Income taxation when markets are incomplete

We investigate the welfare effects of proportional income taxation in a standard general equilibrium model with incomplete markets (GEI). Formally, our analysis is on the allocative effects of state-contingent income tax reforms. Tax reforms are restricted to be anonymous, publicly and truthfully announced before markets open, and they are required to result in an ex-post constrained efficient allocation. Our main result is to show that there do typically exist contingent tax reforms that are Pareto improving. These reforms, acting directly on the asset span, modify private risk-sharing opportunities. Thus, unlike most of the GEI literature, the type of policy transmission mechanism considered does not rely on second-order, relative spot price effects. Yet, the key welfare effects of our tax reforms are substantially equivalent to those induced through changes in relative spot prices, as, for example, in Geanakoplos and Polemarchakis (1986), Geanakoplos et al. (1990), or in Citanna et al. (2001). Mathematics Subject Classification (2000): 58E17, 46N10, 93B29 Journal of Economic Literature Classification: D52, H21, H24, H25     

不完全资本市场与国际贸易赤字

本文通过带有风险资产的两期一般均衡模型研究了不完全资本市场和一国国际贸易之间的相关性。研究表明,当市场是完全的或者没有风险资产时,一国的国际贸易是平衡的,但是当资本市场不完全时会出现贸易不平衡。如果是国家间的不完全市场,由于一些国家的收入对风险资产的回报具有更强的相关性,使得国家间的贸易出现不平衡;如果资产在一个国家内是不完全的,则由于完全市场国家具有更强的国内分散收入变化风险的能力,会减少预防性储蓄,导致更大的贸易赤字。一些国际数据基本支持本文的研究结论。     

Rational expectations equilibrium and the strategic choice of costly information

This paper studies costly information acquisition in one-good production economies when agents acquire private information and prices transmit information. Before asset markets open, agents choose the quality of their private information. After this information stage, agents trade assets in sequentially complete markets taking into account their private information and the information revealed by equilibrium prices (rational expectations equilibrium, (Radner, R., 1979. Rational expectations equilibrium: generic existence and the information revealed by prices, Econometrica 47, 655–678.)). An overall equilibrium in asset and information market is defined as a Nash equilibrium of the information game in which agents’ actions are information choices and their utility payoffs are the ex-ante expected utilities of the corresponding rationale expectations equilibrium. This paper shows that for a generic set of economies parameterized by endowments and productivity shocks, an overall equilibrium in information and asset market (a Nash equilibrium of the induced information game) with costly information acquisition and fully-revealing prices exists. In other words, informational efficiency is in general consistent with costly information acquisition.     

A simple method for computing equilibria when asset markets are incomplete

The problem of computing equilibria for general equilibrium models with incomplete real asset markets, or GEI models for the sake of brevity, is reconsidered. It is shown here that the rank-dropping behavior of the asset return matrix could be dealt with in rather a simple fashion: We first compute its singular value decomposition, and then, through this decomposition, construct, by the introduction of a homotopy parameter, a new matrix such that it has constant rank before a desired equilibrium is reached. By adjunction of this idea to the homotopy method, a simpler constructive proof is obtained for the generic existence of GEI equilibria. For the purpose of computing these equilibria, from this constructive proof is then derived a path-following algorithm whose performance is finally demonstrated by means of three numerical examples.     

Trading constraints penalizing default: A recursive approach

This paper proves existence of an ergodic Markov equilibrium for a class of general equilibrium economies with infinite horizon, incomplete markets, and default. Agents may choose to deny their liabilities and face trading constraints that depend on the adjusted amount of past default on each asset. These constraints replace the usual utility penalties and explore intertemporal tie-ins that appear in dynamic economies. The equilibrium prices and solvency rates present stationary properties that are usually required in econometric models of credit risk.     

Determination of general equilibrium with incomplete markets and default penalties

This paper is concerned with the existence and computation of general equilibrium with incomplete asset markets and default. Due to the incompleteness of asset markets, the excess demand functions are typically not continuous at prices and delivery rates for which the assets have redundant nominal deliveries. This discontinuity results in a serious problem for the existence and computation of general equilibrium. We show that this problem can be resolved by replacing the nominal delivery matrix with a constant-rank one and restricting the macro variables in a subset of the domains. With this approach, the economies with incomplete markets and default penalties can be analyzed with differentiable homotopy techniques, and thus in the same framework as standard general equilibrium models. As a by-product, the existence of equilibrium is ensured for generic economies. Several computational examples demonstrate the effectiveness of the algorithm and show some quantitative features of equilibria in the model with default penalties.     

Approximate equilibrium in pure strategies for a two-stage game of asset creation

The paper studies a two-stage economy where consumers choose first the asset structure and then use it in a standard general equilibrium framework to transfer wealth across time and states of nature. The financial structure is chosen by maximizing indirect utility functions, using continuous random selections from the second-stage equilibrium correspondence. We depart from Bisin (J Econ Theory 82:19–45, 1998) where an endogenous beliefs approach was used and the asset creation was left to financial intermediaries. Moreover, our approach allows us to go beyond a mixed strategies result as we obtain an approximate equilibrium in pure strategies for the economy with incomplete information about future endowments.     

