Perfectly secure property rights and production inefficiencies in Tullock contests.

• Author: Kolmar, Martin

1. Introduction

   From the point of view of institutional economics, property rights have no normative value in themselves but are means to reach productive and allocative efficiency. An economy with perfect property rights induces the incentives for the individuals to produce and trade efficiently. The idea that property rights are an incentive mechanism underlies the popular reading of the Coase theorem. According to this view, externalities are a result of missing or ill-defined property rights, which implies that individual and social costs and benefits fall apart. The approach implies that the creation of property rights should improve efficiency if there are no impediments for efficient bargaining. (1)

   A common feature of this approach is that it does not explicitly focus on the resource costs of the creation of property rights and the motivation of the law-enforcement agency. This assumption has therefore been labeled "outside enforcement approach" in the literature (Hafer 2000). It also underlies the common idea to conceptualize institutions as "rules of the game" (North 1981).

   In the last decade, contest theory has been fruitfully applied to analyze the determinants of claims to property if property rights are not exogenously given and enforced but "produced" by the individuals of an economy using scarce resources. Important examples are Skaperdas (1992), Grossman and Kim (1995), Grossman (2001), and Warneryd (1993); for an excellent and comprehensive survey of the literature, see Garfinkel and Skaperdas (2006). Conceptually, this literature interprets institutions as properties of the equilibria of a game and allows it to focus on the technological prerequisites that determine the emergence and structure of institutions like property rights. (2) According to this view, institutions are only viable if they can be supported as equilibria in an adequately defined game.

   The traditional outside-enforcement approach allows it to focus very sharply on the normative role of property rights, namely their ability to create incentives for efficient production and trade. From a purely Paretian point of view, property rights are only needed if in an anarchic situation the individual incentives for production are distorted, and/or gains from trade are not exploited. In all other situations, there is no economic rationale for property rights from an efficiency point of view.

   Despite the intuitive importance of property rights for efficient incentives, incentives are not at the center of the current debate about the emergence of property rights in the literature on conflict (Garfinkel and Skaperdas 2006). To analyze the incentive effects of endogenously enforced property rights, one possibility is to focus on the incentives for production. To do so, one needs a model that (i) incorporates endogenous production and (ii) allows for the possibility of perfectly secure property rights in equilibrium. It is intuitive that incentives for production are diluted if property rights are less than perfectly secure in equilibrium because part of the returns to production is appropriated by individuals other than the producer. It is less obvious whether perfectly but endogenously enforced property rights can lead to efficient incentives for production.

   The literature on the emergence of perfectly secure property rights is restricted to models with an exogenous rent, which implies that there are no potential disincentive effects. Grossman and Kim (1995) and Grossman (2001), for example, focus on the factors that determine perfectly secure property rights in an economy with conflict about fixed factor endowments. (3) Security of property is realized if the initial claims to resources are not challenged by potential attackers. This definition of perfectly secure property rights is consistent but misses one essential aspect. If property rights are seen as a means to induce efficient behavior of the individuals, one has to embed the discussion about the determinants of perfectly secure property rights in a model where they can in fact distort marginal conditions. In the model by Grossman and Kim (1995), the resource costs of property rights are pure waste from a Paretian point of view because property rights only influence the distribution of a rent without having any effect on its production.

   This paper is, of course, not the first one that focuses attention on the endogenous creation of rents. Contributions by Hirshleifer (1988, 1989, 1991, 1995), Garfinkel (1990), Grossman (1991), Skaperdas (1992), Esteban and Ray (1999), Wittman (2000), and Mehlum, Moene, and Torvik (2004) analyze different aspects of the tradeoff between investments in production and investments in appropriation and defense. A unifying property of all this literature is its focus on a simultaneous game that (at least in a one-shot game) excludes the possibility of perfectly secure property rights for standard contest-success functions. (4) The endogeneity of the rent can also been found in Gonzalez (2007), who integrates a Tullock contest into a growth model. He analyzes how conflict influences the growth rate of this economy. In his model, (simultaneous) defensive and appropriative investments of the individuals influence the security of property rights over a resource one period ahead and thereby, the effective return of capital investments. He concentrates on interior equilibria, where part of the resource is successfully appropriated (insecure property rights in the terminology of our paper). This restriction on interior equilibria does not allow it to show that the incentives for production are diluted even if property rights are perfectly secure, and the sequence of events is exogenous.

   To get a better understanding of the economic role of endogenously enforced property rights for the creation of incentives to produce efficiently, I use a simple Tullock contest with an endogenously produced rent. Given the structure of the Tullock contest-success function, it is well understood in the literature that in a one-shot game perfectly secure property rights will never emerge if appropriative and defensive investments are chosen simultaneously (Grossman 2001). (5) I therefore allow for the sequential determination of appropriation and defense. It follows that in the case where defensive investments are made prior to appropriative investments, perfectly secure property rights emerge in the sense that appropriative investments are set equal to zero, and that the producer maintains all of the production if defense is relatively effective compared with appropriation. However, it can also be shown that incentives for production are still inefficient, even though property rights are perfectly secure. This surprising finding is a consequence of the fact that in equilibrium the investments in property rights are just sufficient to deter a potential attacker. Because the incentive to appropriate depends positively on the quantity of production, an increase in production at this point would create an incentive to start appropriation. This implies that the incentives to produce are distorted even though there will be no appropriation in equilibrium. In addition, I can show that it is never optimal to increase the amount of defense to the extent that property rights shape incentives for production efficiently. In the opposite case where appropriative investments are made prior to defensive investments, the incentives for production are completely eliminated if appropriation is relatively effective compared with defense. This equilibrium has a rather paradoxical structure because both appropriative as well as defensive investments are equal to zero, which implies that property rights appear to be perfectly secure, but nevertheless, there is no production because of a "shadow of appropriation."

   In a number of situations it might be possible for the individuals to endogenously determine the sequence of moves. I allow for this possibility and adopt the idea by Baik and Shogren (1992), who have added a stage where the individuals can choose whether to move simultaneously or sequentially for the case of a contest with exogenous rent. The result of Baik and Shogren (1992) that the "underdog" always moves first carries over to our model: It can be shown that the individual that is less effective in the contest always moves first in equilibrium. (6) In addition, this equilibrium is unanimously preferred to any other outcome of the game. The consequence of this finding is that perfectly secure property rights will never emerge as an equilibrium of this game even if they would be possible in principle. The unanimous support of open conflict reveals that the resource costs of perfectly secure property rights are inefficiently high. As for contests with exogenous rents, the result also challenges the literature that uses simultaneous models of appropriation and defense because individuals would unanimously like to avoid this type of conflict whenever possible, which implies a strong tendency toward the implementation of a commitment mechanism.

   The paper proceeds as follows: I present the model in section 2. The subgames with different sequences of moves are analyzed in section 3. The endogenous choice of moves is analyzed in section 4, and section 5 concludes.

2. The Model

   There exist two individuals, i = 1, 2. Both individuals derive utility, [u.sub.i], from a consumption good, [c.sub.i], and leisure, [[lambda].sub.i]. As in the standard Tullock model, both goods are perfect substitutes, [u.sub.i] = [c.sub.i] + [[lambda].sub.i]. The individuals are endowed with L units of time that they can use for leisure, appropriation, a (individual 2), or defense, d, and production, l (individual 1). For convenience, I assume that L is sufficiently large to guarantee an interior solution in the following. Total production is given by R(l), with marginal productivity [R.sub.l] (l), where...