Dynamic mechanism design with hidden income and hidden actions

We develop general recursive methods to solve for optimal contracts in dynamic principal-agent environments with hidden states and hidden actions. Starting from a general mechanism with arbitrary communication, randomization, full history dependence, and without restrictions on preferences or technology, we show that the optimal contract can be implemented as a recursive direct mechanism. A curse of dimensionality which arises from the interaction of hidden income and hidden actions can be overcome by introducing utility bounds for behavior off the equilibrium path. Environments with multiple actions are implemented using multiple layers of such off-path utility bounds.     

Inflationary expectations and monetary policy: evidence from Bangladesh

This article first estimates inflationary expectations using a Blanchard–Quah VAR model by decomposing the nominal interest rate into expected inflation and the ex ante real interest rate. Then I utilize this expected inflation along with other macroeconomic variables as inputs to the monetary policy function in a recursive VAR model to identify exogenous policy shocks. To calculate inflationary expectations, I assume that ex ante real interest rate shocks do not have a long-run effect on the nominal interest rate. This article finds that the public expects lower inflation for the future during periods of high inflation. Estimated results from the recursive VAR suggest that a contractionary policy shock increases the real interest rate, appreciates domestic currency, and lowers inflationary expectations and industrial output. However, I find a lagged policy response from Bangladesh Bank to higher inflationary expectations.     

Reclaim-proof allocation of indivisible objects

We study desirability axioms imposed on allocations in indivisible object allocation problems. The existing axioms in the literature are various conditions of robustness to blocking coalitions with respect to agentsʼ ex ante (individual rationality and group rationality) and ex post (Pareto efficiency) endowments. We introduce a stringent axiom that encompasses and strengthens the existing ones. An allocation is reclaim-proof if it is robust to blocking coalitions with respect to any conceivable interim endowments of agents. This is an appealing property in dynamic settings, where the assignments prescribed by an allocation to be implemented need to be made in multiple rounds rather than all in one shot. We show that an allocation is reclaim-proof if and only if it is induced by a YRMH–IGYT mechanism (introduced by Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation.     

A 4-Stated DICE: Quantitatively Addressing Uncertainty Effects in Climate Change

We introduce a version of the DICE-2007 model designed for uncertainty analysis. DICE is a wide-spread deterministic integrated assessment model of climate change. Climate change, long-term economic development, and their interactions are highly uncertain. The quantitative analysis of optimal mitigation policy under uncertainty requires a recursive dynamic programming implementation of integrated assessment models. Such implementations are subject to the curse of dimensionality. Every increase in the dimension of the state space is paid for by a combination of (exponentially) increasing processor time, lower quality of the value or policy function approximations, and reductions of the uncertainty domain. The paper promotes a state-reduced, recursive dynamic programming implementation of the DICE-2007 model. We achieve the reduction by simplifying the carbon cycle and the temperature delay equations. We compare our model’s performance and that of the DICE model to the scientific AOGCM models emulated by MAGICC 6.0 and find that our simplified model performs equally well as the original DICE model. Our implementation solves the infinite planning horizon problem in an arbitrary time step. The paper is the first to carefully analyze the quality of the value function approximation using two different types of basis functions and systematically varying the dimension of the basis. We present the closed form, continuous time approximation to the exogenous (discretely and inductively defined) processes in DICE, and we present a numerically more efficient re-normalized Bellman equation that, in addition, can disentangle risk attitude from the propensity to smooth consumption over time.     

Government policy and the probability of coordination failures

This paper introduces an approach to the study of optimal government policy in economies characterized by a coordination problem and multiple equilibria. Such models are often criticized as not being useful for policy analysis because they fail to assign a unique prediction to each possible policy choice. We employ a selection mechanism that assigns, ex ante, a probability to each equilibrium indicating how likely it is to obtain. We show how such a mechanism can be derived as the natural result of an adaptive learning process. This approach leads to a well-defined optimal policy problem, and has important implications for the conduct of government policy. We illustrate these implications using a simple model of technology adoption under network externalities.     

