dynamic procurement under uncertainty optimal design and implications for incomplete contracts we characterize the optimal dynamic contract for a long term basic service when an uncertain add on is required later on introducing firm risk aversion has two impacts profits for the basic service can be backloaded to induce cheaper information revelation for this service an income effect which reduces output distortions the firm must also bear some risk to induce information revelation for the add on this risk effect reduces the level of the add on but hardens information revelation for the basic service the interaction between these effects has important implications for the dynamics of distortions contract renegotiation and the value of incomplete contracts

computational economics and economic theory substitutes or complements abstract this essay examines the idea and potential of a computational approach to theory discusses methodological issues raised by such computational methods and outlines the problems associated with the dissemination of computational methods and the exposition of computational results we argue that the study of a theory need not be confined to proving theorems that current and future computer technologies create new possibilities for theoretical analysis and that by resolving these issues we will create an intellectual atmosphere in which computational methods can make substantial contributions to economic analysis

rational expectations in microeconomic models an overview abstract this paper is an expository introduction to several topics of current research in the general equilibrium theory of rational expectations more specifically we discuss the existence of exact and approximate rational expectations equilibria the implementation of equilibria the behavior of learning and smoothing processes by which traders construct expectations from repeated observations of the market and the lagged use of the information revealed by prices in an intertemporal sequence of markets the purpose of this discussion is to introduce papers on these topics appearing in the journal of economic theory symposium on rational expectations in microeconomic models

computing multi period information constrained optima this paper presents a detailed theoretical derivation and justification for methods used to compute solutions to a multi period including infinite period continuum agent unobservedeffort economy actual solutions are displayed illustrating cross sectional variability in consumption and labour effort in the population at a point in time and variability for a typical individual over time the optimal tradeoff between insurance and incentives is explored and the issue of excess variability is addressed by consideration of the analogue full information economy and various restricted contracting regimes

a macroeconomic evaluation of a carbon tax in overseas territories a cge model for reunion island reunion island similar to most insular regions is ruled by a carbon based economy that is heavily dependent on fossil fuels in recent years the energy transition towards a low carbon economy has become the watchword of this french overseas region with the objective of a 100 renewable energy mix by 2030 reducing fossil fuel use while maintaining economic growth is an important issue for all countries but is even more important for island territories with structural and geographical handicaps energy transition and drastic greenhouse gas emission reductions represent costs and opportunities that need to be quantified this research paper assesses the environmental and macroeconomic effects of the carbon price policy introduced in france to meet the target of the paris agreement the acceptability of the tax significantly depends on the possibility of recycling tax revenues different schemes for recycling tax revenues are considered in simulations the methodology used is a computable general equilibrium cge model for reunion island getrun nrj that takes into account all island specificities the results show that the carbon tax enables substitutions between fossil and renewable energy production and reduces co 2 emissions however the tax has negative effects on the aggregate economy the implemented tax revenue recycling compensation mechanisms mitigate the negative impacts but the results differ significantly as the recycling schemes do not support the same economic actors

strict rational expectations equilibria with diffuseness abstract for smooth static pure exchange economies under uncertainty it is shown that a diffuseness condition on the distribution of traders characteristics as the state of the world varies permits one to use only a weak dimensionality restriction in the proof of the genericity of existence of strict rational expectations equilibria a generic result on the amount of information conveyed by equilibrium price functions and comparisons with some examples of nonexistence are given

a solvable continuous time dynamic principal agent model abstract i study the provision of incentives in a continuous time dynamic moral hazard model with hidden actions and hidden states i consider a principal agent model with linear production and exponential utility whose explicit solution allows me to show how allocations are distorted for incentive reasons and how access to hidden savings further alters allocations i solve the model by applying a stochastic maximum principle where the co state variables from the agent s optimization problem become state variables for the principal s problem of choosing an optimal contract i show that the main effect of moral hazard is a distortion on the effort margin with a smaller effect on the intertemporal consumption allocation access to hidden savings shuts down the intertemporal distortions and increases the effort distortion i also show how the optimal contracts can be implemented via a constant equity share a constant flow payment and a constant tax on savings

