# Center for Economic Research Discussion Papers

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This series of discussion papers arose from seminars and research conducted at the Center for Economic Research and includes work by three Nobel Prize in Economics laureates.

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Item An ANC Payoff Function for Networks with Sequentially Nash Coherent Plans(Center for Economic Research, Department of Economics, University of Minnesota, 2005-10) Nieva, RicardoI add endogenous bargaining possibilities do develop criteria to determine which statements are credible in a three-player model with complete information where pairs, in a sequential order, can formulate simultaneous negotiation statements. Joint plans are credible if they are the outcome of a plan Nash bargaining problem-the pair bargains cooperatively over the equilibrium payoffs induced by tenable and reliable plans-unless one or both bargainers are indifferent to bargaining. Then, a credible plan is up to the future-request by the oldest pair ("of friends") among the past pairs that successfully cooperated and included one of the indifferent players. I interpret this model as an almost non cooperative (ANC) modification of the three-player Aumann-Myerson (1988) sequential network formation game. Whenever discussing a link two players can bargain non cooperatively out of the sum of their Myerson values (1977) in the prospective network and enunciate simultaneous negotiation statements. The disagreement plan suggests link rejection. Sequentially Nash (1950) coherent plans can be defined and exist. Analytical payoffs are unique. In strictly superadditive cooperative games the complete graph never forms.Item A Theory of Demand for Gambles(Center for Economic Research, Department of Economics, University of Minnesota, 2004-09) Nyman, John A.Although gambling is primarily an economic activity, no single theory of the demand for gambles has gained wide-spread acceptance among economists. This paper proposes a simple model of the demand for gambling that is based on the standard economic assumptions that (1) resources are scarce and (2) consumer's utility increases with income at a decreasing rate. This model has the advantages that (1) it is based solely on changes in income, (2) is potentially applicable to most consumers, (3) preserves the assumption of diminishing marginal utility of income, (4) is consistent with the insurance-buying gambler, and (5) has intuitive appeal.Item The Market for Liars: Reputation and Auditor Honesty(Center for Economic Research, Department of Economics, University of Minnesota, 2003-06) McLennan, Andrew; Park, In-UckIn the model there are two types of financial auditors with identical technology, one of which is endowed with a prior reputation for honesty. We characterize conditions under which there exists a "two-tier equilibrium" in which "reputable" auditors refuse bribes offered by clients for fear of losing reputation, while "disreputable" auditors accept bribes because even persistent refusal does not create a good reputation. The main findings are: (a) honest auditors charge higher fees, and have economic profits accruing to reputation; (b) as the fraction of auditors who are honest increases, the premium charged by reputable auditors eventually decreases, which diminishes the incentive to refuse bribes; (c) if the fraction of honest auditors exceeds an upper bound, there does not exist a two-tier equilibrium; (d) thus the reputation mechanism may be undermined by entry into the honest segment of the industry, if it is possible; (e) increasing auditor independence increases the upper bound.Item Economic Effects of Liberalization: The Case of China's Accession to the World Trade Organization(Center for Economic Research, Department of Economics, University of Minnesota, 2003-03) Bajona, Claustre; Chu, TianshuMany developing economies have joined or applied to join the WTO as part of their process of transformation to market-oriented economies. Accession to the WTO involves provisions to liberalize capital markets and to significantly reduce domestic industrial subsidies to the, usually large, state-owned sector. Therefore, any welfare gains derived from such policies are to be considered as part of the welfare gains of trade liberalization. In this paper we develop a dynamic applied general equilibrium model to quantitatively assess the welfare benefits of capital market liberalization and domestic industrial policy reform, and we apply it to the case of China's accession to the WTO. We find that most of China's benefits of accessing the WTO are derived from the reduction of the state-owned sector driven by the reform in domestic policy required by the treaty. The highest welfare benefits occur when both domestic policy reform and capital market liberalization are jointly implemented. Welfare is enhanced by early opening of the capital markets.Item Health Insurance Theory: The Case of the Vanishing Welfare Gain(Center for Economic Research, Department of Economics, University of Minnesota, 2003-01) Nyman, JohnThis paper presents theory that an important source of value is missing from conventional theory of the demand for health insurance, namely, the effect of the transfer of income (from