to switch increases with ϕ, the payoff that firms obtain when their contracts are subject to the inefficient rule B. Likewise the critical mass increases with switching costs c + sm. Similarly, n˙ < 0 if VˆB − VˆA > SCA→B (x). Then n˙ < 0 if and only if n
VA and VB − VA > SCA→B (x). Solving the latter inequality for n, it can be proven that n˙ < 0 if and only if n < n1SR (x). Conversely, n˙ > 0 if VA > VB and VA − VB > SCB→A (x). Solving inequality VA − VB > SCB→A (x) for n, we obtain that n˙ > 0 if and only if n > n2SR (x), where n1SR (x) and n2SR (x) are obtained in Appendix A and n1SR (x) < n2SR (x). As in the restrictive regime, we also find a “no-move area”, where multiple legal rules coexist. This coexistence will be found when n falls in the interval between n1SR (x) and n2SR (x), i.e., when n1SR (x) ≤ n ≤ n2SR (x) We can thus define the set M SR = {(x, n) : n1SR (x) ≤ n ≤ n2SR (x)} as the “no-move region” in the semi-restrictive regime. The functions n1SR (x) and n2SR (x) represent the boundaries of this region. Whenever the initial ◦ ◦ conditions are such that (x , n ) ∈ M SR then countries initially retain their existing legal rules, even if they recognize that the foreign rule is intrinsically more efficient.16 Firms however can adapt their choice of the legal rule and x evolves through time. This is an important difference with respect to the restrictive regime. In the latter regime, when the initial conditions lie in the no-move area, no action is taken: countries keep the rules they have already adopted, regardless of whether they prefer to change them or not. In the semi-restrictive regime, even if countries are in the no-move region, firms can change the rule they use in their contracts and the variable x evolves through time. In turn, this may lead countries to revisit their nomove choice, possibly adopting foreign rules that previously were regarded unworthy of adoption. As we shall see below, this implies the existence of ◦ ◦ multiple steady states, according to the initial conditions n and x . It also implies that, in the equilibrium, only one rule (either A or B) will be used in transactions, even when such consolidated practice by firms is insufficient to motivate countries to adopt the foreign law. Similarly, x˙ > 0 and the share of firms using rule A increases if and only if π A > π B . Therefore, x˙ > 0 if and only if π A − π B > 0. Writing x˙ = π A − π B , we find that x˙ > 0 if and only if n > nx (x), where the function nx (x) is obtained in Appendix B. We can now characterize the dynamic evolution of n and x in the semirestrictive choice-of-law regime. ◦

◦

Proposition 1 1. If the initial conditions (x , n ) are in the no-move region M SR , then three different situations can occur in equilibrium: 16

◦

Initial conditions are given by the share x of firms using A in contracts and the share n of countries adopting A at time t = 0. We normalize the time scale so that the moment when we start analyzing the dynamic system is labelled t = 0. ◦

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◦

(a) if n > nx (x), then x increases over time and, in the equilibrium, ◦ all firms use rule A. If n < n2SR (x) at x = 1, then countries never leave the no-move region and, in the equilibrium, the share ◦ ◦ of countries adopting A is still equal to n . If n > n2SR (x) at x = 1, then countries leave the no move region, driven by firms, and, in the equilibrium, all countries adopt rule A; ◦

(b) if n < nx (x), then x decreases over time and, in the equilibrium, ◦ all firms use rule B. If n > n1SR (x) at x = 0, then countries ◦ never leave the no-move region and n is the equilibrium share of ◦ countries adopting A. If n < n1SR (x) at x = 0, then countries leave the no-move region and, in the equilibrium, they all adopt rule B; ◦

◦

(c) If n = nx (x ) then no change occurs either in x or in n. All points on the nx (x) function belonging to the no-move region are steady states of the evolutionary dynamics. ◦

◦

2. If the initial conditions (x , n ) lie outside the no-move region M SR ◦ ◦ ◦ ◦ and n > nx (x ), n > n2SR (x ), then in the equilibrium all firms use ◦ ◦ rule A and all countries adopt rule A. If initial conditions (x , n ) are ◦ ◦ ◦ ◦ such that n < nx (x ) and n < n1SR (x ), then the equilibrium all firms use rule B and all countries adopt rule B. Proof. See Appendix B. Define “equilibrium A” as the equilibrium where x∗ = 1 and n∗ = 1, i.e., the equilibrium where all countries adopt rule A and all firms use A in their transactions. Similarly, define “equilibrium B” as the equilibrium where x∗ = 0 and n∗ = 0, i.e., the equilibrium where all countries adopt rule B and all firms use B. The intuition for the results in Proposition 1 can be given as follows. ◦ When the number of countries initially adopting rule A, n , is in the “nomove region”, we know that efficiency gains and network effects are too small relative to switching costs to induce countries to change rules. Countries therefore prefer to bear the costs deriving from lack of harmonization (from β) and those deriving from firms’ expenditures in foreign legal expertise (from λ) rather than trying to harmonize. In part 1 of the proposition, we look at a situation where countries are in the no-move region. This implies that, at least in the early stages of the dynamic adjustment, countries retain their existing laws and the share of countries adopting one rule or the other does not change. Firms, however, are not affected by the countries’ switching costs and continue to update their choice of law in their foreign contracts. ◦ This makes x evolve through time (specifically, x increases if n > nx (x), ◦ whereas it decreases if n < nx (x).) ◦ In part 1.a. it is assumed that n > nx (x), so that, at t = 0, x is ◦ increasing. Given that n is in the no move region, at least in the early 13

stages of the dynamic adjustment, n does not change, notwithstanding the increasing popularity of foreign law among firms, as shown by the evolution of x. This may lead to two alternative outcomes. In the first case, switching costs are so high that the trajectory of x, ◦ which follows a straight line parallel to the horizontal axis at n = n , never crosses n2SR (x).17 Then the trajectory of x never leaves the no-move region and the dynamic adjustment reaches an equilibrium where all firms adopt the efficient rule A whereas countries keep the rule they had at t = 0. Here competition leads to the selection of the efficient rule by firms but not by countries. However, in order to use A, firms from B will have to bear the cost λ and countries will bear the cost from lack of harmonization, β. In the second case, switching costs are lower. The function n2SR (x) is ◦ now closer to nx (x) and the trajectory of x, moving eastward at n = n , crosses n2SR (x), leaving the no-move region. The variables x and n are now in an area where n > nx (x) and n ≥ n2SR (x) and both increase until x = n = 1. After the initial period, the increasing popularity of foreign law among firms, shown by the evolution of x, leads countries to revisit their no-move choice. Equilibrium A is reached. Here competition leads to the selection of the efficient rule by both firms and countries. This outcome occurs because of the lower switching costs: as x increases, the total cost stemming from the use of the foreign rule A (which is equal to mxλ for each B country) becomes higher than the switching cost and B countries change to legal rule A. Part 1.b. of the proposition considers the mirror-image case of part 1.a. ◦ Here, n < nx (x), so that, at t = 0, x is decreasing. Again, there are two possible outcomes: one where high switching costs prevent the trajectory of x from leaving the no-move region, and the other where lower switching costs allow the trajectory of x to cross the function n1SR (x) and x and n leave the no-move region. In the first outcome, all firms choose the inefficient rule B whereas countries keep their initial rule. In the second outcome, equilibrium B is reached. Here competition leads to the selection of the inefficient rule B by all firms and all countries. As with the restrictive choiceof-law regime, it is thus possible that the inefficient rule becomes universally adopted and diffused. The difference with respect to the restrictive regime is that now this result is reached notwithstanding rule competition. Similarly, rule competition in the absence of legal change by countries can lead to a situation where all firms choose the inefficient rule B. To understand the rationale for this result, one has to consider that in part 1.b. the assumption ◦ ◦ is n < nx (x ) : the share of countries adopting A is relatively low. Moreover firms face a high probability of being matched with commercial partners 17

By inspection, from the expressions for n1R (x) and n2R (x) in Appendix A, it is immediate to see that the function n1R (x) moves downwards when c and s increase, whereas n2R (x) moves upwards.