incentives learning and compensation a theoretical and empirical investigation of managerial labor contracts this article analyzes properties and implications of multiperiod managerial labor contracts under two alternative hypotheses incentives in which productivity depends on unobservable effort and learning in which ability is unknown and is revealed over time shared and conflicting implications of these competing models are developed in terms of experienceearnings profiles and the relation between compensation and performance i empirically examine these theoretical results by using a longitudinal sample of 1 488 chief executive officers followed from 1974 1985 the data yield mixed evidence that generally supports the learning hypothesis over the incentive hypothesis

managerial turnover in a changing world we develop a dynamic theory of managerial turnover in a world in which the quality of the match between a firm and its managers changes stochastically over time shocks to managerial productivity are anticipated at the time of contracting but privately observed by the managers our key positive result shows that the firm s optimal retention decisions become more permissive with time our key normative result shows that compared to what is efficient the firm s contract induces either excessive retention at all tenure levels or excessive firing at the early stages of the relationship followed by excessive retention after sufficiently long tenure

aggregate fluctuations as an information transmission mechanism a model is presented in which individuals attempt to track shocks with a capital like quantity that is costly to produce and to adjust the shocks have separate individual specific and economy wide components individuals do not have direct access to desired information about economy wide shocks the information is potentially available from the observation of endogenous aggregates but because the aggregates are endogenous there is an informational externality associated with them two polar cases are considered when the desired information is about economy wide real shocks as in townsend 1983 the externality is potentially completely internalized when the desired information is about purely nominal aggregates as in lucas 1973 1975 aggregate fluctuations are a necessary condition of equilibrium

multi period contracts between principal and agent with adverse selection abstract multi period contracts with adverse selection at the time of contracting are studied with risk neutrality and independent private information all inefficiency arises in the first period only with positive serial correlation inefficiency is more pervasive but declines over time

pareto efficient income taxation with stochastic abilities abstract this paper studies pareto efficient income taxation in an economy with finitely lived individuals whose income generating abilities evolve according to a two state markov process the study yields three main results first when individuals are risk neutral in any period the only individuals whose earnings are distorted are those who currently are and have always been low ability in addition the degree to which these perpetual low ability types have their earnings distorted decreases over time converging to zero if the time horizon is long enough second the earnings distortions are continuous with respect to the degree of risk aversion at the risk neutral solution third pareto efficient income tax systems can be time consistent even when the degree of correlation in ability types is large the condition for time consistency suggests a novel theoretical reason why the classic equity efficiency trade off may be steeper in a dynamic environment than previously thought

regulation of a risk averse firm abstract we extend the laffont tirole regulation model to the case of risk averse firms our main results are the impact of risk aversion is to shift the optimal contract toward a cost plus contract as compared with the risk neutral case distortions are greater and informational rents are smaller for high levels of risk aversion the optimal contract involves cost ceilings and the less efficient firms are bunched together journal of economic literature classification numbers d8 l5

aggregation determinacy and informational efficiency for a class of economies with asymmetric information abstract we identify and analyze a class of economies with asymmetric information that we call quasi complete for quasi complete economies we determine equilibrium trades show that the set of fully informative equilibria is a singleton and give necessary and sufficient conditions for the existence of partially informative equilibria besides unifying some familiar settings such as those of grossman 1976 and milgrom and stokey 1982 the following new results are proved a the same restrictions that deliver gorman aggregation under symmetric information are sufficient for gorman aggregation under asymmetric information even under partially informative prices b the traditional assumptions of quadratic utilities and endowment spanning that result in the capm under symmetric information deliver a conditional capm under asymmetric information with prices that need not be fully informative c the linear equilibrium in grossman s 1976 model is the only equilibrium linear or not while minor changes in the normality assumptions result in indeterminacy and partially informative equilibria and d if there is no aggregate endowment risk asymmetrically informed agents with common priors sell the risky part of their endowment in every equilibrium journal of economic literature classification numbers d82 g14 c62

efficient allocations in dynamic private information economies with persistent shocks a first order approach this article studies efficient allocations in a dynamic private information economy with a continuum of idiosyncratic shocks that are persistent i develop a first order approach for this environment and show that the problem has a simple recursive structure that relies on only a small number of state variables making the problem tractable i find sufficient conditions that guarantee that the first order approach is valid to illustrate the first order approach i numerically compute the efficient allocations in a mirrleesean economy with productivity shocks that follow a random walk and verify the validity of the first order approach i show that persistent shocks create a new trade off where the social planner decreases the informational rent of the agent today at the cost of providing higher insurance in the future copyright 2013 oxford university press

