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Article Excerpt
Summary. We extend the model from Tornell and Velasco [13] and Tornell and Lane [12] by adding three features: (i) extracting the common property asset involves a private appropriation cost, (ii) agents derive utility from wealth as well as from consumption, and (iii) agents can be heterogeneous. We show that both an increase in the appropriation cost and, when appropriation costs vary across agents, an increase in the degree of heterogeneity of these costs reduce the growth rate of the public capital stock. We also show that, in the interior equilibrium, the private asset can have either a lower or a higher money rate of return than the common property asset.
Keywords and Phrases: Economic growth, Strategic saving, Differential game, Markov-perfect equilibrium.
JEL Classification Numbers: C73, O40.
1 Introduction
Recently, there has been increased interest in studying economic growth in the absence of secure property rights and the presence of multiple organized and, hence, powerful groups in society; see, e.g., Tornell [11], Tornell and Lane [6, 12], Tornell and Velasco [13], or Lindner and Strulik [8]. When legal or political institutions are weak, powerful groups can influence the fiscal process and thereby in effect redistribute the economywide capital stock among themselves. The development of the economy is therefore more appropriately described by a dynamic resource allocation game than by a traditional neoclassical growth model with perfect competition. Pursuing this line of thought, the above mentioned papers study growth models with finitely many agents (the power groups) who share access to the economy's capital stock. Because this turns the capital stock into a common property asset, the familiar tragedy of the commons becomes relevant: the powerful groups do not internalize the negative effects which their appropriation efforts have on the production capacity of the entire economy and, hence, economic growth is inefficiently low.
Tornell and Velasco [13] and Tornell and Lane [12] add another interesting feature to this general setup: they assume that the players can extract resources from the public and insecure capital stock and convert them into private and secure asset holdings. The private asset stocks could be interpreted, for example, as bank accounts in foreign countries in which property rights are secure. In the models studied in Tornell and Velasco [13] and Tornell and Lane [12], the extraction from the common property asset stock is costless and the authors claim that "including appropriation or adjustment costs would add nothing to the insights provided by the model" [12, p. 26]. (3) We believe, however, that an explicit consideration of the costs of appropriation is important. A model that takes appropriation costs into account is not only more realistic (after all, money laundering and lobbying involve the use of real resources) but, as our analysis shows, it also yields new insights and modifies a few key results from Tornell and Velasco [13] and Tornell and Lane [12] in non-trivial ways. As for the new results, we can show for example that both an increase in the appropriation cost and, when appropriation costs vary across agents, an increase in the degree of heterogeneity of these costs reduce the growth rate of the public capital stock. Thus, we have the striking result that high costs of money laundering are detrimental to economic growth.
Another feature of our model, which is not present in Tornell and Velasco [13] and Tornell and Lane [12], is that the agents derive utility not only from consumption but also from wealth. Wealth is a vehicle for achieving social status, and people do care about social status. Cole et al. [1] argue forcefully that status seeking is a strong motive for economic agents, especially if goods are not allocated through well-functioning markets as it is the case in our model. They show that wealth effects may arise even if wealth is not an argument of the utility function. On the other hand, optimal growth models with wealth appearing directly in the utility function have been considered at least since Kurz [7]. A direct wealth effect arises also quite naturally in resource economics, either because the resource stock provides an amenity value or because harvesting costs depend on the available stock of the resource. As will be pointed out below, the model from Tornell and Velasco [13] and Tornell and Lane [12] has also an interpretation of a common property resource model with private storage facilities, such that our model may be considered as an extension to resource stocks with amenity value.
Including wealth as a ranking device in the utility functions of the power groups allows us to study how the elasticity of substitution between wealth and consumption affects the equilibrium outcome. In particular, we are able to derive a simple condition that ensures that higher substitutability leads to a higher intensity of extraction from the common property asset and therefore to a smaller growth rate of the public capital stock. The combination of the wealth effect and positive appropriation costs has also another interesting consequence. Whereas in the model of Tornell and Velasco [13] and Tornell and Lane [12] the equilibrium money returns on both types of assets must coincide, this is no longer true in our model with wealth effects and positive costs of transferring resources from the public to the private asset. As a matter of fact, depending on the parameter values, the private asset can have either a lower or a higher money rate of return than the public one. (4)
Because of the assumption that the capital stock is a common property asset, our model (as well as that of Tornell and Velasco [13] and Tornell and Lane [12]) is formally very similar to a model of non-cooperative exploitation of a renewable natural resource by finitely many agents. There is a large literature on these models and the paper that is closest to ours in this respect is the one by Sorger [10]. Resource extraction models that allow for private storage of the extracted resource have been studied, for example, by Sinn [9], Kremer and Morcom [5], Gaudet et al. [4], or Dutta and Rowat [2, 3]. (5) Whereas Kremer and Morcom [5], Gaudet et al. [4], and Dutta and Rowat [2] study competitive resource markets, Sinn [9] and Dutta and Rowat [3] deal with strategic resource extraction.
The paper is organized as follows. In Section 2 we formulate the model and state all assumptions. Section 3 characterizes the interior equilibrium under the assumption of homogeneous players. We discuss how the structure of the equilibrium is affected by the presence of appropriation costs and wealth effects. Furthermore, we study how changes in one or more model parameters influence the intensity of appropriation and the net growth rate of the public capital stock. Section 4 introduces heterogeneity of the power groups. We characterize again an interior Nash equilibrium of the game and analyze how the growth rate of the economy depends on the degree of heterogeneity. Finally, in Section 5 we impose an additional constraint on the intensity of extraction from the public capital stock. Such a constraint can be interpreted in terms of capital controls. We show that, in general, there exists a pessimistic equilibrium in addition to the interior equilibrium discussed in Section 3. In the pessimistic equilibrium all players transfer resources from the public capital stock into their private asset holdings as quickly as possible. Finally, Section 6 presents concluding remarks.
2 Model formulation
Time is modelled as a continuous variable. Consider a common property asset with constant rate of return R. We interpret this asset as the aggregate capital stock in an economy with insecure property rights. There are n identical agents with access to this asset. Each agent represents a group of individuals who--because they are organized and because property rights are poorly defined or...
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