Mutual Insurance,Individual Savings,and Limited Commitment

We examine a dynamic model of mutual insurance when households can also engage in self-insurance by storage. We assume that there is no enforcement mechanism, so that any insurance is informal and must be self-enforcing. We show that consumption allocations satisfy a modified Euler condition and that an enhanced storage technology can either improve or diminish welfare. Furthermore we show that the ex ante transfers introduced into dynamic informal insurance models recently by Gauthier et al. (Gauthier, C., Poitevin, M., and González, P. (1997). Journal of Economic Theory76, 106–144) are only used here in the first period, with the role of ex ante transfers being replaced by differential individual storage. Journal of Economic Literature Classification Numbers: C61, C73, D90, E21.     

Ordinary Shares and Managers

We argue that ordinary shares undermine any inherent commitment of its holders to resist renegotiating away ex post inefficiencies. Yet, in a dynamic adverse selection problem, such ex post inefficiencies are optimal from an ex ante point of view. We show that shareholders may use a manager in combination with a golden parachute (managerial severance payments) as a commitment device not to renegotiate ex post.     

Existence and Uniqueness of Equilibrium in Distorted Dynamic Economies with Capital and Labor

In this paper, we provide a set of sufficient conditions under which recursive competitive equilibrium exists and is unique for a large class of distorted dynamic equilibrium models with capital and elastic labor supply. We develop a lattice based approach to the problem. The class of economies for which we are able to obtain our existence and uniqueness result is considerably larger than those considered in previous work. We conclude by applying the new results to some important examples of monetary economies often used in applied work. Journal of Economic Literature Classification Numbers: C62, D51, D90, E10.     

Computing DSGE models with recursive preferences and stochastic volatility

This paper compares different solution methods for computing the equilibrium of dynamic stochastic general equilibrium (DSGE) models with recursive preferences such as those in Epstein and Zin, 1989, Epstein and Zin, 1991 and stochastic volatility. Models with these two features have recently become popular, but we know little about the best ways to implement them numerically. To fill this gap, we solve the stochastic neoclassical growth model with recursive preferences and stochastic volatility using four different approaches: second- and third-order perturbation, Chebyshev polynomials, and value function iteration. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy. Our main finding is that perturbations are competitive in terms of accuracy with Chebyshev polynomials and value function iteration while being several orders of magnitude faster to run. Therefore, we conclude that perturbation methods are an attractive approach for computing this class of problems.     

Optimal multilateral contracts

Summary The purpose of this paper is to derive the structure of optimal multilateral contracts in a costly state verification model with multiple agents who may be risk averse and need not be identical. We consider two different verification technology specifications. When the verification technology is deterministic, we show that the optimal contract is a multilateral debt contract in the sense that the monitoring set is a lower interval. When the verification technology is stochastic, we show that transfers and monitoring probabilities are decreasing functions of wealth. The key economic problem in this environment is that optimal contracts areinterdependent. We are able to resolve this interdependency problem by using abstract measure theoretic tools.We wish to thank Mark Feldman, Wayne Shafer and Nicholas Yannelis for useful comments. We also gratefully acknowledge financial support from the National Science Foundation (SES 89-09242).     

Taxes,permits, and the diffusion of a new technology

This study looks at the effects of the choice between taxes and permits on the pattern of adoption of a new (pollution) emissions abatement technology. It uses a dynamic setting, where the regulator observes the arrival and initial use of the technology and determines the optimal ex post amount of emissions before firms start to adopt the technology.In the model here, the adoption benefits and costs depend on the number of firms that are already using the technology. Thus, each firm decides the optimal date to adopt the technology, considering its benefits and costs, as well as the advantage they will gain over their rivals, producing a sequence of adoption that is “diffused” into the industry over time.With this framework, the study shows that when the output demand is elastic, auctioned permits induce an earlier diffusion than taxes.     

Endogenous Verifiability and Optimality in Agency

This paper investigates the optimal contract design in a principal-agent model where verification of an agent's action is endogenously determined through strategic interactions between contracting parties. We derive a necessary and sufficient condition for the first best outcome to be implemented as an equilibrium. The equilibrium has the following features: (i) The action level that the agent chooses is not verified even if it is possible. (ii) Nevertheless, the first best can be attained by making a contract contingent on the unverified action. Journal of Economic Literature Classification Numbers: D20, K40.     

