Linear-quadratic approximation of optimal policy problems

We consider a general class of nonlinear optimal policy problems with forward-looking constraints, and show how to derive a problem with linear constraints and a quadratic objective that approximates the exact problem. The solution to the LQ approximate problem represents a local linear approximation to optimal policy from the “timeless perspective” proposed in Benigno and Woodford (2004, 2005) [6], [7], in the case of small enough stochastic disturbances. We also derive the second-order conditions for the LQ problem to have a solution, and show how to correctly rank alternative simple policy rules, again in the case of small enough shocks.     

Stable governments and the semistrict core

We consider the class of proper monotonic simple games and study coalition formation when an exogenous weight vector and a solution concept are combined to guide the distribution of power within winning coalitions. These distributions induce players' preferences over coalitions in a hedonic game. We formalize the notion of semistrict core stability, which is stronger than the standard core concept but weaker than the strict core notion and derive two characterization results for the semistrict core, depending on conditions we impose on the solution concept. A bounded power condition, which connects exogenous weights and the solution, turns out to be crucial. It generalizes a condition termed “absence of the paradox of smaller coalitions” that was previously used to derive core existence results.     

GMM estimation of panel data models with time-varying slope coefficients

A difference/system generalized method of moments (GMM) model that imposes time-constant coefficients is common in empirical studies using panel data. However, a rejection by the Sargan–Hansen test is sometimes a serious concern for researchers. We highlight the fact that the Sargan–Hansen test for GMM estimators applied to panel data is a joint test of valid orthogonality conditions and coefficient stability over time. A possible reason for a rejection is therefore that the slope coefficients vary over time. One solution is to estimate an empirical model in which the coefficients are time specific. We apply this solution to the system GMM estimator of simple nondynamic Cobb–Douglas production functions for a selection of Swedish industries and find that relaxing the assumption of constant slope coefficients results in more satisfactory outcomes of the Sargan–Hansen test.     

Simple Flow Games

This paper considers simple flow situations. We introduce the minimum cut solution and characterize it in terms of one-person efficiency, consistency, and converse consistency. Furthermore, we give several relations between the core of a simple flow game and four other solution concepts: the minimum cut solution, the least core, the kernel, and the bargaining set.Journal of Economic LiteratureClassification Numbers: C71.     

Miracle on Sixth Avenue: Information Externalities and Search

After a long dormant period, Lower Sixth Avenue in New York has under gone a rapid revitalisation. We show that a simple search theoretic model with information spillovers can explain both the period of underuse and the rapid turnaround. The model reduces to a simple equation, which allows us to do comparative statics on the duration of vacancies. We show how the solution reacts to changes in market structure and changes in search technology. The model is suggestive of difficulties that may occur in many markets in which there are changes over time in the optimal use of resources.     

Thematic Clubs and the Supremacy of Network Externalities

We explore the issue of minorities' survival in the presence of positive network externalities. We rely on a simple example of thematic clubs to illustrate why and how such survival problems might appear, first considering the case of simple‐network effects (fully anonymous externalities) and then the case of cross‐network effects (type‐dependent externalities). In both cases, the analysis is framed as a simple noncooperative game with a continuum of players and binary action sets. There is a unique and interior Nash equilibrium under mild network effects and two corner equilibria under strong network effects, with one club driven out. A utilitarian planner would accentuate the clustering effects of network externalities, and call for the disappearance of the minority club more often than the noncooperative solution. A simple myopic learning algorithm capturing the progression of network lock‐in effects is studied.     

Envelope and sensitivity analysis ‘in the large’

New results on global sensitivity analysis are derived. Relying on the saddle-point characterization of the Lagrangean, simple yet powerful results are shown to hold under general conditions. A generalized envelope result is obtained. It does not require differentiability assumptions or unique solution, and it holds for discrete changes.     

Elementary results on solutions to the bellman equation of dynamic programming: existence,uniqueness, and convergence

We establish some elementary results on solutions to the Bellman equation without introducing any topological assumption. Under a small number of conditions, we show that the Bellman equation has a unique solution in a certain set, that this solution is the value function, and that the value function can be computed by value iteration with an appropriate initial condition. In addition, we show that the value function can be computed by the same procedure under alternative conditions. We apply our results to two optimal growth models: one with a discontinuous production function and the other with “roughly increasing” returns.     

Iterated potential and robustness of equilibria

For any given set-valued solution concept, it is possible to consider iterative elimination of actions outside the solution set. This paper applies such a procedure to define the concept of iterated monotone potential maximizer (iterated MP-maximizer). It is shown that under some monotonicity conditions, an iterated MP-maximizer is robust to incomplete information [A. Kajii, S. Morris, The robustness of equilibria to incomplete information, Econometrica 65 (1997) 1283-1309] and absorbing and globally accessible under perfect foresight dynamics for a small friction [A. Matsui, K. Matsuyama, An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415-434]. Several simple sufficient conditions under which a game has an iterated MP-maximizer are also provided.     