The combined equilibrium of travel networks and residential location markets

The combined ‘user’ equilibrium of travel networks and residential location markets is shown to exist and to be unique in the expected allocation of households to residential locations and to the routes and links of the network, in the vacancies and rents of residential locations and in the congested travel time and cost of each network link. The formulation combines a multinomial logit model of households' location and route choices derived from utility maximization, a binary logit model of house owners' offer decisions derived from profit maximization and the standard model of network congestion. A travel disutility measure (consistent with utility maximization) replaces the standard ‘generalized cost function’. The proof utilizes a non-linear programming formulation which reproduces the simultaneous equilibrium conditions of the behavioral formulation. The stability of the unique equilibrium position is briefly discussed, a computational algorithm is proposed and hints for generalized formulations are provided.     

Asset prices in an exchange economy when agents have heterogeneous homothetic recursive preferences and no risk free bond is available

We study a pure exchange economy under incomplete markets where households have heterogeneous homothetic recursive preferences and lending and borrowing are precluded. We fully characterize the properties of the efficient allocations and the equilibrium asset price. The ownership distribution dynamics reveal the emergence of a dominant agent, who after some finite time, remains the only investor that increases asset holdings until asymptotically owning the entire wealth. Investors can be ranked according to a unique parameter that aggregates agents’ preference characteristics and we show how time discount rate, attitude towards risk and intertemporal substitution contribute to capital accumulation.     

Perturbed utility and general equilibrium analysis

We study general equilibrium theory of complete markets in an otherwise standard economy with each household having an additive perturbed utility function. Since this function represents a type of stochastic choice theory, the equilibrium of the corresponding economy is defined to be a price vector that makes its mean expected demand equal its mean endowment. We begin with a study of the economic meaning of this notion, by showing that at any given price vector, there always exists an economy with deterministic utilities whose mean demand is just the mean expected demand of our economy with additive perturbed utilities. We then show the existence of equilibrium, its Pareto inefficiency, and the upper hemi-continuity of the equilibrium set correspondence. Specializing to the case of regular economies, we finally demonstrate that almost every economy is regular and the equilibrium set correspondence in this regular case is continuous and locally constant.     

Game contingent claims in complete and incomplete markets

A game contingent claim is a contract which enables both the buyer and the seller to terminate it before maturity. For complete markets Kifer [Finance and Stochastics 4 (2000) 443–463] shows a connection to a (zero-sum) Dynkin game whose value is the unique no-arbitrage price of the claim. But, for incomplete markets one needs a more general approach. We interpret the contract as a generalized non-zero-sum stopping game. For the complete case this leads to the same results as in Kifer [Finance and Stochastics 4 (2000) 443–463]. For the general case we show the existence of an equilibrium point under the condition that both the seller and the buyer have an exponential utility function. For other utility functions such a point need not exist in the context of incomplete markets.     

Utility indifference valuation for jump risky assets

We discuss utility maximization problems with exponential preferences in an incomplete market where the risky asset dynamics is described by a pure jump process driven by two independent Poisson processes. This includes results on portfolio optimization under an additional European claim. Value processes of the optimal investment problems, optimal hedging strategies and the indifference price are represented in terms of solutions to backward stochastic equations driven by the Poisson martingales. Via a duality result, the solution to the dual problems is derived. In particular, an explicit expression for the density of the minimal martingale measure is provided. The Markovian case is also discussed. This includes either asset dynamics dependent on a pure jump stochastic factor or claims written on a correlated non tradable asset.     

Recursive equilibrium in stochastic OLG economies: Incomplete markets

We prove generic existence of recursive equilibrium for overlapping generations economies with uncertainty and incomplete financial markets. Generic here means in a residual set of utilities and endowments. The result holds provided there is sufficient intragenerational household heterogeneity, and transition probabilities and the asset payoff matrix satisfy mild regularity conditions. The paper also provides a new methodological technique to establish comparative statics, or perturbation, properties in such environments.     

Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors

Using the measure of risk aversion suggested by Kihlstrom and Mirman [Kihlstrom, R., Mirman, L., 1974. Risk aversion with many commodities. Journal of Economic Theory 8, 361–388; Kihlstrom, R., Mirman, L., 1981. Constant, increasing and decreasing risk aversion with many commodities. Review of Economic Studies 48, 271–280], we propose a dynamic consumption-savings–portfolio choice model in which the consumer-investor maximizes the expected value of a non-additively separable utility function of current and future consumption. Preferences for consumption streams are CES and the elasticity of substitution can be chosen independently of the risk aversion measure. The additively separable case is a special case. Because choices are not dynamically consistent, we follow the “consistent planning” approach of Strotz [Strotz, R., 1956. Myopia and inconsistency in dynamic utility maximization. Review of Economic Studies 23, 165–180] and also interpret our analysis from the game theoretic perspective taken by Peleg and Yaari [Peleg, B., Yaari, M., 1973. On the existence of a consistent course of action when tastes are changing. Review of Economic Studies 40, 391–401]. The equilibrium of the Lucas asset pricing model with i.i.d. consumption growth is obtained and the equity premium is shown to depend on the elasticity of substitution as well as the risk aversion measure. The nature of the dependence is examined. Our results are contrasted with those of the non-expected utility recursive approach of Epstein–Zin and Weil.     

