Sustainable growth in a model with dual-rate discounting

In an important model of growth and pollution proposed by Stokey [Int. Econ. Rev. 39 (1998) 1] neither the rate of economic growth nor the rate of growth of emissions depends on the time preference of the representative agent, which seems somewhat paradoxical. To resolve this paradox, we introduce into Stokey's model the assumption of dual-rate discounting, prove the existence of a sustainable balanced growth optimal path, and show that the growth rates of output and emissions are increasing in the proportion between the consumption and the environmental discount factors of the representative agent.     

Amenity driven price effects and conservation reserve site selection: A dynamic linear integer programming approach

Most conservation reserve design models presented in the literature are static and ignore the dynamic economic aspects of site selection. Typically conservation programs operate under time-related (e.g. annual) budgets and purchase land over time in a sequential manner. The uncertainty of land development has been incorporated in a few dynamic reserve selection formulations using stochastic dynamic programming. However, the existing formulations do not explicitly deal with inter-temporal price and location linkages. We address this issue here and present a two-period linear integer programming model for conservation reserve design that incorporates amenity driven price feedback effects inherent in the reserve development problem. In addition, the model includes spatial and ecological criteria. We then use this model to answer the question “How suboptimal is ignoring amenity driven price effects in reserve design models?” We apply the model to artificially generated data sets and compare the results with the results of an iterated static model that considers only one period at a time. We find that the dynamic model with price feedback effects selects sites at a lower per-site cost. The policy implication of this finding is that conservation programs should avoid purchasing land in the same neighborhood over multiple time periods.     

The communication requirements of efficient allocations and supporting prices

We show that any communication finding a value-maximizing allocation in a private-information economy must also discover supporting prices (in general personalized and nonlinear). In particular, to allocate L indivisible items between two agents, a price must be revealed for each of the 2^L-1 bundles. We prove that all monotonic prices for an agent must be used, hence exponential communication in L is needed. Furthermore, exponential communication is needed just to ensure a higher share of surplus than that realized by auctioning all items as a bundle, or even a higher expected surplus (for some probability distribution over valuations). When the utilities are submodular, efficiency still requires exponential communication (and fully polynomial approximation is impossible). When the items are identical, arbitrarily good approximation is obtained with exponentially less communication than exact efficiency.     

Complex solutions of nonconcave dynamic optimization models

Summary In this paper we consider a class of time discrete intertemporal optimization models in one dimension. We present a technique to construct intertemporal optimization models with nonconcave objective functions, such that the optimal policy function coincides with any pre-specifiedC ² function. Our result is a variant of the approach presented in a seminal paper by Boldrin and Montrucchio (1986). Whereas they solved the inverse problem for the reduced form models, we address the different question of how to construct both reduced and primitive form models. Using our technique one can guarantee required qualitative properties not only in reduced, but also in primitive form. The fact that our constructed model has a single valued and continuous optimal policy is very important as, in general, nonconcave problems yield set valued optimal policy correspondences which are typically hard to analyze. To illustrate our constructive approach we apply it to a simple nonconcave model.We are grateful for the helpful comments of L. Montrucchio, K. Nishimura, T. Mitra and an anonymous referee. Financial support of the Austrian Science Foundation under contract No. P7783-PHY and No. J01003-SOZ is gratefully acknowledged. This paper was written while M. Kopel was visiting the Department of Economics, Cornell University.     

A structural dynamic microsimulation model of household savings and labour supply

A structural model of the household is described that represents current best-practice in the analysis of savings and labour supply responses to the policy environment. Care has been taken in specifying the model so that it represents an appropriate basis for the analysis of incentive effects to policy change, and for exploring the empirical support for alternative structural assumptions. Matching the model to survey data for the UK reveals some interesting puzzles in relation to the timing of retirement.     

Measuring stress in money markets: A dynamic factor approach

We extract an index of interest rate spreads from various money market segments to assess the level of funding stress in real time. We find that during the 2007–2009 financial crisis, money markets switched between low and high stress regimes except for brief periods of extreme stress. Transitions to lower stress regimes are typically associated with the non-standard policy measures by the Federal Reserve.     

