Dynamic incentive contracts with termination threats

We consider a dynamic moral hazard model where the principal offers a series of short-run contracts. We study the optimal mix of two alternative instruments for incentive provision: a performance based wage (a “carrot”) and a termination threat (a “stick”). At any given point in time, these instruments are substitutes in the provision of incentives. We are particularly interested in the dynamic interaction of these two instruments. Both carrot and stick are used more intensively as the agent approaches the end of his finite life. The sharing of the surplus of the relationship plays a key role: a termination threat is included in the optimal contract if and only if the agent’s expected future gain from the relationship is sufficiently high, compared to the principal’s expected future gain. Also, a termination threat is more likely to be optimal if output depends more on “luck” than on effort, if the discount factor is high, or if the agent’s productivity is low. The model, provided that the optimal contract includes a termination threat, essentially provides an alternative explanation for upward-sloping wage profiles even in the absence of full-commitment.     

A preference foundation for constant loss aversion

Following prospect theory and in particular the concept of loss aversion, introduced by Kahneman and Tversky (1979), we consider decision making under risk in which the decision maker’s preferences depend on a reference outcome. An outcome below this reference outcome is regarded as resulting from a loss: a loss decreases the decision maker’s basic utility more than a comparable gain increases this utility. An elegant and simple way to model this phenomenon was proposed by Shalev (2002): the utility of an outcome below the reference outcome is obtained from the basic utility by subtracting a multiple of the loss in basic utility: this multiple, the loss aversion coefficient, is constant across different reference outcomes. We provide a preference foundation for this loss aversion model.     

Use of a Markov decision process model for treatment selection in an asymptomatic disease with consideration of risk sensitivity

Some potentially dangerous diseases are completely asymptomatic. Their diagnosis as incidental findings of ever-more-sensitive medical imaging can leave patients and physicians in something of a quandary. The patient feels well, and potential interventions to stave off long-term deterioration or death bring with them immediate risks. We discuss the use of a Markov Decision Process (MDP) model (rather than Monte Carlo simulation of a Markov Model) to create a tool for analyzing individual treatment decisions for asymptomatic chronic diseases where a patient’s condition cannot improve. We formulate a finite-horizon MDP model to determine optimal treatment plans and discuss three distinct optimality criteria: (a) maximizing expected quality-adjusted-life years with and without discounting, (b) maximizing the expected number of life years in good health, and (c) maximizing the expected utility for number of years in good health. In (c) we assume exponential utility and consider different risk aversion factors reported in the medical literature. We illustrate the model’s use by considering asymptomatic intracranial aneurysm. Our model builds on a simulation model [19] created to examine treatment recommendations based on cost-effectiveness. We demonstrate that incorporating risk aversion leads to “no treatment” recommendations for some types of aneurysm. Furthermore, the use of alternate patient-selected criteria leads to recommendations that vary from [19] in several scenarios. We also discuss the use of the software as a decision support tool to help make individualized treatment recommendations and demonstrate that the computational performance of the algorithm makes its use feasible during a short office visit.     

Ordinal notions of submodularity

We consider several ordinal formulations of submodularity, defined for arbitrary binary relations on lattices. Two of these formulations are essentially due to Kreps [Kreps, D.M., 1979. A representation theorem for “Preference for Flexibility”. Econometrica 47 (3), 565–578] and one is a weakening of a notion due to Milgrom and Shannon [Milgrom, P., Shannon, C., 1994. Monotone comparative statics. Econometrica 62 (1), 157–180]. We show that any reflexive binary relation satisfying either of Kreps’s definitions also satisfies Milgrom and Shannon’s definition, and that any transitive and monotonic binary relation satisfying the Milgrom and Shannon’s condition satisfies both of Kreps’s conditions.     

Optimal selling mechanisms with countervailing positive externalities and an application to tradable retaliation in the WTO

We study revenue-maximizing mechanisms for a seller who sells an indivisible good to several buyers with positive, type-dependent and countervailing allocative externalities. To cope with the difficulty of types obtaining reservation utilities being endogenously determined, we first solve a minimax version of the seller’s problem by generalizing Myerson’s characterization techniques for the non-regular case. The solution is then shown to solve the seller’s original maximin problem as well in our setting. We find that the seller’s optimal mechanism normally features bunching even in the regular case and the type with the lowest expected payoff is typically not an extreme type. As an important illustration of our characterization procedures, we apply our results to the problem of selling retaliation rights in the WTO.     