insurance and taxation over the life cycle we consider a dynamic mirrlees economy in a life cycle context and study the optimal insurance arrangement individual productivity evolves as a markov process and is private information we use a first order approach in discrete and continuous time and obtain novel theoretical and numerical results our main contribution is a formula describing the dynamics for the labour income tax rate when productivity is an ar 1 our formula resembles an ar 1 with a trend where i the auto regressive coefficient equals that of productivity ii the trend term equals the covariance productivity with consumption growth divided by the frisch elasticity of labour and iii the innovations in the tax rate are the negative of consumption growth the last property implies a form of short run regressivity our simulations illustrate these results and deliver some novel insights the average labour tax rises from 0 to 37 over 40 years whereas the average tax on savings falls from 12 to 0 at retirement we compare the second best solution to simple history independent tax systems calibrated to mimic these average tax rates we find that age dependent taxes capture a sizable fraction of the welfare gains in this way our theoretical results provide insights into simple tax systems copyright 2013 oxford university press

optimal incentive contracts in the presence of career concerns theory and evidence this paper studies optimal incentive contracts when workers have career concerns concerns about the effects of current performance on future compensation we show that the optimal compensation contract optimizes total incentives the combination of the implicit incentives from career concerns and the explicit incentives from the compensation contract thus the explicit incentives from the optimal compensation contract should be strongest for workers close to retirement because career concerns are weakest for these workers we find empirical support for this prediction in the relation between chief executive compensation and stock market performance

power sector reform in small island developing states what role for renewable energy technologies abstract due to various pressures and desires more and more developing countries embark on power sector reform programmes yet there are a wide range of reform options and at present insufficient evidence is available as to which path will deliver best the desired objectives presently most small island developing states sids are dependent on high cost fossil fuel imports for power generation in spite of evidence that harnessing abundant domestic renewable sources of energy can deliver environmental social and economic benefits however depending on the type of power sector reform the transition towards renewable energy technologies rets can be either undermined or facilitated the specific focus on sids is justified because they have inherent characteristics that limit the degree to which the power sector can be transformed in comparison to larger continental developing countries with specific reference to sids this manuscript reviews the drivers and desires for power sector reform as well as presenting the available reform options and their implications on the up take of rets in addition to elaborating aspects of market governance other barriers to the consideration of rets such as financial bias in investment human capacity and environmental policy are discussed in view of this discussion which is based on evidence from recent reform programmes and theoretical academic literature recommendations are formulated that discourage full privatisation of the power sector as well as proposing less dogmatic lending conditions by international assistance bodies

optimal security design and dynamic capital structure in a continuous time agency model we derive the optimal dynamic contract in a continuous time principal agent setting and implement it with a capital structure credit line long term debt and equity over which the agent controls the payout policy while the project s volatility and liquidation cost have little impact on the firm s total debt capacity they increase the use of credit versus debt leverage is nonstationary and declines with past profitability the firm may hold a compensating cash balance while borrowing at a higher rate through the credit line surprisingly the usual conflicts between debt and equity asset substitution strategic default need not arise in this paper we consider a dynamic contracting environment in which a riskneutral agent or entrepreneur with limited resources manages an investment activity while the investment is profitable it is also risky and in the short run it can generate arbitrarily large operating losses the agent will need outside financial support to cover such losses and continue the project the difficulty is that while the probability distribution of the cash flows is publicly known the agent may distort these cash flows by taking a hidden action that leads to a private benefit specifically the agent may i conceal and divert cash flows for his own consumption and or ii stop providing costly effort which would reduce the mean of the cash flows therefore from the perspective of the principal or investors that fund the project there is the concern that a low cash flow realization may be a result of the agent s actions rather than the project s fundamentals to provide the agent with appropriate incentives investors control the agent s wage and may also withdraw their financial support for the project and force its early termination we seek to characterize an optimal contract in this framework and relate it to the firm s choice of capital structure we develop a method to solve for the optimal contract given the incentive constraints in a continuous time setting and study the properties of the credit line debt and equity that implement the contract as in the discrete time model of demarzo and fishman 2003 the continuous time setting offers several peter m demarzo is from stanford university and yuliy sannikov is from u c berkeley we