14

from B and thus even firms that operate in jurisdictions that adopt the efficient rule A are willing to bear the cost of legal expertise λ to use foreign rule B. This drives the system either towards an equilibrium where x = 0 ◦ and n = n (when switching costs are high) or towards equilibrium B (if switching costs are low). ◦ ◦ In part 1.c. it is assumed that n = nx (x ). This implies that firms are indifferent between choosing rule A and B for their contracts and x ◦ ◦ does not change. Given that we are considering points (x , n ) in the nomove region, neither x nor n evolves. By definition, all points belonging to the portion of the function nx (x) included in the no-move region present the ◦ ◦ property n = nx (x ) hence being potential steady states of the evolutionary dynamics.18 Part 2 of Proposition 1 considers all cases where initial conditions lie ◦ ◦ outside the no-move region. When (x , n ) are both high enough, countries ◦ ◦ and firms converge to equilibrium A. Conversely, when (x , n ) are low, countries and firms prefer rule B and they both converge to equilibrium B. Given that we are out of the no-move region, by definition network effects are more salient than switching costs. The results in Proposition 1 are depicted in Fig. 1, where a1 and a2 represent the trajectories discussed in part 1.a. As we can see, a1 lies always in the no-move region, whereas a2 starts in the no-move region, then crossing n2SR (x) and ending up at equilibrium A. The trajectories b1 and b2 are relative to part 1.b. The function nx (x) lies between n1SR (x) and n2SR (x) ◦ ◦ and consists of all steady states such that n = nx (x ). Finally, trajectory c and d are relative to part 2 of Proposition 1.

3.3

Legal evolution under liberal choice-of-law

Liberal choice of law regimes allow firms to opt out of domestic law and choose foreign rules for their contracts. Under liberal choice-of-law regimes, firms are able to choose the legal rule independently of the nationality of their commercial counterpart. In this choice-of-law regime, firms that have both domestic and foreign legal expertise would write contracts using the efficient rule, given that the latter yields higher payoffs. Again, n˙ < 0 if VB − VA > SCA→B (x). Solving this inequality for n, it is possible to see that n˙ < 0 if and only if n < n1L (x). Conversely, n˙ > 0 if VA − VB > SCB→A (x). The last inequality can be solved for n, obtaining that n˙ > 0 if and only if n > n2L (x), where the expressions for n1L (x) and n2L (x) can be found in Appendix A and n1L (x) < n2L (x). Change of rules at the country level occurs if and only if n is outside the “no-move” area. As in the more restrictive regimes discussed above, it can happen that a country 18

It should be noted, however, that these are extremely unstable steady states. Any shock moving the system away will lead to a different equilibrium.

15

retains its original legal rule even if it recognizes the intrinsic superiority of a rule from a foreign legal system. The no-move area in the liberal regime is defined as the set M L = ◦ ◦ {(x, n) : n1L (x) ≤ n ≤ n2L (x)}. When the initial conditions (x , n ) lie in M L , countries keep their original rules but firms can opt out of their domestic law when drafting their contracts. Hence the variable x evolves. Again, the dynamic system exhibits multiple steady states. ˜ A − π B and As before, x˙ > 0 if and only if π ˜ A > π B . Writing x˙ = π solving it for n, we obtain that x˙ > 0 if and only if n > nxL (x), where the function nxL (x) is obtained in Appendix C. We can now characterize the evolutionary dynamics in the liberal choiceof-law regime. ◦

◦

Proposition 2 1. If the initial conditions (x , n ) are in the no-move region M L , then ◦

(a) if n > nxL (x), then x increases over time and, in the equilibrium, ◦ all firms use rule A. If n < n2L (x) at x = 1, then countries never leave the no-move region and, in the equilibrium, the share ◦ ◦ of countries adopting A is still equal to n . If n > n2L (x) at x = 1, then the dynamic adjustment drives x and n out of M L and equilibrium A is reached in the long run; ◦

(b) If n < nxL (x) then x decreases over time. In the equilibrium, all ◦ firms use rule B. If, in addition, n > n1L (x) at x = 0, countries ◦ ◦ never leave the no-move region and n∗ = n . If n < n1L (x) at x = 0 then the dynamic adjustment drives x and n out of M L and equilibrium B is reached in the long run; ◦

◦

◦

◦

(c) If n = nxL (x ) then, in the equilibrium, x∗ = x and n∗ = n . All points on the nxL (x) function belonging to M L are steady states of the evolutionary dynamics. ◦

◦

2. If the initial conditions (x , n ) lie outside the no-move region M L , then ◦

◦

◦

◦

(a) If n > nxL (x ) then x increases over time. If and n > n2L (x ), ◦ ◦ then equilibrium A is reached in the long run. If n < nx (x ) and ◦ ◦ n < n1L (x ), then equilibrium B is reached in the long run; ◦

◦

(b) If β +λ < 1, λ+ϕ < 1 and initial conditions (x , n ) are such that ◦ ◦ ◦ ◦ n > nxL (x ) and n < n1L (x ), then x increases and n decreases over time. In the equilibrium, all firms use rule A whereas all countries adopt rule B. Proof. See Appendix C.

16

The results in Proposition 2 follow a logic similar to that of the results in Proposition 1. Case (b) in Part 2, however, needs further characterization. Define “equilibrium D” as the equilibrium where x∗ = 1 and n∗ = 0. In this equilibrium countries and firms converge to different rules: all countries adopt B, whereas all firms use A in transactions. When λ + ϕ < 1 and β + ϕ < 1, the dynamic adjustment admits three steady states out of the no-move region: A, B and D. In all these steady states, countries harmonize their legal systems. Steady state D is quite interesting: in that steady state, all countries harmonize by adopting the inefficient rule B. All firms however opt out of domestic law and adopt the efficient rule, A, in their contracts. Intuitively, when β + λ < 1 and φ + λ < 1, we are in a situation where the parameters λ, β and ϕ are relatively low. When the cost of legal expertise, λ, is low, countries are not overly concerned about firms’ choice-of-law expenditures. In this case, firms have an especially high incentive to learn A, and to be prepared to opt out of the inefficient domestic law by adopting foreign law (the gains ϕ obtainable by contracting with rule B are low). On the other hand, a low β implies that the costs from lack of harmonization and missing trade opportunities are substantial. The initial conditions that guarantee that ◦ equilibrium D is the steady state are such that n is quite small. Hence network externalities, coupled with the strong incentives for firms to solve inefficiencies by themselves at a reasonable cost, induce countries to adopt rule B already used by the majority of other countries.19 In this case, we might say that the market outperforms the state, meaning that the market is able to select the efficient rule, in the shadow of what countries do. Equilibrium D exists only in the liberal choice-of-law regime. As Figure 2 shows, it is reached when the initial conditions of the dynamic system consist of a relatively high share of firms already adopting A in transactions (high x) and the majority of countries adopt rule B (trajectory c1 ). Equilibrium D might thus look as an efficient solution, especially if the equilibrium induced by alternative choice-of-law regimes is one where B is universally adopted by countries and universally used by all firms. However, in equilibrium D firms have to bear the cost of foreign legal expertise λ to use A, even if the harmonization of legal systems has eliminated the cost β. The efficiency of equilibrium D should be evaluated against the possibility that alternative choice-of-law rules might lead to equilibrium A. These results raise some interesting questions regarding the superiority of permissive choice-of-law regimes. In the following section, we will explore 19 Abusing terminology, we might say that rule A has become "lex mercatoria" or "soft law": a rule that is used in commercial practice although it is not formally enacted in any country. It should be noted that in some situations commercial practice may be judicially enforced as customary law. These cases of adjudication of commercial practice fall outside the scope of our work.