A stochastic differential game of capitalism

We develop a stochastic differential game of capitalism to analyze the role of uncertainty. In the deterministic game, the firm’s rent is completely taxed away and the firm stops investing completely. In the stochastic game, the government does not tax the firm’s rent completely. The firm posts a positive rate of investment if the firm’s rent exceeds the labor’s income. Although the cooperative solution is indeterminate, cooperation is always Pareto optimal compared to the non-cooperative Markovian Nash equilibrium. For individual rationality, we apply a payoff distribution procedure based on Yeung and Petrosyan (2006) to derive a subgame-consistent solution.     

The econometrics of auctions with asymmetric anonymous bidders

We consider standard auction models when bidders’ identities are not-or are only partially-observed by the econometrician. We first adapt the definition of identifiability to a framework with anonymous bids and explore the extent to which anonymity reduces the possibility of identifying private value auction models. Second, in the asymmetric independent private value model which is nonparametrically identified, we generalize Guerre, Perrigne and Vuong’s estimation procedure [Optimal nonparametric estimation of first-price auctions, Econometrica 68 (2000) 525-574] and consider the asymptotic properties of our multi-step kernel-based estimator. Monte Carlo simulations illustrate the practical relevance of our estimation procedure in small data sets.     

The design of feedback rules in linear stochastic rational expectations models

This paper is concerned with optimal and sub-optimal feedback rules for linear stochastic continuous time models with rational expectations. We consider four types of feedback rules: (1) the optimal but time-inconsistent rule which is available if the controller is able to commit himself or herself; (2) quasi-optimal and time-inconsistent rules of the form w = Dy where w is the vector of instruments, y the state vector and D a matrix of constants possibly with constraints; (3) the optimal time-consistent rule which is also linear in y; (4) ‘over-stable’ rules which have ‘too many’ stable roots. We show that rules of type (1) can be expressed and implemented as a form of integral control, all except type (2) satisfy certainty equivalence and that rules of type (4) will always be inferior to the optimal rule (1). These results are demonstrated in two illustrative examples.     

Indifference pricing with uncertainty averse preferences

We consider the indifference valuation of an uncertain monetary payoff from the perspective of an uncertainty averse decision maker. We study how the indifference valuation depends on the decision maker’s attitudes toward uncertainty. We obtain a characterization of comparative uncertainty aversion and various characterizations of increasing, decreasing, and constant uncertainty aversion.     

Corruption and auctions

We investigate how corruption affects the outcome of a first-price auction (bidding behavior, efficiency and the seller’s expected revenue). The auctioneer approaches the winner to offer the possibility of a reduction in his bid in exchange for a bribe. The bribe can be a percentage of the difference between the winning and the second-highest bid or a fixed amount. We show that there exists a symmetric bidding strategy equilibrium that is monotone, i.e., higher valuation buyers bid higher. Corruption does not affect efficiency but both the auctioneer’s expected bribe and the seller’s expected revenue depend on the format of the bribe payments. We also find the optimal bribe scheme.     

When Ross meets Bell: The linex utility function

At first glance, there would appear to be no relationship between Bell’s (1988) concept of one-switch utility functions and that of a stronger measure of risk aversion due to Ross (1981). We show however that specific assumptions about the behavior of the stronger measure of risk aversion also give rise to the linex utility function which belongs to the class of one-switch utility functions. In particular, this utility class is the only one that satisfies a stronger version of Kimball’s (1993) standard risk aversion over all levels of wealth. We apply our results to consider n$n$th-degree deteriorations in background risk and their effect on risk taking behavior.     

Sieve estimation of panel data models with cross section dependence

In this paper we consider the problem of estimating semiparametric panel data models with cross section dependence, where the individual-specific regressors enter the model nonparametrically whereas the common factors enter the model linearly. We consider both heterogeneous and homogeneous regression relationships when both the time and cross-section dimensions are large. We propose sieve estimators for the nonparametric regression functions by extending Pesaran’s (2006) common correlated effect (CCE) estimator to our semiparametric framework. Asymptotic normal distributions for the proposed estimators are derived and asymptotic variance estimators are provided. Monte Carlo simulations indicate that our estimators perform well in finite samples.     

Modeling college major choices using elicited measures of expectations and counterfactuals

The choice of a college major plays a critical role in determining the future earnings of college graduates. Students make their college major decisions in part due to the future earnings streams associated with the different majors. We survey students about what their expected earnings would be both in the major they have chosen and in counterfactual majors. We also elicit students’ subjective assessments of their abilities in chosen and counterfactual majors. We estimate a model of college major choice that incorporates these subjective expectations and assessments. We show that both expected earnings and students’ abilities in the different majors are important determinants of a student’s choice of a college major. We also consider how differences in students’ forecasts about what the average Duke student would earn in different majors versus what they expect they would earn both influence one’s choice of a college major. In particular, our estimates suggest that 7.8% of students would switch majors if they had the same expectations about the average returns to different majors and differed only in their perceived comparative advantages across these majors.     