information aggregation in a noisy rational expectations economy abstract this paper analyzes a general equilibrium model of a competitive security market in which traders possess independent pieces of information about the return of a risky asset each trader conditions his estimate of the return both on his own private source of information and price which in equilibrium serves as a noisy aggregator of the total information observed by all traders a closed form characterization of the rational expectations equilibrium is presented a counter example to the existence of fully revealing equilibrium is developed

corporate financial hedging with proprietary information abstract if a firm has information pertinent to its own dividend stream that is not made available to its shareholders it may be in the interests of the firm and its shareholders to adopt a financial hedging policy this is in contrast with the modigliani miller theorem which implies that with informational symmetry such financial hedging is irrelevant in certain cases hedging policies are identified that are unanimously supported by shareholders

a privately revealing rational expectations equilibrium for the futures market abstract this paper develops a model of the futures market with two types of participants farmers and speculators farmers undertake production decisions and face both output and spot price risk as opposed to speculators who face only spot price risk agents have constant absolute risk aversion von neumann morgenstern utility functions and form rational expectations about the future output shock and spot price we assume that traders specialize in information collection in our model the futures price is not a sufficient statistic for the market information we show that the rational expectations equilibrium ree futures price is privately revealing to traders who purchase costly information this ree is efficient in the sense that in equilibrium traders are in possession of all market information we demonstrate that traders a have an incentive to collect costly information and b are better off by specializing in collecting the information in which they have a comparative advantage in terms of the quality of the information that they can obtain finally we show that the futures market stabilizes the spot price

the generic existence of rational expectations equilibrium in the higher dimensional case abstract the study of the generic existence of rational expectations equilibrium has concentrated on three cases according to whether the space of states of private information has dimension less than equal to or greater than the price space previous results have shown that in the first case fully revealing equilibria exist generically and in the second case there are open sets of environments with no equilibrium this paper shows that in the third case there is a residual set of environments which permits equilibria which are arbitrarily close to fully revealing

rational behavior and rational expectations abstract this paper presents a new definition of rational expectations equilibrium in security markets characterized by a rigorous treatment of the decision problem facing each agent a rational expectations equilibrium is one in which it is common knowledge among the agents that all of them are rational and that the price observed is the market clearing price the paper shows that such equilibria always exist and that they need not have the property that for generic economies the equilibrium price reveals all economically relevant information the paper also shows that the new definition generalizes existing definitions of rational expectations equilibrium

expectations equilibria with dispersed information existence with approximate rationality in a model with a continuum of agents and finitely many states of the world a model of a large economy in which prices transmit information about the state of the world which is an argument in consumers utility functions from more informed to less informed agents is analysed the basic hypothesis is that the forecast functions of imperfectly informed agents are suitably dispersed for any such distribution of forecasts market clearing prices exist moreover there is always an equilibrium in which each agent s expectations are approximately rational

the provision of incentives in firms i ncentives are the essence of economics despite many wide ranging claims about their supposed importance there has been little empirical assessment of incentive provision for workers the purpose of this paper is to critically overview existing work on the provision of incentives since the interests of workers and their employers are not always aligned a large theoretical literature has emphasized how firms design compensation contracts to induce employees to operate in the firm s interest this literature has reached into many areas of compensation and has pointed to a multitude of different mechanisms that can be used to induce workers to act in the interests of their employers these include piece rates options discretionary bonuses promotions profit sharing efficiency wages deferred compensation and so on my objective here is to evaluate this literature in the light of a growing empirical literature on compensation where possible i will address the literature from two perspectives first an underlying assumption of this literature is that individuals respond to contracts that reward performance accordingly i consider whether agents behave in this way and whether these responses are always in the firm s interest second i address whether firms write contracts with these responses in mind in other words do contracts look like the predictions of the theory incentives are provided to workers

robust contracting with additive noise abstract we investigate the idea that linear contracts are reliable because they give the same incentives for effort at every point along the contract we ask whether this reliability leads to a microfoundation for linear contracts when the principal is profit maximizing we consider a principal agent model with risk neutrality and limited liability in which the agent observes the realization of a mean zero shock to output before choosing how much effort to exert we show that such a model can indeed provide a foundation for reliable contracts and illustrate what elements are required in particular we must assume that the principal knows a lower bound but not an upper bound on the shocks

