Consistent Probabilistic Social Choice

Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non‐probabilistic social choice, these axioms are incompatible with each other. We show that in the context of probabilistic social choice, these axioms uniquely characterize a function proposed by Fishburn (1984). Fishburn's function returns so‐called maximal lotteries, that is, lotteries that correspond to optimal mixed strategies in the symmetric zero‐sum game induced by the pairwise majority margins. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming.     

Female Labor Supply,Human Capital,and Welfare Reform

We estimate a dynamic model of employment, human capital accumulation—including education, and savings for women in the United Kingdom, exploiting tax and benefit reforms, and use it to analyze the effects of welfare policy. We find substantial elasticities for labor supply and particularly for lone mothers. Returns to experience, which are important in determining the longer‐term effects of policy, increase with education, but experience mainly accumulates when in full‐time employment. Tax credits are welfare improving in the U.K., increase lone‐mother labor supply and marginally reduce educational attainment, but the employment effects do not extend beyond the period of eligibility. Marginal increases in tax credits improve welfare more than equally costly increases in income support or tax cuts.     

Competition and The Operational Performance of Hospitals: The Role of Hospital Objectives

We examine the effect of a hospital's objective (i.e., non‐profit vs. for‐profit) in hospital markets for elective care. Using game‐theoretic analysis and queueing models to capture the operational performance of hospitals, we compare the equilibrium behavior of three market settings in terms of such criteria as waiting times and patient costs from waiting and hospital payments. In the first setting, a monopoly, patients are served exclusively by a single non‐profit hospital; in the second, a homogeneous duopoly, patients are served by two competing non‐profit hospitals. In our third setting, a heterogeneous duopoly, the market is served by one non‐profit hospital and one for‐profit hospital. A non‐profit hospital provides free care to patients, although they may have to wait; for‐profit hospitals charge a fee to provide care with minimal waiting. A comparison between the monopolistic and each of the duopolistic settings reveals that the introduction of competition can hamper a hospital's ability to attain economies of scale and can also increase waiting times. Moreover, the presence of a for‐profit sector may be desirable only when the hospital market is sufficiently competitive. A comparison across the duopolistic settings indicates that the choice between homogeneous and heterogeneous competition depends on the patients' willingness to wait before receiving care and the reimbursement level of the non‐profit sector. When the public funder is not financially constrained, the presence of a for‐profit sector may allow the funder to lower both the financial costs of providing coverage and the total costs to patients. Finally, our analysis suggests that the public funder should exercise caution when using policy tools that support the for‐profit sector—for example, patient subsidies—because such tools may increase patient costs in the long run; it might be preferable to raise the non‐profit sector's level of reimbursement.     

A Polynomial Optimization Approach to Principal–Agent Problems

This paper presents a new method for the analysis of moral hazard principal–agent problems. The new approach avoids the stringent assumptions on the distribution of outcomes made by the classical first‐order approach and instead only requires the agent's expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent's utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn transforms the principal's utility maximization problem into a nonlinear program. Under the additional assumptions that the principal's expected utility is a polynomial and the agent's expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows how to first approximate expected utility functions that are not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal–agent models with multidimensional action sets.     

Poverty and Self‐Control

We argue that poverty can perpetuate itself by undermining the capacity for self‐control. In line with a distinguished psychological literature, we consider modes of self‐control that involve the self‐imposed use of contingent punishments and rewards. We study settings in which consumers with quasi‐hyperbolic preferences confront an otherwise standard intertemporal allocation problem with credit constraints. Our main result demonstrates that low initial assets can limit self‐control, trapping people in poverty, while individuals with high initial assets can accumulate indefinitely. Thus, even temporary policies that initiate accumulation among the poor may be effective. We examine implications concerning the effect of access to credit on saving, the demand for commitment devices, the design of financial accounts to promote accumulation, and the variation of the marginal propensity to consume across income from different sources. We also explore the nature of optimal self‐control, demonstrating that it has a simple and behaviorally plausible structure that is immune to self‐renegotiation.     