those who purchase insurance and remain healthy to those who purchase insurance and become ill) on purchases of medical care. Because the portion of moral hazard that is attributable to income is welfare increasing and would replace some of moral hazard that is spuriously deemed to be welfare decreasing, the new theory suggests that the value of health insurance has been dramatically undervalued. Implications for policy are outlined.Item A Theoretical Investigation of Handguns, Cops and Robbers(Center for Economic Research, Department of Economics, University of Minnesota, 2003-01) Boyd, John H.; Kim, JinWe study a theoretical general equilibrium environment in which the only activity of interest is armed robbery. Agents choose whether to be citizens or robbers, and whether to purchase handguns. Armed citizens can protect themselves from robbery but any armed agent runs the risk of accidentally shooting himself or another agent. The government chooses a gun tax, and the intensity of police efforts to arrest would-be robbers and citizens who arm for self-defense. Properties of an equilibrium are characterized and the model is calibrated and solved. In all cases unique equilibria are obtained. We find that guns are an inefficient way of redistributing wealth, in the sense that social costs are very large relative to actual wealth redistribution. In this model society would be vastly better off if handguns could be eliminated. We do find, however, that handguns substantially deter crime when crime is defined as taking another's wealth by force. Yet handguns cause accidental deaths and resultantly in this model policymakers confront a fundamental trade-off between property rights and gun deaths.Item Consumption-Based CAPM and Option Pricing under Jump-Diffusion Uncertainty(Center for Economic Research, Department of Economics, University of Minnesota, 2003-04) Kusuda, KojiIn Kusuda [45], we developed equilibrium analysis in security market economy with jump-Wiener information where no finite number of securities can complete markets. Assuming approximately complete markets (Bjork et al. [11] [12]) in which a continuum of bonds are traded and any contingent claim can be replicated with an arbitrary precision, we have shown sufficient conditions for the existence of approximate security market equilibrium, in which every agent is allowed to choose any consumption plan that can be supported with any prescribed precision. In this paper, we derive the Consumption-Based Capital Asset Pricing Model (CCAPM) using the framework in case of heterogeneous with additively separable utilities (ASUs) and of homogeneous agents with a common stochastic differential utility (SDU). The CCAPM says that the risk premium between a risky security and the nominal-risk-free security can be decomposed into two groups of terms. One is related to the price fluctuation of the risky security, and the other is related to that of commodity. Each group can be further decomposed into two terms related to consumption volatility and consumption jump in case of ASUs, and into three terms related to consumption volatility, continuation utility volatility, and jumps of consumption and continuation utility in case of SDU. Next, we present a general equilibrium framework of jump-diffusion option pricing models in each case of heterogeneous agents with CRRA utilities and of homogeneous agents with a common Kreps-Porteus utility. Finally, we construct a general equilibrium version of an affine jump-diffusion model with jump-diffusion volatility for option pricing using the framework.Item Existence, Uniqueness, and Determinacy of Equilibria in Complete Security Markets with Infinite Dimensional Martingale Generator(Center for Economic Research, Department of Economics, University of Minnesota, 2002-12) Kusuda, KojiThere is a strong evidence that most of financial variables are better described by a combination of diffusion and jump processes. Considering such evidence, researchers have studied security market models with jumps, in particular, in the context of option pricing. In most of their models, jump magnitude is specified as a continuously distributed random variable at each jump time. Then, the dimensionality of martingale generator, which can be interpreted as the "number of sources of uncertainty" in markets is infinite, and no finite set of securities can complete markets. In security market economy with infinite dimensional martingale generator, no equilibrium analysis has been conducted thus far. We assume approximately complete markets (Bjork et al. [10] [11]) in which a continuum of bonds are traded and any contingent claim can be approximately replicated with an arbitrary precision. We introduce the notion of approximate security market equilibrium in which an agent is allowed to choose a consumption plan approximately supported with any prescribed precision. We prove that an approximate security market equilibrium in approximately complete markets can be identified with an Arrow-Debreu equilibrium. Then, we present sufficient conditions for the existence of equilibria in the case of stochastic differential utilities with Inada condition, and for the existence, uniqueness, and determinacy of equilibria in the case of additively separable utilities.Item The Expected