the existence of fully rational expectations approximate equilibria with noisy price observations abstract nonrevealing fully rational expectations approximate equilibria exist in microeconomic pure exchange economies in which uninformed agents have suitably dispersed noisy price observations such traders maximize a state dependent expected utility conditional on the price vector they observe the distributions of noisy price observations and the correct equilibrium relationship between states of the world and prices in equilibrium aggregate excess demand is small with high probability in every state of the world and its expectation is also small this magnitude diminishes as the noisy price observations become more accurate equilibria are obtained by applying a fixed point argument to state dependent excess demand functions which are smooth because of the noisy price observations

dynamic managerial compensation a variational approach abstract we study the optimal dynamics of incentives for a manager whose ability to generate cash flows changes stochastically with time and is his private information we show that distortions aka wedges under optimal contracts may either increase or decrease over time in particular when the manager s risk aversion and ability persistence are small distortions decrease on average over time for sufficiently high degrees of risk aversion and ability persistence instead distortions increase on average with tenure our results follow from a novel variational approach that permits us to tackle directly the full program thus bypassing some of the difficulties of the first order approach encountered in the dynamic mechanism design literature

large risks limited liability and dynamic moral hazard we study a continuous time principal agent model in which a risk neutral agent with limited liability must exert unobservable effort to reduce the likelihood of large but relatively infrequent losses firm size can be decreased at no cost or increased subject to adjustment costs in the optimal contract investment takes place only if a long enough period of time elapses with no losses occurring then if good performance continues the agent is paid as soon as a loss occurs payments to the agent are suspended and so is investment if further losses occur accumulated bad performance leads to downsizing we derive explicit formulae for the dynamics of firm size and its asymptotic growth rate and we provide conditions under which firm size eventually goes to zero or grows without bounds

information aggregation and policy the function of monetary policy to alter the informational content of money price signals is examined in a model where traders can observe an economy wide financial signal and a local commodity price under a passive policy money demand disturbances which are not directly observable are shown to be confused with real productivity shocks and thereby preclude prices from fully reflecting all information even when the policy authority has no informational advantage prospective money growth feedback rules can improve the structure of available information applications of the rational expectations hypothesis to monetary theory have focused on the informational aspects of money price signals a key element of the models of lucas 1972 1975 barro 1976 and sargent and wallace 1975 is that agents have limited powers of information acquisition and use prices as imperfect summaries from the rest of the world those works have suggested that monetary policy can affect the informational content of observed price signals and thereby affect real variables in weiss 1980a it was shown systematic money growth feedback rules can contribute to economic efficiency when the money demands of one group are based on factors not directly observed by all in this context monetary policy can alter the information content transmitted from the informed to the uninformed through observation of nominal price signals a limitation of these analyses is the omission of economy wide financial signals clearly stock and bond prices are observed accurately and costlessly empirically there are strong comovements between financial signals and economic activity traditional keynesian theory argues that financial signals exert an important influence on output by affecting the demand for new capital goods understanding the informational role of such signals is crucial to any theory which explains fluctuations as arising from incomplete information the present analysis investigates the structure of available information with its implications for real variables in a model where agents trade on both an economy wide capital market and a local commodity market the model has positive implications for the comovements of money demand disturbances aggregate investment expected and realized returns as well as normative implications for the conduct of policy the structure of exogenous information in the model differs from that of my earlier paper rather than assuming two types of traders informed and uninformed the model considers traders to have symmetric although noisy exogenous private information in this framework the economy wide market both aggregates and transmits individuals information about an aggregate structural variable this modification is both analytically convenient and illustrates how noise in the price system alters the importance of public relative to private sources of information the idea that prices aggregate individual information was first formalized in grossman 1976 in that paper a non monetary model of a speculative market was developed in which the price system conveyed all relevant information so as to yield an efficient allocation however this feature was also shown to break down if prices are influenced by

dynamic contracting with persistent shocks abstract in this paper we develop continuous time methods for solving dynamic principal agent problems in which the agent s privately observed productivity shocks are persistent over time we characterize the optimal contract as the solution to a system of ordinary differential equations and show that under this contract the agent s utility converges to its lower bound immiserization occurs unlike under risk neutrality the wedge between the marginal rate of transformation and a low productivity agent s marginal rate of substitution between consumption and leisure will not vanish permanently at her first high productivity report also the wedge increases with the duration of a low productivity report we apply the methods to numerically solve the mirrleesian dynamic taxation model and find that the wedge is significantly larger than that in the independently and identically distributed i i d shock case