17

the implications of our findings with respect to legislative policy and the effects of alternative choice-of-law regimes in the evolution of formal law and commercial practice.

4

The effects of choice of law on substantive law and commercial practice

Ideally, an optimal choice of law regime is one that minimizes the costs of reduced international trade, favoring the selection of efficient legal rules and commercial practices, leading to (efficient) steady states at least cost. In this section we discuss our results in light of these normative objectives. We investigate whether choice-of-law regimes allowing more freedom to economic agents have better chances of achieving these goals and whether efficient rules are more likely to “win the competition” under liberal choiceof-law regimes. The answers we are going to find run somewhat against the conventional wisdom in the choice of law literature. Competition triggered by liberal choice of law regimes is not always the best instrument for curing legal inefficiencies. Sometimes restrictive regime outperform less restrictive regimes either in terms of speed of convergence to efficient steady states or in terms of welfare levels in both transition and steady state periods. It can in fact happen that more liberal choice-of-law regimes lead to less desirable equilibria, where inefficient rules are either used in transactions or adopted by countries more often than efficient rules. In this section we will elaborate on this point with the aid of three examples. In the first example, we consider a case where the restrictive regime leads to higher levels of overall welfare than more liberal choice-oflaw regimes. Specifically, under the restrictive regime, rule A is adopted by a larger number of countries than in more liberal regimes. These results run against the conventional wisdom in the literature. In the second example, we observe results that are instead consistent with the conventional wisdom. In this case, the liberal regime is the one maximizing overall welfare, whereas other, more restrictive regimes would lead to the less desirable outcome, B. Finally, in the third example, we present an interesting case where the restrictive regime leads to the worst outcome, the liberal regime leads to an outcome where many countries adopt rule B but all firms use A in their transactions. We use these examples to consider the initial conditions and the values of the parameters that determine the outcome under each choice-of-law regime, in order to draw general conclusions and policy recommendations.

18

4.1

Case I. Restrictive choice-of-law regimes as triggers of efficiency

In the first example, we assume that the parameters β and λ are both high, so that equilibrium D never exists under liberal choice-of-law regimes. Specifically, we assume β + λ > 1 and λ + ϕ > 1. Initial conditions lie in the region labelled H in Figure 3.20 In region H all points are outside the no-move regions of all three regimes. Region H is above the no-move region of the restrictive regime. As we know from Section 4.1, whenever n is above the no-move region, a restrictive choice-of-law regime leads to equilibrium A. When the chosen regime is semi restrictive, all points in region H lead to equilibrium B, since region H is below the lines nx (x) and n1SR (x), implying that both x and n decrease through time. A similar situation occurs in the liberal regime, where equilibrium B is also reached. The intuition for this result can be given as follows. In this example, the initial value of x is relatively low. With more liberal regimes, most firms contract using rule B and have little incentive to change to A. Thus countries would gain little if they switched to A. In restrictive regimes, countries’ choices are not at all affected by firms’ behavior, since firms have no possibility of choosing legal rules. Figure 4a plots total welfare through time (where the subscripts R, SR and L stand for “restrictive,” “semi-restrictive” and “liberal” respectively). In the case under consideration total welfare is always higher in the restrictive regime. Legal systems converge towards the efficient equilibrium and more and more transactions are made using the efficient rule. Figure 4b shows that more firms use A in a liberal than in a semirestrictive regime. Firms have greater opportunity to take advantage of the efficient rule, since liberal regimes also allow them to use foreign law in contracts with domestic partners. This is reflected in Figure 4b, where x eventually goes to zero in both semi-restrictive and liberal regimes but xSR is slightly lower than xL : in the liberal regime, firms are more reluctant to abandon A. Interestingly, given that firms are slower to abandon A, in a liberal regime countries converge faster to B (see Figure 4c). Countries can take advantage of network effects (the large number of other countries already adopting B) thus eliminating the costs from the absence of harmonization (due to β), while at the same time trusting that firms will continue to follow efficient commercial practices by adopting A in their contracts. The losses that countries create by adopting less efficient rules will be mitigated by the firms’ free choice of law.21 20

Figure 3 (like other figures pertaining to this first example), are obtained using simulation techniques. Parameter values are β = 0.65, ϕ = 0.45, λ = 0.6, m = 1, N = 10. ◦ ◦ Initial conditions are x = 0.15; n = 0.5. 21 Note that this is the same logic that we used to explain equilibrium D.

19

We continue to consider a second example where switching costs are very high. As a result of high switching costs, the no-move region in all regimes is very wide (see Figure 5a). The initial conditions lie in the no-move region and the dynamic system remains in the no-move region for all choice-of-law regimes. However, initial conditions are such that the share of countries initially adopting A is relatively high (n0 = 0.4), whereas the share of firms using A is low (x0 = 0.2). This implies that where choice of law is allowed, all firms end up using rule B. Figure 5b shows that final total welfare is higher under the restrictive regime, since this regime preserves some use of the efficient rule A. However, high switching costs imply the coexistence of multiple legal rules with different levels of efficiency.

4.2

Case II. The virtues of liberal choice-of-law regimes

In the second example we use the same parameter values used for Case I in the first example (low switching costs). We now take initial conditions lying close to the left boundary of region F in Figure 3, which is outside all no-move regions. All points in F are below nx (x) and nx2L (x), but are above n2SR (x) and n2L (x).This implies that in both semi-restrictive and liberal regimes x˙ < 0 and n˙ > 0. The issue now is whether the trajectories originating from F bend towards equilibrium B or whether they bend toward A. Analytically, we can have both types of behavior. However, when the initial conditions are closer to the left boundary of region F (i.e., with lower values of x) it is more likely that a trajectory bends towards B. Moreover, for any given point (x, n) in F, it is more likely that the trajectory bends towards B if we are in a semi-restrictive regime than in a liberal regime. To see why, recall that, as in Case I, we are assuming large values of λ (β + λ > 1, λ + φ > 1). In region F the share x is always very high, so that a large number of firms uses A at the initial conditions. In a liberal choice-of-law regime more contracts are written using A than in a semirestrictive regime. This gives a strong incentive to firms in B to bear the (high) cost λ to take advantage of the efficient rule A. Thus liberal choiceof-law regimes make it especially attractive for countries to adopt A, as it helps them reduce the impact of cost λ. On the contrary, in semi-restrictive choice-of law-regimes, the impact of network effects (due to the very low n in region F ) might dominate the efficiency gains and drive countries towards B. Figure 6 presents this case.22 In Figure 6a we can see that in a liberal choice-of-law regime, both x and n increase through time and converge to A, whereas the other two regimes converge to B (the initial condition lies underneath the no-move region for the restrictive regime). Interestingly, 22

The simulations run to obtain Figure 5 use β = 0.65, ϕ = 0, 45, λ = 0.6, m = 1, ◦ ◦ N = 10, as in Figure 4. Initial conditions are however different: x = 0.78; n = 0.1.