Inefficiency of equilibria with incomplete markets

As is well known, equilibria with incomplete markets are generically Pareto inefficient. In this paper, we demonstrate the leading role of a budget constraint in the occurrence of Pareto inefficiency of equilibria with incomplete markets. Specifically, on the basis of the classical two-period one-good pure exchange model we prove that so long as a budget constraint is met for all agents, equilibria with incomplete markets are generically Pareto inefficient in initial endowments and utility functions regardless of the optimization behavior of each agent. All we require of utility functions is a very weak hypothesis called current monotonicity. A simple unified method applicable to both a real asset case and a nominal asset case is presented, so that our claim is proved in both cases.     

On the convergence to the Cournot equilibrium in a productive asset oligopoly

We derive a feedback equilibrium of a dynamic Cournot game where production requires exploitation of a renewable asset. As in the classical Cournot model, quantity-setting firms compete in the same market for a given homogeneous good. We show that, when the asset stock grows sufficiently fast, the unique globally asymptotically stable steady state of the dynamic Cournot game corresponds to the static Cournot solution. Initial differences between firms’ production rates due to asymmetric allocations of asset stocks tend to disappear over time. When instead the asset stock grows slowly, the system does not converge to any stationary point. We also show that, within the class of linear feedback equilibrium strategies, besides the couple of strategies that stabilizes the states for every possible initial conditions, there exists another couple which is more efficient, in that it leads to higher stationary equilibrium profits for both firms, closer to the collusive outcome. Finally, we show that, as the discount rate approaches zero, there exist multiple linear feedback equilibrium strategies that induce a price trajectory that converges asymptotically to a price which is above the static Cournot equilibrium price.     

城市空间结构理论——单中心城市静态模型

首先介绍了在西方城市经济理论中被广泛接受的单中心城市空间结构静态模型。然后,利用比较静态分析方法(comparativestaticanalysis),分析区位、居民收入及交通费用(区位,居民收入及交通费用为模型的外生变量(exogenousvariable))对价格和房屋消费量(价格和房屋消费量为模型的内生变量(endogenousvariable))的影响。最后,理论模型通过引进一般住房生产函数,推导出土地价格及资本密度(即建筑高度)的空间变化规律。通过对城市经济模型进一步分析(对极值条件或解的微分解析分析)得出地价(地租),资本密度(或称容积率),人口密度的空间分布规律,这些规律对城市规划,城市政策,引进市场原则和价格机制来提高城市土地利用效率都有理论指导意义。     

Health insurance reform: The impact of a Medicare buy-in

The steady-state general equilibrium and welfare consequences of a Medicare buy-in program, optional for those aged 55–64, is evaluated in a calibrated life-cycle economy with incomplete markets. Incomplete markets and adverse selection create a potential welfare improving role for health insurance reform. We find that adverse selection eliminates any market for a Medicare buy-in if it is offered as an unsubsidized option to individual private health insurance. The subsidy needed to bring the number of uninsured to less than 5 percent of the target population could be financed by an increase in the labor income tax rate of just 0.03–0.18 percent depending on how the program is implemented.     

Revealed preference theory on the choice of lotteries

The choice behavior of a decision-maker is said to be consistent with expected utility maximization if there exists a utility function defined on the set of prizes such that the decision-maker chooses lotteries with the highest expected utility. We present a revealed preference characterization of choice behavior that is consistent with expected utility maximization. A necessary and sufficient condition for expected utility maximization is that there does not exist a way to compound lotteries such that the probability distribution over the final prizes generated by the chosen lotteries of each observation is equal to that generated by the rejected lotteries of each observation. Our result is quite general and can be applied to any compact set of prizes and any choice correspondence.     

The no-arbitrage condition and financial markets with heterogeneous information

This paper examines the role of the no-arbitrage condition in financial markets with heterogeneous expectations. We consider a single-period, state-contingent claims model, withM risky securities andS states. There exist two types of heterogeneously informed investors, where the information heterogeneity is defined with respect to either the security payoff matrix, the state probability vector, or state partitions. When the information heterogeneity is defined with respect to either the security payoff matrix or state partitions, the no-arbitrage condition imposes a constraint on the dispersion of information between informed and uninformed investors. Further, the no-arbitrage condition is useful in ascertaining the patterns of heterogeneity among investors that are consistent with equilibrium. However, when the information heterogeneity is defined with respect to state probabilities, the role of the no-arbitrage condition is severely restricted. Finally, the no-arbitrage condition may have important implications for the (necessary and sufficient) conditions for the existence of an equilibrium price vector in financial markets with heterogeneous expectations.