Minimum payments and induced effort in moral hazard problems

Consider a moral hazard problem in which there is a constraint to pay the agent no less than some amount m. This paper studies the effect of changes in m on the effort that the principal chooses to induce from the agent. We present sufficient conditions on the informativeness of the signal observed by the principal and on the agentʼs utility under which when m increases, induced effort (and hence productivity) falls. We also study how the cost minimizing contract for any given effort level varies in m. We present an efficient algorithm for numerically calculating optimal contracts for given parameters and show that induced effort falls when m is increased in many cases even when our sufficient conditions fail.     

A political economy theory of the soft budget constraint

Why do soft budget constraints exist and persist? In this paper we argue that the prevalence of soft budget constraints can be best explained by the political desirability of softness. We develop an infinite horizon political economy model where neither democratic nor autocratic politicians can commit to policies that are not ex post optimal. We show that because of the dynamic commitment problem inherent in the soft budget constraint, politicians can in essence commit to make transfers to entrepreneurs which otherwise they would not be able to do. This encourages such entrepreneurs to support them politically. Though the soft budget constraint may induce economic inefficiency, it may be politically rational because it influences the probability of political survival. In consequence, even when information is complete, politicians may fund bad projects which they anticipate they will have to bail out in the future. We show that, maybe somewhat surprisingly, dictators who are less likely to lose power, are more likely to use the soft budget constraint as a strategy to gain political support.     

Unemployment insurance design: Inducing moving and retraining

Evidence suggests that unemployed individuals can affect their job prospects by undertaking a costly action like deciding to move or retrain. Realistically, such an opportunity only arises for some individuals and the identity of those may be unobservable ex ante. The problem of characterizing constrained optimal unemployment insurance in this case has been neglected in previous literature. We construct a model of optimal unemployment insurance where multiple incentive constraints are easily handled. The model is used to analyze the case when an incentive constraint involving moving costs must be respected in addition to the standard constraint involving costly unobservable job-search. Absent wealth effects on behavior, we derive closed-form solutions showing that when the moving/retraining incentive constraint binds, unemployment benefits should increase over the unemployment spell, with an initial period with low benefits and an increase after this period has expired.     

Recursive methods for incentive problems

Many dynamic incentive problems have a primal recursive formulation in which utility promises serve as state variables. We associate dual recursive formulations with these problems. We make transparent the connections between recursive primal and dual approaches, relate value iteration under each and give conditions for such value iteration to be convergent to the true value function.     

Growth Dynamics and Returns to Scale: Bifurcation Analysis

We investigate the dependence of the dynamic behavior of an endogenous growth model on the degree of returns to scale. We focus on a simple (but representative) growth model with publicly funded inventive activity. We show that constant returns to reproducible factors (the leading case in the endogenous growth literature) is a bifurcation point, and that it has the characteristics of a transcritical bifurcation. The bifurcation involves the boundary of the state space, making it difficult to formally verify this classification. For a special case, we provide a transformation that allows formal classification by existing methods. We discuss the new methods that would be needed for formal verification of transcriticality in a broader class of models. Journal of Economic Literature Classification Numbers: O41, O30.     

Location decisions of a polluting firm and the time consistency of environmental policy

This paper considers location decisions of a monopolist, who faces a tax on its emissions in the home country, under ex post that is, time consistent, and ex ante, that is precommitment, environmental policies. We show that the monopolist will relocate more often under ex post optimal emission taxes. A government which cannot commit to an ex ante emission tax and sets its tax ex post after abatement effort has been chosen, is unable to affect the monopolist’s location decision, because it cannot commit to strategically reduce its tax level in the first stage. Domestic welfare is often higher under ex post emission taxes whenever the monopolist relocates under both policy regimes. Otherwise, welfare is higher under government commitment to an ex ante emission tax level. Thus, government commitment to a policy is not always welfare improving.