20

in the semi-restrictive regime, the dynamic system initially lies outside the no-move region. As n increases and x decreases switching costs become larger and larger (switching costs from B to A are proportional to 1 − x). This implies that the no-move region will be reached at some stage, where the benefits from legal change are not large enough to outweigh switching costs. Once in the no-move region, however, firms continue to introduce choice-of-law clauses in their contracts and the fraction x of firms using A keeps on decreasing. This stage is depicted by the straight trajectory between n1SR (x) and n2SR (x) in Figure 6a. The firm’s initiative thus leads the system out of the no move region and then towards equilibrium B. Figure 6b depicts total welfare through time. The liberal regime, while allowing the highest total welfare in equilibrium, initially yields lower levels of welfare than the restrictive regime. This is because n is initially very low and many firms from jurisdictions that adopt B use A in their contracts. The efficiency gains from using A in a relatively larger number of transactions do not compensate for the costs necessary to acquire legal expertise in using A. As the number of A countries increases through time in liberal regimes, the situation is reversed and total welfare becomes higher than in more restrictive regimes. Semi-restrictive regimes yield a welfare level that is always lower than that of restrictive regimes. This happens for the same reasons discussed above: the high costs necessary to acquire foreign legal expertise (high λ) exceed the efficiency gains of a more frequent use of A. Such costs, coupled with the very low and decreasing probability that firms are able to use the efficient rule keeps welfare lower than in the restrictive regime.23 In this example, common wisdom is restored and the liberal regime dominates the other two regimes in the long run. In the short run, however, less competitive regimes yield higher welfare levels. So far we have assumed that the choice-of-law regime is exogenously given. Let us assume now that a country has to choose a regime at time t = 0. Figure 6b shows that introducing a liberal choice-of-law regime under initial conditions like those used in this example creates a trade-off between present and future welfare. This implies that future generations will enjoy a global welfare higher than that available to present generations. Legislators with high discount rates who are willing to protect present generations (and voters) may thus prefer a restrictive regime. A last question remains as to whether there exists initial conditions that would lead semi-restrictive regimes to steady state A and liberal regimes to steady state B. This brings to mind the previous discussion about the possibility that trajectories originating from a given point (x, n) bend towards A in the semi-restrictive regime while bending towards B in the liberal regime. 23

This result changes if we slightly increase the initial value of x (taking, for instance, x = 0.85) so that also the semi-restrictive regime leads to equilibrium A. ◦

21

The answer to this question would need a complex mathematical analysis. Simulations have proven that this never happens. We can provide a brief intuition for this conclusion. For any given n, in liberal regimes a higher share of firms uses A. At any given x, the incentives for a country with legal rule B to switch to A are therefore higher in a liberal regime. It follows that it can never be the case that a country chooses not to adopt A (or to switch from A to B) in the liberal regime while choosing A in the semi-restrictive regime.

4.3

Case III: Efficient commercial practices in the shadow of inefficient law

In this last example we assume that β + λ < 1 and ϕ + λ < 1. From Proposition 2, we know that in liberal choice-of-law regimes equilibrium D exists under these parameter values. We choose initial conditions that lead the system to equilibrium B in the restrictive regime, to equilibrium A in the semi-restrictive and to D in the liberal regime. Given the parameter configuration used in this example,24 such outcome is reached with x0 = 0.8 and n0 = 0.22. Initial conditions lie underneath the no-move region for the restrictive and the liberal regimes and above the no-move region of the semi-restrictive regime. Moreover, it lies above nx (x) and nx2L (x), which makes sure that x increases in both regimes allowing competition. The share x converges to 1 in both the semi-restrictive and liberal regimes (see Figure 7a). The speed of convergence is faster in liberal regimes, because a larger number of firms is allowed to use A in this regime. All firms end up using B in the restrictive regime, as they cannot choose a different rule. Similarly, n reaches 1 in the semi-restrictive regime, as equilibrium A is the steady state of the evolutionary dynamics. In both the restrictive and liberal regimes n approaches 0, since all countries adopt B. The restrictive regime always yields the lowest welfare, whereas we can observe a trade-off between the semi-restrictive and the liberal regime (see Figure 7b). The liberal regime yields a higher payoff in the early stages of the evolutionary process: given the share of countries adopting B, the liberal regime allows more firms to use the efficient rule A. However, as the number of countries adopting A increases in the semi-restrictive regime and decreases in the liberal regime, the semi-restrictive regimes become relatively more efficient over time. Notwithstanding the faster growth of xL , in liberal regimes firms have to bear the cost λ in order to use A, and the final payoff will be lower than in semi-restrictive regimes. 24

Parameter values in this simulation are: β = 0.4, ϕ = 0.5, λ = 0.1.

22

4.4

Can legislators outperform the market?

The three examples considered above illustrate the general results derived in Section 3: the outcome obtainable under alternative choice-of-law regimes depends crucially on the institutional and legal framework in which the global market operates at the time when a given choice-of-law regime is introduced. This could be the reason why countries have changed choice-of-law regimes through time, adapting their level of receptiveness of foreign law to changing conditions.25 It could also explain why different choice-of-law regimes exist through time in different localities. So far we have assumed that countries are symmetric, except for the substantive law they initially adopt. Therefore, they all prefer the same choice-of-law regime, according to values of ◦ ◦ the parameters and to the initial conditions (x , n ). In the Section 5, we relax this assumption and try to analyze the strategic choice of choice-of-law regimes by asymmetric countries that commerce in a global market.

5

Choosing choice-of-law rules

In this section we analyze the possibility that choice-of-law regimes may be strategically chosen by asymmetric countries.26 At a given time t, normalized to t = 0, countries can select a specific choice-of-law regime among those considered in the previous sections: restrictive, semi-restrictive and liberal. Countries can be asymmetric in the number of firms and in the legal rules initially adopted. In the analysis presented above we have seen that, given any choice-oflaw regime followed by B countries, the evolutionary path will be the same regardless of whether A countries adopt semi-restrictive or liberal regimes. For instance, for any given regime followed by B countries, the welfare of A countries will be the same no matter whether they follow a semi-restrictive or liberal regime. This is because, as seen in Section 2.5, the payoff functions for A countries are the same under the two regimes, so that the dynamic adjustment of x is entirely determined by the choice of B countries. From the payoff functions in Section 2.5 it is possible to see that countries adopting less efficient rules obtain a higher payoff when adopting liberal choice-of-law regimes. We can thus expect that countries with rule B at time t = 0 will adopt a liberal choice-of-law regime. Conversely, countries that initially adopt the efficient legal rule A will have no incentive no change their choice-of-law regimes and the regime that they follow will ultimately 25

The change in conditions could be seen as a structural break that modifies the values of the parameters at a time tˆ, where x(tˆ), n(tˆ) become the initial conditions in the system that ensues after the structural break itself. 26 To simplify the analysis, in this section too we are going to assume that switching costs are zero.

23

be determined by history. For instance, assume that a certain group of legal systems (e.g., European countries with a Romanistic legal tradition) has adopted efficient substantive law and used it in a large number of international transactions. Assume further that, for historical reasons, those countries followed a semi-restrictive choice-of-law regime. At some point, imagine a structural break: the superiority of the older legal systems is breached by a different legal family (e.g., Anglo-American systems) that is able to enact new laws that more efficiently respond to the changing needs of international commerce. These new systems are gradually recognized as more efficient: they become the “efficient rule” A. Given this structural break in substantive law, it would then be optimal for European systems to respond, changing their choice-of-law regimes, allowing greater freedom for domestic firms to adopt the new foreign rule in their contracts. The rising percentage x of firms that adopts the new efficient rule in the global market might boost the rate of transplantation of the new rule in legal systems that adopted the older, less efficient rule. Assume now that in a subsequent time period the older legal systems regain their efficiency primacy (in our example, imagine the case where European countries enact a new rule that improves upon the Anglo-American rule). The countries that regained their efficiency primacy (in our example, European countries) may have no incentive to change their choice-of-law regime again. A liberal choice-of-law regime might survive in spite of the supremacy of those systems, furthering the evolution of efficient substantive law. The interesting result is that rule competition is not something advocated by efficient legal regimes and resisted by inefficient ones. On the contrary, liberal choice-of-law regimes and rule competition may be chosen by legal regimes with less efficient substantive law.27 So far we have compared semi-restrictive and liberal choice-of-law regimes. Undoubtedly, such regimes are the most common nowadays and historically we have witnessed a growing openness of legal systems to rule competition (Reimann 1999.) It would be interesting to see whether it is strategically optimal for either A or B countries to adopt a restrictive regime, and to examine what would be the best response by the other group of countries in the face of such choice. The analysis presented in Sections 3 and 4 can provide some guidance in answering this question. Consider the case where B countries follow a restrictive choice-of-law regime. The adoption of a restrictive choice-of-law regime operates like a precommitment strategy that renders B countries’ “threat” of not using rule A credible. If initial conditions are such that they assure convergence to B anyway, then the strategic adoption of a restrictive choice of law regime may be optimal: it would in fact lead to a faster convergence towards the steady 27

This result holds also in the presence of switching costs, especially when such costs are decreasing in the percentage of domestic firms acquiring foreign legal expertise.