Optimal investment decisions when time-horizon is uncertain

Many investors do not know with certainty when their portfolio will be liquidated. Should their portfolio selection be influenced by the uncertainty of exit time? In order to answer this question, we consider a suitable extension of the familiar optimal investment problem of Merton [Merton, R.C., 1971. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373–413], where we allow the conditional distribution function of an agent’s time-horizon to be stochastic and correlated to returns on risky securities. In contrast to existing literature, which has focused on an independent time-horizon, we show that the portfolio decision is affected.     

How useful are no-arbitrage restrictions for forecasting the term structure of interest rates?

We develop a general framework for analyzing the usefulness of imposing parameter restrictions on a forecasting model. We propose a measure of the usefulness of the restrictions that depends on the forecaster’s loss function and that could be time varying. We show how to conduct inference about this measure. The application of our methodology to analyzing the usefulness of no-arbitrage restrictions for forecasting the term structure of interest rates reveals that: (1) the restrictions have become less useful over time; (2) when using a statistical measure of accuracy, the restrictions are a useful way to reduce parameter estimation uncertainty, but are dominated by restrictions that do the same without using any theory; (3) when using an economic measure of accuracy, the no-arbitrage restrictions are no longer dominated by atheoretical restrictions, but for this to be true it is important that the restrictions incorporate a time-varying risk premium.     

A model of the firm in time and space

We consider a multi-plant monopoly that sells to markets which are geographically separated and which stores product over time via an inventory capability. It is assumed that plant average production cost is U-shaped and that, if the output of a plant's production run were sold to a single market at only one point in time, the plant would operate on the falling portion of its average cost curve. Hence, it is in the interest of the firm to aggregate markets, both spatially and temporally, to lower average production cost. We develop the optimal joint interplant spacing-inventory policy. We also consider the effects changes in freight costs, storage costs, and interest charges have on the firm's optimal policy.     

On finite sample properties of alternative estimators of coefficients in a structural equation with many instruments

We compare four different estimation methods for the coefficients of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum empirical likelihood (MEL) estimator and the generalized method of moments (GMM) (or the estimating equation) estimator. Tables and figures of the distribution functions of four estimators are given for enough values of the parameters to cover most linear models of interest and we include some heteroscedastic cases and nonlinear cases. We have found that the LIML estimator has good performance in terms of the bounded loss functions and probabilities when the number of instruments is large, that is, the micro-econometric models with “many instruments” in the terminology of recent econometric literature.     

Optimal inference for instrumental variables regression with non-Gaussian errors

This paper is concerned with inference on the coefficient on the endogenous regressor in a linear instrumental variables model with a single endogenous regressor, nonrandom exogenous regressors and instruments, and i.i.d. errors whose distribution is unknown. It is shown that under mild smoothness conditions on the error distribution it is possible to develop tests which are “nearly” efficient in the sense of Andrews et al. (2006) when identification is weak and consistent and asymptotically optimal when identification is strong. In addition, an estimator is presented which can be used in the usual way to construct valid (indeed, optimal) confidence intervals when identification is strong. The estimator is of the two stage least squares variety and is asymptotically efficient under strong identification whether or not the errors are normal.     

Informational cascades with endogenous prices: The role of risk aversion

In this paper, we show that long run market informational inefficiency and informational cascades can easily happen when trades occur at market clearing prices. We consider a sequential trade model where: (i) the investors’ set of actions is discrete; (ii) dealers and investors differ in risk aversion; (iii) investors’ information is bounded. We show that informational cascade occurs as soon as traders’ beliefs do not differ too sharply. Thus, prices cannot fully incorporate the private information dispersed in the economy.     

Estimating dynamic local interactions models

This paper presents empirical methods for studying a class of local interactions models in which agents’ transitions are affected by their neighbors’ states. We consider an application to urban unemployment and social networks in job search using publicly available cross-section and retrospective data. Most links in our model are local, but some span an entire metropolitan area. Our methods are designed to accommodate the presence of strong cross-sectional dependence arising from these few cross-metro-area links. We also present simple methods to compare data and model spell distributions and to illustrate the model's dynamic properties.