Learning while voting: determinants of collective experimentation

This paper analyzes collective decision making when individual preferences evolve through learning. Votes are affected by their anticipated effect on future preferences. The analysis is conducted in a two-arm bandit model with a safe alternative and a risky alternative whose payoff distribution, or “type”, varies across individuals and may be learned through experimentation. Society is shown to experiment less than any of its members would if he could dictate future decisions, and to be systematically biased against experimentation compared to the utilitarian optimum. Control sharing can even result in negative value of experimentation: society may shun a risky alternative even its expected payoff is higher than the safe one’s. Commitment to a fixed alternative can only increase efficiency if aggregate uncertainty is small enough. Even when types are independent, a positive news shock for anyone raises everyone’s incentive to experiment. Ex ante preference correlation or heterogeneity reduces these inefficiencies.

Renegotiation-Proof Contracts with Moral Hazard and Persistent Private Information

How does renegotiation affect contracts between a principal and an agent subject to persistent private information and moral hazard? This paper introduces a concept of renegotiation-proofness, which adapts to stochastic games the concepts of weak renegotiation-proofness and internal consistency by exploiting natural comparisons across states. When the agent has exponential utility and cost of effort, each separating renegotiation-proof contract is characterized by a single “sensitivity" parameter, which determines how the agent's promised utility varies with reported cash flows. The optimal contract among those always causes immiserization. Reducing the agent's cost of effort can harm the principal by increasing the tension between moral hazard and reporting problems. Truthfulness of the constructed contracts is obtained by allowing jumps in cash flow reports and turning the agent's reporting problem into an impulse control problem. This approach shows that self-correcting reports are optimal off the equilibrium path. The paper also discusses the case of partially pooling contracts and of permanent outside options for the agent, illustrating the interaction between cash-flow persistence, renegotiation, moral hazard, and information revelation.Repeated Agency, Asymmetric Information, Persistent Information, Contract Theory, Principal Agent, Limited Commitment, Renegotiation, Recursive Contracts JEL Classification Numbers: D82, D86, C73, G30

On the Smoothness of Value Functions

We prove that under standard Lipschitz and growth conditions, the value function of all optimal control problems for one-dimensional diffusions is twice continuously differentiable, as long as the control space is compact and the volatility is uniformly bounded below, away from zero. Under similar conditions, the value function of any optimal stopping problem is continuously differentiable. For the first problem, we provide sufficient conditions for the existence of an optimal control, which is also shown to be Markov. These conditions are based on the theory of monotone comparative statics.Super Contact; Smooth Pasting; HJB Equation; Optimal Control; Markov Control; Comparative Statics; Supermodularity; Single-Crossing; Interval Dominance Order

Increasing Interdependence of Multivariate Distributions

Orderings of interdependence among random variables are useful in many economic contexts, for example, in assessing ex post inequality under uncertainty; in comparing multidimensional inequality; in valuing portfolios of assets or insurance policies; and in assessing systemic risk. We explore five orderings of interdependence for multivariate distributions: greater weak association, the supermodular ordering, the convex-modular ordering, the dispersion ordering, and the concordance ordering. For two dimensions, all five orderings are equivalent, whereas for an arbitrary number of dimensions n > 2, the five orderings are strictly ranked. For the special case of binary random variables, we establish some equivalences among the orderings.dependence ordering; stochastic orders; supermodularity; weak association; concordance JEL Classification Numbers: D63, D81, G11, G22

Direct Democracy, Political Delegation, and Responsibility Substitution

Can direct democracy provisions improve welfare over pure representative democracy? This paper studies how such provisions affect politicians’ incentives and selection. While direct democracy allows citizens to correct politicians’ mistakes, it also reduces the incentives of elected representatives to search for good policies. This responsibility substitution reduces citizens’ ability to screen competent politicians, when elections are the only means to address political agency problems. A lower cost of direct democracy induces a negative spiral on politicians incentives, which we characterize by a disincentive multiplier. As a consequence, introducing initiatives or lowering their cost can reduce voters’ expected utility. Moreover, when elections perform well in selecting politicians and provide incentives, this indirect welfare reducing effect is stronger.Direct Democracy, Initiative, Referendum, Political Agency, Delegation JEL Classification Numbers: D72, D78, P16

Concepts and Properties of Substitute Goods

We distinguish two notions of substitutes for discrete inputs of a firm. Class substitutes are defined assuming that units of a given input have the same price while unitary substitutes treat each unit as a distinct input with its own price. Unitary substitutes is necessary and sufficient for such results as the robust existence of equilibrium, the robust inclusion of the Vickrey outcome in the core, and the law of aggregate demand, while the class substitutes condition is necessary and sufficient for robust monotonicity of certain auction/tatonnement processes. We analyze the concept of pseudo-equilibrium which extends, and in some sense approximates, the concept of equilibrium when no equilibrium exists. We characterize unitary substitutes as class substitutes plus two other properties. We extend the analysis to divisible inputs, with a particular focus on robustness of the concepts and their relation to the generalized law of aggregate demand.

Capital Mobility and Asset Pricing

We present a model for the equilibrium movement of capital between asset markets that are distinguished only by the levels of capital invested in each. Investment in that market with the greatest amount of capital earns the lowest risk premium. Intermediaries optimally trade off the costs of intermediation against fees that depend on the gain they can offer to investors for moving their capital to the market with the higher mean return. Those fees also depend on the bargaining power of the investor, in light of potential alternative intermediaries. In equilibrium, the speeds of adjustment of mean returns and of capital between the two markets are increasing in the degree to which capital is imbalanced between the two markets.capital mobility, market frictions, financial intermediation, law of one price

Discounting and Patience in Optimal Stopping and Control Problems

This paper establishes that the optimal stopping time of virtually any optimal stopping problem is increasing in "patience," understood as a particular partial order on discount rate functions. With Markov dynamics, the result holds in a continuation- domain sense even if stopping is combined with an optimal control problem. Under intuitive additional assumptions, we obtain comparative statics on both the optimal control and optimal stopping time for one-dimensional diusions. We provide a simple example where, without these assumptions, increased patience can precipitate stopping. We also show that, with optimal stopping and control, a project's expected value is decreasing in the interest rate, generalizing analogous results in a deterministic context. All our results are robust to the presence of a salvage value. As an application we show that the internal rate of return of any endogenously-interrupted project is essentially unique, even if the project also involves a management problem until its interruption. We also apply our results to the theory of optimal growth and capital deepening and to optimal bankruptcy decisions.capital growth, comparative statics, discounting, internal rate of return, optimal control, optimal stopping, patience, present value, project valuation