24

state, eliminating costs from foreign legal expertise and lack of legal harmonization. However, this leads to the universal adoption of an intrinsically inefficient rule. Conversely, if initial conditions are such that equilibrium A is reached absent B 0 s precommitment, clearly B 0 s choice of following a restrictive regime is highly inefficient.

6

Conclusions

In this paper we have studied the process of convergence of substantive law in the presence of legal competition through choice of law. We considered different choice-of-law regimes: in the first regime, which we have labeled restrictive, firms are bound to use domestic law in all their contracts; in the second regime, which we have labeled semi-restrictive, firms are allowed to use foreign law when entering into contracts with a foreign party; in the third regime, which we have labeled liberal, firms are allowed to opt out of domestic law and to use foreign law in both domestic and foreign contracts. The restrictive and the semi-restrictive choice-of-law regimes share the same type of steady states. In fact, in both regimes, two steady states are possible. In both steady states we observed convergence between legal systems and commercial practice: a unique rule is adopted by all countries and only that rule is used by all firms (universal diffusion). In such cases the final equilibrium is one of legal uniformity. The main difference between these two regimes is that the semi-restrictive one allows firms to opt out of domestic law when trading with foreign partners. Therefore, the actual use of legal rules is not entirely determined by the choice of rule by countries, as in the restrictive regime. With semi-restrictive regimes we observed that in the equilibrium, only one rule will be used in commercial practice, regardless of the rule initially used by their country of origin and subsequently adopted by legal systems. The ability of firms to opt out of domestic law introduces an important feature in less restrictive regimes vis-à-vis more restrictive ones. In more restrictive regimes, when switching costs are high, countries keep their original legal rules, and firms are bound to use those rules, with possible constraints on their ability to engage in international commerce. In less restrictive choice-of-law regimes, firms exercise choice of law. This, in turn, affects countries’ switching costs, changing their incentives to adopt foreign rules through time. We might thus observe situations in which a semi-restrictive regime could lead to uniformity, at least in commercial practice if not in the law formally adopted, whereas in a restrictive regime high switching costs would prevent such legal uniformity. However, legal convergence occurs, but not necessarily towards more efficient rules. When the initial diffusion of the efficient rule is low we might observe convergence towards an ineffi-

25

cient rule. Countries minimize lack-of-harmonization costs by adopting the legal system most common worldwide. In liberal choice-of-law regimes, firms are given the opportunity to correct these legal inefficiencies through contractual choice of law. In liberal regimes, we therefore observe a third possible steady state, where all firms choose the efficient rule even in the face of the countries’ uniform adoption of inefficient legal rules. The contractual solution to countries’ inefficient legal rules is not however without limits and costs. Transaction costs create two possible losses. First, transaction costs could be so high as to prevent firms from effectively contracting around inefficient legal rules. Second, when transaction costs do not impede renegotiation, they nevertheless force firms to incur costs.28 In such case, the evolutionarily stable equilibrium is only second-best efficient, since it forces firms to incur positive transaction costs in order to escape inefficient local rules. A coordinated move from such equilibrium to a situation where all countries adopt the efficient rule could enhance the welfare of all countries. Such coordinated solutions would however necessitate the negotiation and signing of international treaties with the likely emergence of the strategic implementation problems considered by Carbonara and Parisi (2007). The outcome of alternative choice-of-law regimes is strictly dependent on the institutional and legal framework in which the global market operates and the coexistence of different regimes in different localities can thus be explained by changes in the framework in which countries and their commercial partners operate. From the point of view of policy prescriptions, in general it is true that the market leads to the selection of efficient rules in a higher number of cases than the state. Also, open choice-of-law regimes are more suited to overcome the barriers imposed by switching costs and to destabilize countries’ inefficient legal rules. In this respect we can say that the market outperforms the state in the selection of rules. It is important to note that, although our findings indicate that more liberal regimes are preferable and yield a higher overall welfare, the degree of openness has to be calibrated carefully. When barriers to trade due to the lack of legal harmonization are substantial and the costs to firms of using foreign rules are low, excessively liberal regimes do not guarantee efficiency and a semi-restrictive regime might be preferable. An interesting corollary of our analysis is that more permissive choiceof-law regimes are preferred by countries with less efficient legal systems. Liberal regimes should then be adopted by countries with inefficient legal systems facing high switching costs. The adoption of liberal regimes by countries with inefficient substantive law would also be to the benefit of countries with efficient legal rules that would otherwise attempt to reduce 28

These are the same costs that would affect firms had they always the possibility to contract around inefficient rules. A world without mandatory rules would therefore have the same equilibria of a world with liberal choice-of-law and an equilibrium with inefficient rules would still be possible.

26

barriers to trade by fostering legal unification and adopting the inefficient foreign rules into their systems. Further extensions should consider alternative objective functions. For example, countries could compete in the creation of efficient rules to attract foreign investments. An implicit assumption in our model is that firms cannot change their nationality. When firms’ mobility is taken into consideration, countries could face a new set of incentives. Given that in our model the degree of efficiency of a rule is endogenous, our framework could be extended to provide new insights to the "race-to-the-top" versus "raceto-the-bottom" debate regarding freedom of incorporation and the related incentives for lawmakers. Future research should also consider the impact of alternative choice-of-law regimes in other areas of law, like tort law. The proposed Rome II Convention on the Regulation on the law applicable to non-contractual obligations is trying to create a harmonized set of choiceof-law rules within the European Union for disputes about torts and other non-contractual obligations. Although the proposed regulation is still in the workings by the European Parliament, the latest drafts seem to go in the direction of a “liberal” choice-of-law regime, where parties to a dispute can choose the law from a third country within the European Union. Also in other situations, lawmakers worldwide seem to be moving towards more and more permissive choice-of-law regimes. The analysis of the effects of alternative choice-of-law regimes in areas different from contracts, commercial law and regulation would be extremely important in evaluating these recent trends and legislative proposals.

A A.1

The boundaries of the no-move regions in the semi-restrictive and liberal regimes Semi-restrictive regime

We know that, n˙ < 0 if VB − VA > SCA→B (x). The last condition can be rewritten, using equation (8), as n˙ < 0 ⇔ n < n1SR (x)

(13)

where ¤ £ ¯ (2λ + β(1 − 2φ)) − (c + sxm) m λ + φ(1 − β) − x ¯2 βφ − x n1SR (x) = m(1 + φ(1 − 2β) − 2xβ(1 − 2φ) + 2x2 βφ) (14) Conversely, n˙ > 0 if VA − VB > SCB→A (x). Substituting the values for VA and VB from (8) and solving VA − VB = SCB→A (x) with respect to n, obtain

27

¤ £ ¯ (2λ + β(1 − 2φ)) + c + s(1 − x)m m λ + φ(1 − β) − x ¯2 βφ − x n2SR (x) = m(1 + φ(1 − 2β) − 2xβ(1 − 2φ) + 2x2 βφ) (15) and (16) n˙ < 0 ⇔ n < n1SR (x)

A.2

Liberal regime

Using the same procedure followed above, obtain ¤ £ m λ + ϕ(1 − β) − x(2λ + β(1 − 2ϕ)) + x2 (1 − ϕ(1 − β)) − (c + sxm) . n1L (x) = m [1 − 2xβ(1 − 2ϕ) + (1 − 2β)ϕ + x2 (1 − φ(1 − 2β))] (17) ¤ £ m λ + ϕ(1 − β) − x(2λ + β(1 − 2ϕ)) + x2 (1 − ϕ(1 − β)) + c + s(1 − x)m n2L (x) = m [1 − 2xβ(1 − 2ϕ) + (1 − 2β)ϕ + x2 (1 − φ(1 − 2β))] (18)