generic existence of completely revealing equilibria for economies with uncertainty when prices convey information conditions which imply the existence of strict rational expectations equilibria for most static pure exchange economies where prices convey information about the state of the world are analyzed information is aggregated and transmitted by prices because agents have different initial information and maximize the conditional expectation of state dependent utility functions major results state that if with probability one agents characteristics do not vary too much as the state of the world varies then generically there exist equilibrium price functions which reveal all initial information more precisely if the support of the image measure is contained in a compact c1 manifold satisfying some technical conditions which is of sufficiently low dimension relative to the number of commodities then existence of completely revealing equilibria is generic any economy satisfying these assumptions can be approximated by a sequence of economies which also obey these assumptions and have completely revealing equilibrium price functions slight perturbations do not destroy the existence property

using cost observation to regulate firms the paper emphasizes the use of accounting data in regulatory or procurement contracts when the supplier 1 has superior information about the cost of the project and 2 invests in cost reduction the main result states that under risk neutrality the supplier announces an expected cost and is given an incentive contract linear in cost overruns this optimal contract moves toward a fixed price contract as the announced cost decreases an investment choice is then introduced and the use of a rate of return regulation is studied

long term contracting with markovian consumers to study how a firm can capitalize on a long term customer relationship we characterize the optimal contract between a monopolist and a consumer whose preferences follow a markov process the optimal contract is nonstationary and has infinite memory but is described by a simple state variable under general conditions supply converges to the efficient level for any degree of persistence of the types and along any history though convergence is history dependent in contrast as with constant types the optimal contract can be renegotiation proof even with highly persistent types these properties provide insights into the optimal ownership structure of the production technology

importance of islands in renewable energy production and storage the situation of the french islands abstract the islands are often not or only partially connected to continental electrical networks and have to manage their energy supplies in reaching themselves the production demand balance while ensuring the quality of the delivered electricity the low consumption and the lack of interconnections induce higher energy costs than in other regions for increasing their security the islands prefer to use indigenous sources as renewable ones unfortunately the intermittence and stochastic character of these fatal energy sources make them more difficult to manage and it is aggravated in the case of small island networks the islands are good locations for using and testing new technologies of energy production and storage most islands have a good renewable energy re potential often underused the difficulties of electricity management in island grids are first shown particularly with the impact on the energy production cost then the problem of the integration of renewable energy sources res in island electrical grids is highlighted the energy situation of french islands is presented with a particular focus on the part of renewable sources a higher share of renewable energy in the energy mix can be reached only with the development of the energy production efficient prediction with the development of energy storage means and with an optimal management of the energy flux via the utilization of smart grids

on endogenous formation of price expectations abstract we study a two period exchange economy with complete financial markets and endogenous borrowing constraints contrary to perfect foresight paradigm we assume that agents are heterogeneous in their ability to forecast future prices we introduce a new equilibrium concept called informationally constrained equilibrium where the formation of price expectations is endogenous and reflects the revelation of information from observing bounds on liabilities designed to ensure solvency at any contingency we prove that under standard assumptions an equilibrium always exists and we characterize the degree of information revealed by the endogenous debt limits

optimal long term financial contracting we develop an agency model of financial contracting we derive long term debt a line of credit and equity as optimal securities capturing the debt coupon and maturity the interest rate and limits on the credit line inside versus outside equity dividend policy and capital structure dynamics the optimal debt equity ratio is history dependent but debt and credit line terms are independent of the amount financed and in some cases the severity of the agency problem in our model the agent can divert cash flows we also consider settings in which the agent undertakes hidden effort or can control cash flow risk

approximate equilibria in microeconomic rational expectations models abstract for general equilibrium models in which prices transmit information among asymmetrically informed traders strict rational expectations approximate equilibria are defined a state dependent price function is an e equilibrium if when agents use their own information and that conveyed by prices aggregate excess demand in each state of the world does not exceed e for any positive e existence requires only very mild assumptions continuity and compact support moreover there are revealing e equilibria for all smooth economies satisfying a dimensionality condition in an open neighborhood of this case existence of maximally revealing e equilibria holds