Cautious Expected Utility and the Certainty Effect

Many violations of the independence axiom of expected utility can be traced to subjects' attraction to risk‐free prospects. The key axiom in this paper, negative certainty independence ([Dillenberger, 2010]), formalizes this tendency. Our main result is a utility representation of all preferences over monetary lotteries that satisfy negative certainty independence together with basic rationality postulates. Such preferences can be represented as if the agent were unsure of how to evaluate a given lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one. The set of utilities is unique in a well defined sense. We show that our representation can also be derived from a “cautious” completion of an incomplete preference relation.     

Bootstrap Testing of Hypotheses on Co‐Integration Relations in Vector Autoregressive Models

It is well known that the finite‐sample properties of tests of hypotheses on the co‐integrating vectors in vector autoregressive models can be quite poor, and that current solutions based on Bartlett‐type corrections or bootstrap based on unrestricted parameter estimators are unsatisfactory, in particular in those cases where also asymptotic χ² tests fail most severely. In this paper, we solve this inference problem by showing the novel result that a bootstrap test where the null hypothesis is imposed on the bootstrap sample is asymptotically valid. That is, not only does it have asymptotically correct size, but, in contrast to what is claimed in existing literature, it is consistent under the alternative. Compared to the theory for bootstrap tests on the co‐integration rank (Cavaliere, Rahbek, and Taylor, 2012), establishing the validity of the bootstrap in the framework of hypotheses on the co‐integrating vectors requires new theoretical developments, including the introduction of multivariate Ornstein–Uhlenbeck processes with random (reduced rank) drift parameters. Finally, as documented by Monte Carlo simulations, the bootstrap test outperforms existing methods.     

Sign Restrictions,Structural Vector Autoregressions,and Useful Prior Information

This paper makes the following original contributions to the literature. (i) We develop a simpler analytical characterization and numerical algorithm for Bayesian inference in structural vector autoregressions (VARs) that can be used for models that are overidentified, just‐identified, or underidentified. (ii) We analyze the asymptotic properties of Bayesian inference and show that in the underidentified case, the asymptotic posterior distribution of contemporaneous coefficients in an n‐variable VAR is confined to the set of values that orthogonalize the population variance–covariance matrix of ordinary least squares residuals, with the height of the posterior proportional to the height of the prior at any point within that set. For example, in a bivariate VAR for supply and demand identified solely by sign restrictions, if the population correlation between the VAR residuals is positive, then even if one has available an infinite sample of data, any inference about the demand elasticity is coming exclusively from the prior distribution. (iii) We provide analytical characterizations of the informative prior distributions for impulse‐response functions that are implicit in the traditional sign‐restriction approach to VARs, and we note, as a special case of result (ii), that the influence of these priors does not vanish asymptotically. (iv) We illustrate how Bayesian inference with informative priors can be both a strict generalization and an unambiguous improvement over frequentist inference in just‐identified models. (v) We propose that researchers need to explicitly acknowledge and defend the role of prior beliefs in influencing structural conclusions and we illustrate how this could be done using a simple model of the U.S. labor market.     

Competition and Coordination in a Two‐Channel Supply Chain

We study competition and coordination in a supply chain in which a single supplier both operates a direct channel and sells its product through multiple differentiated retailers. We study analytically the supply chain with symmetric retailers and find that the supplier prefers to have as many retailers as possible in the market, even if the retailers' equilibrium retail price is lower than that of the supplier, and even if the number of retailers and their cost or market advantage prevent sales through the direct channel. We find that the two‐channel supply chain may be subject to inefficiencies not present in the single‐channel supply chain. We show that several contracts known to coordinate a single‐channel supply chain do not coordinate the two‐channel supply chain; thus we propose a linear quantity discount contract and demonstrate its ability to perfectly coordinate the two‐channel supply chain with symmetric retailers. We provide some analytical results for the supply chain with asymmetric retailers and propose an efficient solution approach for finding the equilibrium. We find numerically that the supplier still benefits from having more retailers in the market and that linear quantity discount contracts can mitigate supply chain inefficiency, though they no longer achieve perfect coordination.