B

Proof of Proposition 1

First of all we need to establish the following result. x

Lemma 1 There exists a function nx (x) with 0 < nx (x) < 1 and dndx(x) < 0 ∀x ∈ [0, 1] , such that x˙ R 0 if and only if n R nx (x); the function nx (x) is 2ϕ−1 not defined at x = 2ϕ−1 ˙ = sign[λ(2n − 1)]. 2ϕ . If x = 2ϕ , then sign[x] Proof. Using the expressions for the payoffs for countries given in (6) and (7) write x˙ = π A − π B as x˙ = n[2λ + β(1 − 2ϕ(1 − x))] − n2 β[1 − 2ϕ(1 − x)] − λ

(19)

Solving expression (19) with respect to n, it can be seen that x˙ = 0 if

n = n+ = n = n− =

q 2λ + β (1 − 2ϕ (1 − x)) + 4λ2 + β 2 (1 − 2ϕ (1 − x))2

(20)

2β (1 − 2ϕ (1 − x)) q 2λ + β (1 − 2ϕ (1 − x)) − 4λ2 + β 2 (1 − 2ϕ (1 − x))2 2β (1 − 2ϕ (1 − x))

It can be checked that either n+ < 0 or n+ > 1 for all values of x ∈ [0, 1] and of the parameters β, ϕ and λ and that 0 < n− < 1 always. Given that 28

n+ lies outside the admissible range for n, we set nx (x) = n− . Then, x˙ > 0 iff n > nx (x). x To prove that dndx(x) < 0 differentiate nx (x) with respect to x, obtaining µ ¶ q 2 2 2 2λϕ 2λ − 4λ + β (1 − 2ϕ (1 − x)) dnx (x) q = (21) dx 2 2 2 2 β (1 − 2ϕ (1 − x)) 4λ + β (1 − 2ϕ (1 − x))

which is always negative, since the denominator is positive, given that β > 0 and the numerator is negative, given that λ, ϕ > 0. This proves part a. To prove part b. it suffices to notice that, when 1 − 2ϕ (1 − x) = 0, the denominator of nx (x) is zero and nx (x) is not defined. We have that x 1−2ϕ (1 − x) = 0 ↔ x = 2ϕ−1 2ϕ . When n (x) is not defined, to check the sign of x, ˙ we have to look at expression (19) directly. When 1 − 2ϕ (1 − x) = 0, expression (19) becomes x˙ = λ [2n − 1] and x˙ R 0 ↔ n R 12 . For x 6= 2ϕ−1 2ϕ , x˙ > 0 ↔ n > nx (x), as proved in part a. This concludes the proof of Lemma 1.

B.1

Proof of Proposition 1 ◦

◦

1. Here Proposition 1 analyzes the case where (x , n ) ∈ M SR . ◦ ◦ 1.a. Assumption n > nx (x ) implies that π A > π B , as condition proven ◦ in Lemma 1. Thus x˙ > 0 and x increases £whereas n=n . ¤ ◦ ◦ ◦ ◦ dnx (x) If n > nx (x ), then nx (x) < n ∀x ∈ x , 1 . This is because £ ◦ ¤ dx < 0 ◦ x ∀x ∈ [0, 1] . If n (x) < n2SR (x) and n < n2SR (x) ∀x ∈ x , 1 , then the trajectory of x is always in M SR , x stops increasing at x = 1 and n£ remains ¤ ◦ ◦ ◦ ˆ ∈ x , 1 at at n = n . Vice-versa, if n > n2SR (1), there exist some x which the trajectory of x crosses n2SR (x). Then x leaves M SR . Since ◦ n ≥ n2SR (x) > nx (x) ∀x ∈ [ˆ x, 1] , both x and n increase until x = 1 and n = 1 and equilibrium A is reached. ◦ ◦ ◦ 1.b. If n < nx (x ) then π A < π B . Thus x˙ < 0 and n = n . £ x ◦ ◦ ◦ ◦¤ n ¤ < nx (x) ∀x ∈ 0, x . If Since dndx(x) < 0, n < nx (x ) implies £ ◦ ◦ nx (x) > n1SR (x) and n > n1SR (x) ∀x ∈ 0, x , then the trajectory of x is ◦ always in M SR . x stops decreasing at x = 0 and £ n◦ ¤remains at n = n . Vice◦ ˇ ∈ 0, x at which the trajectory versa, if n < n1SR (0), there exist some x ◦ of x crosses n1SR (x). Then x leaves M SR . Since n ≤ n1SR (x) < nx (x) ∀x ∈ [0, x ˆ] , both x and n decrease until x = 0 and n = 0 and equilibrium B is reached. ◦ ◦ ◦ 1.c. If n = nx (x ) then x˙ = 0 and n = n . All points in the set I = {(x, n) : n = nx (x)}, I ⊂ M SR , are thus equilibrium points of the dynamic adjustment. However, such points are unstable rest points: if an exogenous shock hits the system, then the dynamic adjustment will lead the ◦ ◦ system away from (x , n ) ∈ I. This concludes the proof of part 1. 29

◦

◦

2. Here Proposition 1 analyzes the case where (x , n ) ∈ / M SR . This ◦ ◦ ◦ ◦ ◦ x happens when (x , n ) are such that either n > n (x ) and n◦ > n2SR (x ) ◦ ◦ ◦ or n < nx (x ) and n◦ < n1SR (x ). ◦ ◦ ◦ ◦ When n > nx (x ) and n > n2SR (x ), x˙ > 0, n˙ > 0. The rest point is at x = 1, n = 1 and equilibrium A is reached. ◦ ◦ ◦ ◦ When n < nx (x ) and n < n1SR (x ), then x˙ < 0, n˙ < 0. The rest point is at x = 0, n = 0 and equilibrium B is reached. This concludes the proof of part 2.

C

Proof of Proposition 2

First of all we need to establish the following result, analogous to Lemma 1. Lemma 2 a) If δ(x) > 0, then x˙ > 0 ∀n ∈ [0, 1] such that n > nx2L (x); if δ(x) < 0, then x˙ > 0 ∀n ∈ [0, 1] such that n < nx1L (x) and n > nx2L (x); b) 0 < nx2L (0) < 1 ∀x ∈ [0, 1] and nx2L (1) < 0 if and only if λ + ϕ < 1. If nx2L (1) > 0 then nx2L (1) < 1 ∀x ∈ [0, 1] ; β(1−2ϕ) then sign[x] ˙ can vary, according to c) If x = x ˆ, where x ˆ = 1−ϕ(1+2β) values of the parameters.

Proof. Substituting expressions (9) and (7)write x˙ = π ˜ A − π B as x˙ = n [2λ + β (1 − 2ϕ) − 2x (1 − φ (1 + β))] +

(22)

2

−n [β (1 − 2ϕ) − 2x (1 − φ (1 + 2β))] + x(1 − ϕ) − λ

Solve (22) with respect to n and define the functions nx1 (x) and nx2 (x) as follows

nx1L (x) = nx2L (x) =

(23)

√

2

(1−2ϕ(1−x))2

√

2

(1−2ϕ(1−x))2

2λ+β(1−2ϕ)−2x(1−ϕ(1+β))+ 4λ(λ−x(1−ϕ))+β 2δ(x)

2λ+β(1−2ϕ)−2x(1−ϕ(1+β))− 4λ(λ−x(1−ϕ))+β 2δ(x)

(24)

where δ (x) = β(1 − 2φ) − x(1 − φ(1 + 2β)).