aggregation and linearity in the provision of intertemporal incentives we consider the problem of providing incentives over time for an agent with constant absolute risk aversion the optimal compensation scheme is found to be a linear function of a vector of n accounts which count the number of times that each of the n kinds of observable events occurs the number n is independent of the number of time periods so the accounts may entail substantial aggregation in a continuous time version of the problem the agent controls the drift rate of a vector of accounts that is subject to frequent small random fluctuations the solution is as if the problem were the static one in which the agent controls only the mean of a multivariate normal distribution and the principal is constrained to use a linear compensation rule if the principal can observe only coarser linear aggregates such as revenues costs or profits the optimal compensation scheme is then a linear function of those aggregates the combination of exponential utility normal distributions and linear compensation schemes makes computations and comparative statics easy to do as we illustrate we interpret our linearity results as deriving in part from the richness of the agent s strategy space which makes it possible for the agent to undermine and exploit complicated nonlinear functions of the accounting aggregates

an introduction to the theory of rational expectations under asymmetric information every good economics textbook contains the cliche that market prices provide signals which facilitate the allocation of resources to their best use in a world not subject to random shocks consumers and producers when faced with competitive prices need look no further than their own preferences or production technology to be able to make a decision they need give no thought to the tastes endowments or technology of other agents however in a world subject to random shocks this is no longer the case agents are faced with the problem of forecasting future states of nature and more importantly of forecasting the impact of these states on the actions of other agents rational expectations theories provide a model of how agents make those forecasts in a world subject to random shocks it will be the case that agents acquire or at least attempt to acquire information about the future realization of the shocks it will in general be the case that different agents have access to different information the fact that information is dispersed throughout the economy has the potential to cause a misallocation of resources relative to what would be the case if all agents knew everything an efficient allocation of resources will in general require the transfer of information from consumers who have some information about their future demands to producers who can take current actions to mitigate avoidable scarcities or surpluses though many classical and neo classical writers emphasize the informational role of prices the standard marshallian or walrasian model of competitive equilibrium does not involve prices transferring information across traders the purpose of this paper is to show that rational expectations models are radically different from walrasian models in an economy where traders have diverse information this is demonstrated by showing that unlike what occurs in a walrasian equilibrium of an economy with heterogeneous information if there is a complete set of insurance markets and utility is additively separable over time then there exists a rational expectations equilibrium which gives consumers the same allocation as if each consumer has access to all of the economy s information this implies that under the above assumptions a central planner with all the economy s information could not pareto dominate the competitive allocation achieved when traders have diverse information and rational expectations this paper makes no attempt to survey the literature on rational expectations the reader is referred to shiller 1978 barro 1981 for a survey of macroeconomics and rational expectations and radner 1980 for a survey of the microeconomics and mathematical theory of rational expectations this paper will however try to outline the evolution of the rational expectations concept from a notion of optimal forecasting to a virtually complete departure from the walrasian model of equilibrium the rest of this section is devoted to a discussion of pre rational expectations ideas

a continuous time version of the principal agent problem this paper describes a new continuous time principal agent model in which the output is a diffusion process with drift determined by the agent s unobserved effort the risk averse agent receives consumption continuously the optimal contract based on the agent s continuation value as a state variable is computed by a new method using a differential equation during employment the output path stochastically drives the agent s continuation value until it reaches a point that triggers retirement quitting replacement or promotion the paper explores how the dynamics of the agent s wages and effort as well as the optimal mix of short term and long term incentives depend on the contractual environment the understanding of dynamic incentives is central in economics how do companies motivate their workers through piece rates bonuses and promotions how is income inequality connected with productivity investment and economic growth how do financial contracts and capital structure give incentives to the managers of a corporation the methods and results of this paper provide important insights to many such questions this paper introduces a continuous time principal agent model that focuses on the dynamic properties of optimal incentive provision we identify factors that make the agent s wages increase or decrease over time we examine the degree to which current and future outcomes motivate the agent we provide conditions under which the agent eventually reaches retirement in the optimal contract we also investigate how the costs of creating incentives and the dynamic properties of the optimal contract depend on the contractual environment the agent s outside options the difficulty of replacing the agent and the opportunities for promotion our new dynamic insights are possible due to the technical advantages of continuous time methods over the traditional discrete time ones continuous time leads to a much simpler computational procedure to find the optimal contract by solving an ordinary differential equation this equation highlights the factors that determine optimal consumption and effort the dynamics of the agent s career path are naturally described by the drift and volatility of the agent s pay offs the geometry of solutions to the differential equation allows for easy comparisons to see how the agent s wages effort and incentives depend on the contractual environment finally continuous time highlights many essential features of the optimal contract including the agent s eventual retirement in our benchmark model a risk averse agent is tied to a risk neutral principal forever after employment starts the agent influences output by his continuous unobservable effort input the principal sees only the output a brownian motion with a drift that depends on the agent s effort the agent dislikes effort and enjoys consumption we assume that the agent s utility function has the income effect that is as the agent s income increases it becomes costlier to compensate him for the effort also we assume that the agent s utility of consumption is bounded from below