Number of Nash Equilibria of a Normal Form Game(Center for Economic Research, Department of Economics, University of Minnesota, 2002-05) McLennan, AndrewItem The Informational Efficiency of Finite Price Mechanisms(Center for Economic Research, Department of Economics, University of Minnesota, 2002-02) Hurwicz, Leonid; Marschak, ThomasThis paper obtains finite counterparts of previous results that showed the informational efficiency of the Walrasian mechanism among all mechanisms yielding Pareto-optimal individually rational trades in an exchange economy while using a continuum of possible messages. Such mechanisms lack realism, since it is not possible to transmit or announce all points of a continuum, and it generally takes infinite time to find an equilibrium message, among all the messages in a continuum. Accordingly, the paper studies approximations of the continuum Walrasian mechanism, in which the number of messages is finite. It applies general results from a companion paper, which considered finite approximations of continuum mechanisms in general organizations, with exchange economies as a particular example. For classic exchange economies, we compare the continuum Walrasian mechanism with alternative continuum mechanisms that also find a Pareto-optimal and individually rational allocation. There are many of them, and some of them, like the continuum Direct Revelation mechanism, do not use prices at all. A finite approximation to a continuum mechanism will have an error. Its overall error for a given class of economies is the worst distance (over all members of the class) between the continuum mechanism's final allocation and the approximation's final allocation. We measure a finite mechanism's cost by the number of its (equilibrium) messages. We consider exchange economies in which traders' utility functions are quasi-linear and strictly concave. We find that the overall error of a sufficiently fine finite approximation of the Walrasian mechanism is arbitrarily close to the overall error of a not more costly approximation of an alternative continuum mechanism that has the same number of message variables. The former overall error is smaller than the latter if the alternative continuum mechanism has a larger number of message variables. A continuum Direct Revelation mechanism is an example of an alternative mechanism with a larger number of message variables than the Walrasian mechanism. Thus the informational superiority of the Walrasian mechanism emerges again when we approximate it and take the finite number of messages as our cost measure.Item The Demand for Insurance: Expected Utility Theory from a Gain Perspective(Center for Economic Research, Department of Economics, University of Minnesota, 2001-07) Nyman, John A.Expected utility theory holds that the demand for insurance is a demand for certainty, because under the conventional specification of the theory, it appears as if buyers of insurance prefer certain losses to actuarially equivalent uncertain ones. Empirical studies, however, show that individuals actually prefer uncertain losses to actuarially equivalent certain ones. This paper attempts to reconcile expected utility theory with this empirical evidence by suggesting that insurance is demanded to obtain an income payoff in the "bad" state. This specification is mathematically equivalent to the conventional specification and consistent with this and other empirical evidence, but it implies that the demand for insurance has nothing to do with demand for certainty.Item The Second Welfare Theorem of Classical Welfare Economics(Center for Economic Research, Department of Economics, University of Minnesota, 2001-08) Hurwicz, Leonid; Richter, Marcel K.We extend the Second Fundamental Theorem of Welfare Economics in several directions. For pure exchange economies, we drop all insatiability requirements on preferences. For economies with production, we use a concept of directional optimality to provide necessary and sufficient conditions for a given allocation to be competitive. This enables us to show, for example, that not all consumers need to be locally nonsatiated, if the economy is "connected." (An example due to Stanley Reiter shows that such extra conditions are unavoidable.) We use weak assumptions on feasibility sets, allowing, but not requiring, short sales and a very general form of disposability. We do not require that preferences be reflexive, transitive, total, or negatively transitive; and we replace full continuity of preferences by a semicontinuity condition for strict preferences. This provides decentralization results extending some of Arrow's original results [1], as well as those in Arrow and Hahn [2, Theorem 4, pp. 93-94] Debreu [6, Theorem 6.4, p. 95], [4, p. 281], and elsewhere.Item The Theory of the Demand for Health Insurance(Center for Economic Research, Department of Economics, University of Minnesota, 2001-03) Nyman, JohnConventional theory holds that moral hazard--the additional health care purchased as a result of becoming insured--is an opportunistic price response and is welfare-decreasing because the value of the additional health care purchased is less than its costs. The theory of the demand for health insurance presented here suggests that moral hazard is primarily an income transfer effect. In an estimation based on parameters from the literature, the value of moral hazard consumption is found to be 3 times greater than its costs, suggesting that income transfer effects dominate price effects and that moral hazard is welfare-increasing.Item Vertical Specialization with Heterogeneous Entrepreneurs: Can Trade Promote Industrialization of Developing Countries?