A life-cycle model of outmigration and economic assimilation of immigrants in Germany

This paper estimates a forward-looking life-cycle model of outmigration and labor force participation. The estimated model is used to evaluate the impact of enforcing a maximum stay duration for newly admitted immigrants on labor force participation and outmigration. Restricting the migration duration is found to have little effect on the labor force participation of skilled immigrants, and a negative effect on that of unskilled immigrants. Restricting the migration duration is also found to encourage the departure of unskilled and unsuccessful immigrants before the maximum duration is reached. These results are obtained by estimating the model with data that contain no information on outmigration decisions. It is shown that the assumption of a continuous state variable affecting attrition only through outmigration allows the probability of outmigration to be identified from the panel attrition. This probability can then be estimated using standard dynamic programming techniques. The migration durations so estimated are found to differ substantially from those estimated under the assumption that immigrants are myopic decision makers.     

An extension of the home-attachment criteria under dynamic tax competition

In this short note we extend the home attachment setting of Mansoorian and Myers (1993) and Ogura (2006) to allow the study of tax competition in a dynamic framework when international business relocation occurs over successive periods. The dynamic framework we propose also helps to understand why tax rates may change over time. Our modified home-attachment rule is illustrated by a simple model of dynamic tax competition in discrete time.     

Computing open-loop noncooperative solution in discrete dynamic games

The purpose of this paper is to introduce a new algorithm for the approximation of non-quadratic, non-linear open-loop Nash Cournot equilibrium in a difference game of fixed duration (multiperiod) and initial state. The algorithm based on adaptive search procedure called genetic algorithm has been used to optimize strategies for N-person dynamic games. Since genetic algorithms require little knowledge of the problem itself, computations based on these algorithms are very attractive to complex dynamic optimization problems. The empirical evidences are also provided to show the success of the algorithm developed. A typical example in US macroeconomic policy selection for 1933-1936 yields evidence of political inference in the economy.     

Robust control and model misspecification

A decision maker fears that data are generated by a statistical perturbation of an approximating model that is either a controlled diffusion or a controlled measure over continuous functions of time. A perturbation is constrained in terms of its relative entropy. Several different two-player zero-sum games that yield robust decision rules are related to one another, to the max-min expected utility theory of Gilboa and Schmeidler [Maxmin expected utility with non-unique prior, J. Math. Econ. 18 (1989) 141-153], and to the recursive risk-sensitivity criterion described in discrete time by Hansen and Sargent [Discounted linear exponential quadratic Gaussian control, IEEE Trans. Automat. Control 40 (5) (1995) 968-971]. To represent perturbed models, we use martingales on the probability space associated with the approximating model. Alternative sequential and nonsequential versions of robust control theory imply identical robust decision rules that are dynamically consistent in a useful sense.     

Efficiency and information aggregation in large uniform-price auctions

We prove that the equilibria of a large interdependent-value, uniform-price auction model where bidders have arbitrary preferences for multiple units can be approximated by a nonatomic exchange economy. We show that the uniform-price auction is approximately efficient with a large number of participants and asymptotically aggregates idiosyncratic bidder information into the market price. More generally our analysis framework provides conditions justifying the use of nonatomic limit model approximations to analyze the large-market behavior of game-theoretic models. We demonstrate continuity requirements on the economic primitives sufficient for the equilibrium strategies of the two models to converge as the number of participants in the finite game approaches infinity.     

Stability and limit cycles in one-dimensional dynamic optimisations of competitive agents with a market externality

This paper considers low dimensional (more precisely, one state variable) dynamic optimisation problems of competitive agents. These individual decisions lead to a dynamic externality for the evolution of the system. However, the impact of an individual and competitive agent is negligible and thus each agent considers this evolution as exogenous data. This leads, assuming rational expectations (perfect foresight due to the deterministic set up), to motions in the three dimensional space of state, costate and externality. Considering the fact that such externalities are widespread, e.g., R&D in the literature on new growth theory, pollution in environmental economics, etc., the incorporation of such externalities due to competitive markets is important, yet this incorporation may alter the stability of the system. Indeed, complex policies such as stable limit cycles are sustainable in such a low-dimensional economy, even for a separable and strictly concave model.     