On second order conditions for equality constrained extremum problems

We prove a relationship between the bordered Hessian in an equality constrained extremum problem and the Hessian of the equivalent lower-dimension unconstrained problem. This relationship can be used to derive principal minor conditions for the former from the relatively simple and accessible conditions for the latter.     

Coordination on saddle-path solutions: the eductive viewpoint—linear multivariate models

We examine local strong rationality (LSR) in multivariate models with both forward-looking expectations and predetermined variables. Given hypothetical common knowledge restrictions that the dynamics will be close to those of a specified minimal state variable solution, we obtain eductive stability conditions for the solution to be LSR. In the saddlepoint stable case the saddle-path solution is LSR provided the model is structurally homogeneous across agents. However, the eductive stability conditions are strictly more demanding when heterogeneity is present, as can be expected in multisectoral models. Heterogeneity is thus a potentially important source of instability even in the saddlepoint stable case.     

Equilibrium selection in bargaining models

This paper examines evolutionary equilibrium selection in bargaining models. We show that random best-response and continuous best-response learning dynamics give rise to (different) simple sufficient conditions for identifying outcomes as stochastically stable. This allows us to characterize the implications of these dynamics in simple bargaining games.     

Cooperative economic growth

We comparatively study optimal economic growth in a simple endogenous growth model and under two different games, i.e., dynamic sequential game and cooperative stochastic differential game, between a representative household and a typical self-interested politician. Sequential equilibrium solution is derived by applying Backward Induction Principle and corresponding optimal economic growth rate is endogenously determined. Moreover, cooperative equilibrium solution is established with group rationality, individual rationality and sub-game consistency requirements fulfilled, and it is further confirmed that the representative household will save more, and the self-interested politician will tax less, thereby leading to much faster economic growth, when compared to those of the sequential equilibrium solution.     

Necessary and sufficient conditions for transitivity in voting theory

In this paper we provide necessary and sufficient conditions for transitivity of the social preferences given by two types of social decision processes. We consider transitivity of the dominance relation of a proper simple game and that of the social preference given by the simple majority decision rule.     

Multidimensional screening under nonlinear costs: Limits of standard approach

We generalize the usual screening approach and conditions for efficiency-at-the-top and acyclic property from linear to fixed-plus-separable or concave costs and multidimensional commodities. But under non-concave costs, like capacity constraints, an example shows a cycle in the solution graph. The cycle makes the standard screening solution non-implementable and approach inadequate.     

Welfare criteria for tax reforms : An extension

Pazner and Sadka (1981) offer simple sufficient conditions for accepting or rejecting tax reforms based on the theory of index numbers. We provide not only sufficient conditions but also necessary conditions for the validity of tax reforms. Thus, a complete characterization of tax reforms is obtained.     

How much to share: Welfare effects of fiscal transfers

Recent sovereign debt crisis has challenged policy makers to explore the possibility of establishing a fiscal transfer system that could alleviate the negative impact of asymmetric shocks across countries. Using a simple labour production economy, we first derive an analytically tractable solution for optimal degree of fiscal transfers. In this economy, fiscal transfers can improve welfare by moving the competitive equilibrium with fiscal transfers closer to the social planner's solution. We then extend the model to a DSGE setting with capital, international bond and linear taxes, and we analyze how implementation of a simple revenue sharing rule affects welfare and macroeconomic variables over time. Simulation results show that risk sharing through fiscal transfers always improves welfare in the long run. However, under certain model specifications, short‐run transitional welfare loss can outweigh the long‐run benefits. These results suggest that, in designing fiscal transfers across countries, government should take into consideration the intertemporal nature of welfare gains.     

Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly

The seller of N distinct objects is uncertain about the buyer's valuation for those objects. The seller's problem, to maximize expected revenue, consists of maximizing a linear functional over a convex set of mechanisms. A solution to the seller's problem can always be found in an extreme point of the feasible set. We identify the relevant extreme points and faces of the feasible set. We provide a simple algebraic procedure to determine whether a mechanism is an extreme point. We characterize the mechanisms that maximize revenue for some well-behaved distribution of buyer's valuations.     

Forest Value and Optimal Rotations in Continuous Cover Forestry

The Faustmann forest rotation model is a celebrated contribution in economics. The model provides a forest value expression and allows a solution to the optimal rotation problem valid for perpetual rotations of even-aged forest stands. However, continuous forest cover forest management systems imply uneven-aged dynamics, and while a number of numerical studies have analysed specific continuous cover forest ecosystems in search of optimal management regimes, no one has tried to capture key dynamics of continuous cover forestry in simple mathematical models. In this paper we develop a simple, but rigorous mathematical model of the continuous cover forest, which strictly focuses on the area use dynamics that such an uneven-aged forest must have in equilibrium. This implies explicitly accounting for area reallocation and for weighting the productivity of each age class by the area occupied. We present results for unrestricted as well as area-restricted versions of the models. We find that land values are unambiguously higher in the continuous cover forest models compared with the even-aged models. Under area restrictions, the optimal rotation age in a continuous cover forest model is unambiguously lower than the corresponding area restricted Faustmann solution, while the result for the area unrestricted model is ambiguous.