(Center for Economic Research, Department of Economics, University of Minnesota, 2001-01) Chu, TianshuThis paper explores the theoretical link between trade liberalization and industrial development in developing economies. A two-country, three-good, and three-factor computable general equilibrium model is developed, which features a capital-intensive intermediate good, and a special factor of production, the entrepreneurial skill. The numerical results suggest that with free trade, the developing economy can import the cheaper capital-intensive intermediate good and largely expand its manufacture sector. Moreover, the developing economy can export its manufactured product to the developed economy. Unlike the conventional static trade models that predict that developing economies will de-industrialize with free trade, this theory helps to understand the rapid industrial expansion in newly industrialized economies while liberalizing their international trade.Item R&D Composition over the Product Life Cycle(Center for Economic Research, Department of Economics, University of Minnesota, 1999-12) Saha, SoureshFirms do product R&D (making new and better products) as well as process R&D (making cheaper products). There is evidence that firms devote an increasing share of R&D to process R&D over the life cycle of a product. There is also evidence that over time, the composition of buyers of a product shifts towards the lower end of the market. This paper distinguishes product and process R&D in terms of their relationship to the composition of buyers of a product. It uses this distinction to link the aforementioned facts and to explain the change in R&D composition over time.Item The Welfare Economics of Insurance Contracts that Pay Off by Reducing Price(Center for Economic Research, Department of Economics, University of Minnesota, 1999-04) Nyman, John A.Item The Expected Number of Real Roots of a Multihomogeneous System of Polynomial Equations(Center for Economic Research, Department of Economics, University of Minnesota, 1999-03) McLennan, AndrewThe methods of Shub and Smale [SS93] are extended to the class of multihomogeneous systems of polynomial equations, yielding Theorem 1, which is a formula expressing the mean (with respect to a particular distribution on the space of coefficient vectors) number of real roots as a multiple of the mean absolute value of the determinant of a random matrix. Theorem 2 derives closed form expressions for the mean in special cases that include: (a) Shub and Smale's result that the expected number of real roots of the general homogeneous system is the square root of the generic number of complex roots given by Bezout's theorem; (b) Rojas' [Roj96] characterization of the mean number of real roots of an "unmixed" multihomogeneous system. Theorem 3 gives upper and lower bounds for the mean number of roots, where the lower bound is the square root of the generic number of complex roots, as determined by Bernstein's [Ber75] theorem. These bounds are derived by induction from recursive inequalities given in Theorem 4.Item The Expected Number of Nash Equilibria of a Normal Form Game(Center for Economic Research, Department of Economics, University of Minnesota, 1999-03) McLennan, AndrewItem Staggered Contracts and Business Cycle Persistence(Center for Economic Research, Department of Economics, University of Minnesota, 1999-01) Huang, Kevin Xiaodong; Liu, ZhengStaggered price and staggered wage mechanisms are commonly viewed similar in generating persistent real effects of monetary shocks. In this paper, we distinguish these two mechanisms with individuals' optimizing behavior being explicitly taken into account. We show that, although the dynamic price and wage setting equations are alike, a key parameter governing persistence in these two equations is linked to the underlying preferences and technologies in very different ways. Consequently, the two mechanisms have quite different implications on persistence. While the staggered price mechanism by itself is incapable, the staggered wage mechanism has a much greater potential of generating persistence.Item Infinite-Horizon Optimal Hedging Under Cone Constraints(Center for Economic Research, Department of Economics, University of Minnesota, 1999-01) Huang, Kevin XiaodongWe address the issue of hedging in infinite horizon markets with a type of constraints that the set of feasible portfolio holdings forms a convex cone. We show that the minimum cost of hedging a liability stream is equal to its largest present value with respect to admissible stochastic discount factors, thus can be determined without finding an optimal hedging strategy. We solve for an optimal hedging strategy by solving a sequence of independent one-period hedging problems. We apply the results to a variety of trading restrictions and also show how the admissible stochastic discount factors can be characterized.