Optimal stopping with dynamic variational preferences

We solve optimal stopping problems in uncertain environments for agents assessing utility by virtue of dynamic variational preferences as in Maccheroni, Marinacci and Rustichini (2006) [16] or, equivalently, assessing risk in terms of dynamic convex risk measures as in Cheridito, Delbaen and Kupper (2006) [4]. The solution is achieved by generalizing the approach in Riedel (2009) [21] introducing the concept of variational supermartingales and variational Snell envelopes with an accompanying theory. To illustrate results, we consider prominent examples: dynamic multiplier preferences and a dynamic version of generalized average value at risk introduced in Cheridito and Tianhui (2009) [5].     

Monotone equilibria in Bayesian games of strategic complementarities

For Bayesian games of strategic complementarities, we provide a constructive proof of the existence of a greatest and a least Bayesian Nash equilibrium, each one in strategies that are monotone in type. Our main assumptions, besides strategic complementarities, are that each player's payoff displays increasing differences in own action and the profile of types and that each player's interim beliefs are increasing in type with respect to first-order stochastic dominance (e.g., types are affiliated). The result holds for general action and type spaces (single-, multi-, or infinite-dimensional; continuous or discrete) and no prior is assumed. We also provide the following comparative statics result: the greatest and least equilibria are higher if there is a first-order stochastic dominant shift in the interim beliefs. We apply this result to strategic information revelation in games of voluntary disclosure.     

Set coverage and robust policy

We show that confidence regions covering the identified set may be preferable to confidence regions covering each of its points in robust control applications.     

Prior symmetry, similarity-based reasoning, and endogenous categorization

This paper presents a rational theory of categorization and similarity-based reasoning. I study a model of sequential learning in which the decision maker infers unknown properties of an object from information about other objects. The decision maker may use the following heuristics: divide objects into categories with similar properties and predict that a member of a category has a property if some other member of this category has this property. The environment is symmetric: the decision maker has no reason to believe that the objects and properties are a priori different. In symmetric environments, categorization is an optimal solution to an inductive inference problem. Any optimal solution looks as if the decision maker categorizes. Various experimental observations about similarity-based reasoning coincide with the optimal behavior in my model.     

Country factors and the investment decision-making process of sovereign wealth funds

In this paper, we examine the complex decision-making processes that lead to sovereign wealth funds' (SWFs’) choice of investment location. Using a two-tiered dynamic Tobit panel model, we find that country-level factors do not have the same impacts on the investment decision and the amount to invest and that SWFs tend to invest more frequently and at higher amounts in countries in which they have already invested. More specifically, we find that SWFs prefer to invest in countries with higher political stability, whereas they are more prone to invest large amounts in countries that are less democratic and more financially open. Our results also lend support to the idea that SWFs are prudent in their choice of a target country with regard to their investment decision but behave as more opportunistic investors with regard to the amounts to be invested.     

Bounding the inefficiency of equilibria in nonatomic congestion games

Equilibria in noncooperative games are typically inefficient, as illustrated by the Prisoner's Dilemma. In this paper, we quantify this inefficiency by comparing the payoffs of equilibria to the payoffs of a “best possible” outcome. We study a nonatomic version of the congestion games defined by Rosenthal [Int. J. Game Theory 2 (1973) 65], and identify games in which equilibria are approximately optimal in the sense that no other outcome achieves a significantly larger total payoff to the players—games in which optimization by individuals approximately optimizes the social good, in spite of the lack of coordination between players. Our results extend previous work on traffic routing games.     

Interim Bayesian Nash equilibrium on universal type spaces for supermodular games

We prove the existence of a greatest and a least interim Bayesian Nash equilibrium for supermodular games of incomplete information. There are two main differences from the earlier proofs and from general existence results for non-supermodular Bayesian games: (a) we use the interim formulation of a Bayesian game, in which each player's beliefs are part of his or her type rather than being derived from a prior; (b) we use the interim formulation of a Bayesian Nash equilibrium, in which each player and every type (rather than almost every type) chooses a best response to the strategy profile of the other players. There are no restrictions on type spaces and action sets may be any compact metric lattices.