C.1

(25)

Part a)

To prove Part a) we will proceed in three steps. First of all we need to determine the sign of δ(x) in the interval [0, 1].

30

We then need to establish the behavior of nx1L (x) and nx2L (x) according to the sign of δ(x). Finally, we have to check the dynamic behavior of x given the results obtained in the two preceding steps. Step 1 It can be readily seen, from direct inspection of (25), that sign[δ(x)] is invariant with respect to x iff either one of the following sets of mutually exclusive conditions hold: 1. if ϕ >

1 1+2β

2. if ϕ >

1 1+2β ,

3. if ϕ
0 ∀x ∈ [0, 1] ;

and β + ϕ < 1 then δ(x) < 0 ∀x ∈ [0, 1] ;

and ϕ > ϕ
1 then δ(x) > 0 ∀x ∈ [0, 1].

In all other cases, there exists x ˆ ∈ [0, 1] such that δ(ˆ x) = 0 and δ(x) changes sign in the intervals [0, x ˆ] and [ˆ x, 1] . 1 and ϕ < 12 . From (25) we have Consider first the case where ϕ < 1+2β that δ(x) > 0 iff β(1 − 2ϕ) (26) x 1 then x ˆ > 1 and δ(x) > 0 ∀x ∈ [0, 1] . If β + ϕ < 1, δ(x) > 0 ∀x ∈ [0, x ˆ] and δ(x) < 0 ∀x ∈ [ˆ x, 1].

1 and ϕ > 12 . From (25) we have Consider then the case where ϕ > 1+2β that δ(x) > 0 iff β(2ϕ − 1) (27) x > −ˆ x= ϕ(1 + 2β) − 1

thus δ(x) < 0 ∀x ∈ [0, x ˆ] and δ(x) > 0 ∀x ∈ [ˆ x, 1]. Again, −ˆ x < 1 if and only if β + ϕ > 1. If β + ϕ < 1 then x ˆ > 1 and δ(x) < 0 ∀x ∈ [0, 1] . Step 2 We can now establish the result that nx1L (x) > 1 whenever δ(x) > 0. From (23), it can be obtained that nx1L (x) > 1 if and only if the following condition holds 4λδ(x) > 0 which is always true whenever δ(x) > 0. Hence, when δ(x) > 0, nx1L (x) > 1 ∀x ∈ [0, 1] and the sign of the dynamic adjustment of x is thus determined exclusively by how n relates to nx2L (x).

31

We can also prove that nx1L (0) < 0 when δ(x) < 0 and nx1L (1) > 1 always, independently of the sign of δ(x). In fact, q β(1 − 2φ) + 2λ + 4λ + β 2 (1 − 2)2 x n1L (0) = 2β(1 − 2ϕ) Since we are analyzing the sign of nx1L (x) close to zero, we must be either in the case where δ(x) < 0 ∀x ∈ [0, 1] or where δ(x) < 0 for x ∈ [0, x ˆ] . From conditions (2) and (3) above and (27), this case occurs if ϕ > 12 . Then nx1L (0) < 0 if either λ > β(2φ−1) or if λ < β(2φ−1) and 4βλ(2ϕ − 1) > 0. 2 2 x Hence n1L (0) < 0 always when δ(x) < 0. To see that nx1L (1) > 1 always, write q 2λ − β + β 2 + 4λ (λ + ϕ − 1) nx1L (1) = 2 (β + φ − 1)

If β + φ > 1 then nx1L (1) > 1 ↔ 4λ(β + ϕ − 1) > 0, which is always true. Conversely, if β + φ < 1, then nx1L (1) > 1 ↔ 4λ(β + ϕ − 1) < 0, which again is always true. On the basis of these general results, we are not able to exclude that nx1L (1) lies always outside the relevant range for x and n when δ(x) < 0 and we have to conclude that the sign of the dynamic adjustment of x is determined by the values of n relatively to both nx1L (x) and n2L (x). This concludes the proof of part 1. Step 3

It is now possible to conclude that when δ(x) < 0, x˙ > 0 if and only if n > nx2L (x) and, when δ(x) > 0, x˙ > 0 if and only if n < nx1L (x) and n > n2L (x). In fact, δ(x) is the coefficient of n2 in the expression for x˙ (see equation (22)) and n2 is preceded by a minus sign. When δ(x) > 0, x˙ > 0 for values of n that, given x, are between the two solutions for x˙ = 0,29 whereas δ(x) > 0 implies that x˙ > 0 for values of n that lie outside the interval limited by the two solutions. This proves part a) of the Lemma.

C.2

Part b)

We now state some properties of the function nx2L (x) (the proof goes along the lines followed for nx1L (x) and is thus omitted). First of all, 0 < nx2L (0) < 1 and nx2L (1) < 0 if λ + ϕ < 1. Finally, when nx2L (1) > 0, nx2L (1) < 1 always. 29

Recalling that nx1L (x) > 1 in this case, the relevant condition becomes n > nx2L (x).

32

C.3

Part c)

If δ(x) = 0, the solutions nx2L (x) and nx1L (x) are not well defined. Sign[x] ˙ has then to be inferred directly from expression (22). By inspection, it can < λ < x(1 − ϕ). If λ > x(1 − ϕ) then be seen that x˙ > 0 if x(1−ϕ(1+4β)) 2 λ−x(1−ϕ) x˙ > 0 iff n > 2λ−x(1−ϕ(1+4β)) . Finally, if λ < x(1−ϕ(1+4β)) < x(1 − ϕ), then 2

x(1−ϕ)−λ x˙ > 0 iff n < x(1−ϕ(1+4β))−2λ . In the analysis that follows we will concentrate on cases where the values of the parameters are such that nx1L (x) is either negative or greater than one when δ(x) < 0. This implies that only the function nx2L (x) matters for the dynamic adjustment and nxL (x) = nx2L (x). For the values of the parameters under which δ(x) < 0 and 0 < nx1L (x) < 1 there are several problems with the functions nx1L (x), nx2L (x) and n1L (x), n2L (x), that are often discontinuous or take imaginary values. Computational problems are therefore substantial and the gains in terms of results are not worthwhile. It is in fact possible to show that the main qualitative properties of the dynamics are preserved also in case δ(x) < 0 and 0 < nx1L (x) < 1.

C.4

Proof of Proposition 2

The proof of Part 1, case a1., b., c. and of Part 2, case a1. follows the same procedure used in the proof of Proposition 1 and the reader is referred to that Proposition. Here we concentrate on Part 1, case a2. and Part 2., case a2. In Part 1, case a2., if β + λ > 1 and c + s is sufficiently small, then there exist x1 and x2 in [0, 1] such that n1L (x1 ) = 0 and n2L (x2 ) = 0. In fact β + λ > 1 is a necessary and sufficient condition for the function njL (x), j = 1, 2 to have the property njL (1) < 0. ◦ ◦ ◦ ◦ Then, any trajectory starting from (x , n ) with n > nxL (x ) (such that ◦ ◦ ◦ x increases through time) and n < n2L (x ) is bound to cross n2L (x ) at some point, thus leaving M L . In Part 2, case a2., β + λ < 1 guarantees that n1L (1) > 0 and n12 (1) > 0 too. Similarly, φ + λ < 1 leads to nxL (x) < 0 (see Lemma 2, part 2). Therefore, there is a region in the {x, n} space where points lie with the following characteristics: n > nxL (x) and n < n1L (x), implying that, in that particular region, x˙ > 0 whereas n˙ < 0. Thus, equilibrium D is the only ◦ ◦ steady state that can be reached when the initial condition (x , n ) is such ◦ ◦ ◦ ◦ that n > nxL (x ) and n < n2L (x ).

References [1] Carbonara, E. and F. Parisi (2007), The economics of legal harmonization, Public Choice, 132: 367-400.