on repeated moral hazard with discounting in this paper we analyze optimal contracts in an infinitely repeated agency model in which both the principal and agent discount the future we show that there is a stationary representation of the optimal contract when the agent s conditional discounted expected utility is used as a state variable this representation reduces the multi period problem to a static variational problem which can be analyzed using standard variational techniques this reduction is used to obtain several properties of the contract

on the existence of rational expectations equilibrium abstract we prove a theorem on the existence of rational expectations general economic equilibrium when agents condition on prices as well as on private information and maximize the expectation of a state dependent utility function the key to the result is a new idealization of what it means for a set of empirical distributions to support agents expectations this idealization depends on the notion that agents compare their expectations with continuous versions of the random empirical distributions that are generated by the workings of the economy the existence theorem covers all strictly concave utility functions arbitrary distributions of the state variable and situations in which the dimension of the state variable is large relative to the number of commodities

the revelation of information and self fulfilling beliefs abstract at a rational expectations equilibrium ree individuals are assumed to know the map from states to prices this hypothesis has two components that agents agree consensus and that they have point expectations degeneracy we consider economies where agents beliefs are described by a joint distribution on states and prices and these beliefs are fulfilled at equilibrium beliefs are self fulfilling if every price in the support of the distribution is an equilibrium price the corresponding equilibria are beliefs equilibria be the further restriction that agents have the same beliefs results in common beliefs equilibria cbe we study the relationship between be cbe and ree thus isolating the role of consensus and of degeneracy in achieving rational expectations journal of economic literatureclassification numbers d51 d82

partially revealing rational expectations equilibrium in a competitive economy abstract a class of pure exchange economies is considered in which some agents are informed of private information and others are uninformed existence of a partially revealing rational expectations equilibrium ree is proved without restricting attention to particular functional forms for utility functions and probability distributions without introducing noise into the model and without departing from the standard definition of ree the equilibrium is robust in the sense that if the primitives of the economy are slightly perturbed the economy continues to have a qualitatively similar ree with somewhat stronger assumptions placed on the economy the equilibrium is also the unique measurable ree

optimal information disclosure in auctions and the handicap auction we analyze a situation where a monopolist is selling an indivisible good to risk neutral buyers who only have an estimate of their private valuations the seller can release without observing certain additional signals that affect the buyers valuations our main result is that in the expected revenue maximizing mechanism the seller makes available all the information that she can and her expected revenue is the same as it would be if she could observe the part of the information that is new to the buyers we also show that this mechanism can be implemented by what we call a handicap auction in interesting applications in the first round of this auction each buyer picks a price premium from a menu offered by the seller a smaller premium costs more then the seller releases the additional signals in the second round the buyers bid in a second price auction where the winner pays the sum of his premium and the second highest non negative bid in the case of a single buyer this mechanism simplifies to a menu of european call options

executive compensation a modern primer this article studies traditional and modern theories of executive compensation bringing them together under a simple unifying framework accessible to the general interest reader we analyze assignment models of the level of pay and static and dynamic moral hazard models of incentives and compare their predictions to empirical findings we make two broad points first traditional theories find it difficult to explain the data suggesting that compensation results from rent extraction by ceos however more modern shareholder value theories that arguably better capture the ceo setting do deliver predictions consistent with observed practices suggesting that these practices need not be inefficient second seemingly innocuous features of the modeling setup often made for tractability or convenience can lead to significant differences in the model s implications and conclusions on the efficiency of observed practices we close by highlighting apparent inefficiencies in executive compensation and additional directions for future research