33

[2] De Alessi, L. and R. J. Staaf (1991), The Common Law Process: Efficiency or Order?, Constitutional Political Economy, 2: 107-116. [3] Epstein, R.A. (1989), The unintended revolution in product liability law, Cardozo Law Review, 10: 2193-2202. [4] Guzman, A. (2002), Choice of law: new foundations, Georgetown Law Journal, 90: 883-940. [5] Kobayashi, B. and L. Ribstein (1997), Federalism, efficiency and competition, manuscript, available at http://www.ssrn.com/. [6] La Porta, R., F. Lopez-de-Silanes, A. Shleifer and R. Vishny (1998), Law and finance, Journal of Political Economy, 106(6): 1113 - 1155. [7] Lando, O. (1976), Contracts, in International encyclopedia of comparative law, vol. III: private international law, Tubingen: JCB Mohr. [8] Matsuyama, K., N. Kiyotaki and A. Matsui (1993), Toward a theory of international currency, Review of Economic Studies, 60: 283-307. [9] Mattei, U. (1997), Comparative law and economics, Univrsity of Michigan Press, Ann Arbor, MI, United States. [10] Ogus, A. (1999), Competition between national legal systems: a contribution of economic analysis to comparative law, International and Comparative Law Quarterly, 48: 405-418. [11] Ogus, A. (2002), The economic basis of legal culture: networks and monopolisation, Oxford Journal of Legal Studies, 22:419-434. [12] Parisi, F. (2001), The formation of customary law, George Mason University School of Law Working Paper No. 01-06. [13] Parisi and Ribstein (1998), Choice of Law, in The new Palgrave dictionary of economics and the law. Palgrave - McMillan, New York, NY, United States. [14] Posner, R. (2003), The economic analysis of law, 6th edition, Aspen Law and Business, New York, NY, United States, [15] Reimann, M. (1999), Savigny’s triumph? Choice of law in contract cases in the close of the twentieth century, Virginia Journal of International Law, 39: 571-606. [16] Rodrik, D. (2004), Globalization and growth - Looking in the wrong places, Journal of Policy Modeling, 26:517 - 517.

34

[17] Romano, R. (2005), Is regulatory competition a problem or irrelevant for corporate governance?, Oxford Review of Economics and Policy, 21: 212-231. [18] Ruhl, Giesela (2006), Methods and approaches in choice of law: an economic perspective, Berkeley Journal of International Law, 24: 801 - 841. [19] Turrini, A. and T. van Ypersele (2006), Legal costs as barriers to trade, CEPR Discussion Paper No. 5751. [20] Weibull, J. (1995), Evolutionary game theory, Cambridge: MIT Press. [21] Zywicki, Todd J. (2003),The Rise and Fall of Efficiency in the Common Law: A Supply-Side Analysis. Northwestern University Law Review, 97: 1581-1634.

35

Investment in flexibility and probability of investment

Firm operates in

A

B

λ 1-x

A Firm operates in

B

λ 1-x 0 x λ x 0 1-x

0 x

A A

A

B

No transaction

λ x

0 1-x

A

B

A

No transaction

B

TABLE 1: MATCHING PROCESS AND RULES CHOSEN FOR CONTRACT WITH A SEMI – RESTRICTIVE CHOICE-OF-LAW REGIME

Investment in flexibility and probability of investment

Firm operates in

A

B

λ 1-x

A Firm operates in

B

λ 1-x 0 x λ x 0 1-x

0 x

A

λ x

0 1-x

A

B

A

No transaction

A

A

A

B

B

No transaction

B

B

TABLE 2: MATCHING PROCESS AND RULES CHOSEN FOR CONTRACT WITH A LIBERAL CHOICE-OF-LAW REGIME

A

n

a2 °

(0,n )

b1

n2SR(x) (1,n° )

a1 b2

nx(x)

n1SR(x) B 1

x

FIGURE 1: POSSIBLE STEADY STATES IN THE SEMI-RESTRICTIVE REGIME

A

n

n2L(x) a2

(0,n° ) n1L(x)

B

(1,n° ) b1

a1 b2 c1

nxL(x) FIGURE 2: POSSIBLE STEADY STATES IN THE LIBERAL REGIME

D x

n

 

H

  VA − VB > SCB → A ( x)

 

nx(x)   

  VB − VA > SC A→ B ( x)  

F

n2xL ( x )    

 

n1SR(x)

n1L(x) n2SR(x)

n2L(x)

x

FIGURE 3: IN ZONE H THE RESTRICTIVE REGIME DOMINATES, IN ZONE F THE SEMI-RESTRICTIVE REGIME AND THE LIBERAL REGIME DOMINATE, ACCORDING TO INITIAL CONDITIONS. FIGURE OBTAINED WITH PARAMETERS β=0.65, ϕ=0.45, λ=0.6.  

FIGURE 4.a: EVOLUTION OF WELFARE IN THE THREE REGIMES. INITIAL CONDITIONS BELONG TO ZONE H (x°=0.15, n°=0.5). FIGURE OBTAINED WITH PARAMETERS β=0.65, ϕ=0.45, λ=0.6.

FIGURE 4.b: EVOLUTION OF x IN THE THREE REGIMES. INITIAL CONDITIONS BELONG TO ZONE H (x°=0.15, n°=0.5). FIGURE OBTAINED WITH PARAMETERS β=0.65, ϕ=0.45, λ=0.6.

FIGURE 4.c: EVOLUTION OF n IN THE THREE REGIMES. INITIAL CONDITIONS BELONG TO ZONE H (x°=0.15, n°=0.5). FIGURE OBTAINED WITH PARAMETERS β=0.65, ϕ=0.45, λ=0.6.

n

VˆA − VˆB > SCB −> A ( x)       n2F(x)

(x0, n0)

nx(x)

n2xL ( x )    

n2SR(x)

x

FIGURE 5.a: HIGH SWITCHING COSTS. FIGURE OBTAINED WITH PARAMETERS β=0.65, ϕ=0.45, λ=0.6, c=0.7, s=0.1. INITIAL CONDITIONS x0=0.2, n0=0.4.  

WR WSR WL 

    FIGURE 5.b: TOTAL WELFARE WITH HIGH SWITCHING COSTS. FIGURE OBTAINED WITH PARAMETERS β=0.65, ϕ=0.45, λ=0.6, c=0.7, s=0.1. INITIAL CONDITIONS x0=0.2, n0=0.4.    

n

 

  VA − VB > SC B → A ( x )   nx(x)   

  VB − VA > SC A→ B ( x )   n2xL ( x )  

x0, n0    

n1SR(x)

n1L(x) n2SR(x)

n2L(x)

x

FIGURE 6.a: FROM THE INITIAL CONDITION IN ZONE F THE RESTRICTIVE AND THE SEMI-RESTRICTIVE REGIMES LEAD TO EQUILIBRIUM B, THE LIBERAL REGIME DOMINATES. FIGURE OBTAINED WITH PARAMETERS β=0.65, ϕ=0.45, λ=0.6. INITIAL CONDITIONS: x0=0.78, n0=0.1.

WR WSR WL 

FIGURE 6.b: TOTAL WELFARE. FIGURE OBTAINED WITH PARAMETERS β=0.65, ϕ=0.45, λ=0.6, c=0.1, s=0.1. INITIAL CONDITIONS x0=0.78, n0=0.1.  

 

    FIGURE 7.a: EVOLUTION OF x IN THE THREE REGIMES. INITIAL CONDITIONS x0=0.8, n0= 0.2. FIGURE OBTAINED WITH PARAMETERS β=0.4, ϕ=0.5, λ=0.1, C=0.005, S=0.1.

  FIGURE 7.b: TOTAL WELFARE IN THE THREE REGIMES. INITIAL CONDITIONS x0=0.8, n0= 0.2. FIGURE OBTAINED WITH PARAMETERS β=0.4, ϕ=0.5, λ=0.1, C=0.005, S=0.1.