On the first-order approach in principal-agent models with hidden borrowing and lending

We provide sufficient conditions for the validity of the first-order approach for two-period dynamic moral hazard problems where the agent can save and borrow secretly. The first-order approach is valid if the following conditions hold: (i) the agent has non-increasing absolute risk aversion utility (NIARA), (ii) the output technology has monotone likelihood ratios (MLR), and (iii) the distribution function of output is log-convex in effort (LCDF). Moreover, under these three conditions, the optimal contract is monotone in output. We also investigate a few possibilities of relaxing these requirements.     

Contracts with endogenous information

I study covert information acquisition and reporting in a principal agent problem allowing for general technologies of information acquisition. When posteriors satisfy two dimensional versions of the standard First Order Stochastic Dominance and Concavity/Convexity of the Distribution Function conditions, a first-order approach is justified. Under the same conditions, informativeness and riskiness of reports are equivalent. High powered contracts, that make the agent's informational rents more risky, are used to increase incentives for information acquisition, insensitive contracts are used to reduce incentives for information gathering. The value of information to the agent is always positive. The value of information to the principal is ambiguous.     

Distributions for the first-order approach to principal-agent problems

Summary. The first-order approach is a technical shortcut widely used in agency problems. The best known set of sufficient conditions for its validity are due to Mirrlees and Rogerson and require that the distribution function is convex in effort and has a likelihood ratio increasing in output. Only one nontrivial example was so far known to satisfy both properties. This note provides two rich families of examples displaying both properties. Received: December 4, 2000; revised version: December 10, 2001     

Computing Cournot equilibrium through maximization over prices

This paper presents a characterization of internal Cournot equilibrium based on first-order conditions corresponding to profit maximization over prices. This characterization may yield significant computational advantage as demand functions need not be inverted and simple first-order conditions are obtained.     

Orthogonal Parameters and Panel Data

This paper describes a class of consistent estimators for short panels with fixed effects. The method is to find an orthogonal reparametrization of the fixed effects and then to integrate the new effects from the likelihood with respect to an appropriately chosen prior density. The resulting marginal posterior densities of the common parameters have modes that are shown to be consistent in the models examined here. The main result concerns the first-order autoregressive model with agent specific intercepts where the likelihood is conditional on the set of initial observations. This paper provides a consistent likelihood-based estimator for this model. Some numerical illustrations are given. The first-order conditions for the posterior mode can also be thought of as new moment conditions for GMM estimation.     

Multi-unit auctions with private information: an indivisible unit continuous price model

We construct a model of multi-unit auctions in which I bidders bid for two indivisible units of a common value good. Using a first-order approach, we find that there are equilibria in which bidders bid the same price for both units in the discriminatory auction, but not in the uniform auction. When there are only two bidders, under certain conditions, there are linear equilibria for both the discriminatory and the uniform auction formats. In all equilibria, bidders equalize the expected marginal benefit of bidding to the marginal costs of bidding. We show that comparison of the seller??s expected revenue across auction formats depends only on the ratio of the precision of private information to the precision of public information.     

Ranking agencies under moral hazard

Summary. We provide rankings across uncertain outputs generated by agents functioning within the Principal-Agent paradigm. For agents who are identical except for their productivity, a necessary (but not sufficient) condition for an agent to be preferred is that her output dominates that of lower agents in the sense of First Degree Stochastic Dominance (FDSD) at every level of effort. Sufficient conditions are based on Blackwells ranking of information systems and involves a characterization of FDSD using stochastic matrices. Our conditions for ranking outputs extends earlier results concerning the value of information within the agency framework. We also show how our techniques can be adapted to rank agents even if the first-order approach for determining optimal contracts fails to hold.Received: April 2, 1996; revised version: October 30, 1996This revised version was published online in February 2005 with corrections to the cover date.     

The Theory of Moral Hazard and Unobservable Behaviour: Part I

Principal-agent models are studied, in which outcomes conditional on the agent's action are uncertain, and the agent's behaviour therefore unobservable. For a model with bounded agent's utility, conditions are given under which the first-best equilibrium can be approximated arbitrarily closely by contracts relating payment to observable outcomes. For general models, it is shown that the solution may not always be obtained by using the agent's first-order conditions as constraint. General conditions of Lagrangean type are given for problems in which contracts are finite-dimensional.     

Computation of non-linear continuous optimal growth models: experiments with optimal control algorithms and computer programs

In this paper we discuss the use of optimal control methods for computing non-linear continuous optimal growth models. We have discussed various recently developed algorithms for computing optimal control, involving step-function approximations, Runge–Kutta solutions of differential equations, and we suggest that the discretization approach is preferable to methods which solve first-order optimality conditions. We have surveyed some powerful computer programs by : , and for computing such models numerically. These programs have no substantial optimal growth modelling applications yet, although they have numerous engineering and scientific applications. A computer program named by is developed in this study. Results are reported for computing the Kendrick–Taylor optimal growth model using and programs based on the discretization approach. References are made to the computational experiments with and . The results are used to compare and evaluate mathematical and economic properties, and computing criteria. While several computer packages are available for optimal control problems, they are not always suitable for particular classes of control problems, including some economic growth models. The -based and , however, offer good opportunities for computing continuous optimal growth models. It is argued in this paper, that optimal growth modellers may find that these recently developed algorithms and computer programs are relatively preferable for a large variety of optimal growth modelling studies.     

Bunching and second-order conditions: A note on optimal tax theory

We present in this note a simple non-linear taxation model in which the agents are indexed by a one-dimensional parameter. Our purpose is to propose a method of resolution and to compute the optimal solution. We point out that the solution could not always be obtained with a simple derivation of the first-order conditions of the control problem under consideration, and we show the necessity to take into account the second-order conditions.     

Relative performance evaluation in a multi-plant firm

Summary. We analyze optimal compensation schedules for the directors of two plants belonging to the same owner and producing the same good but serving geographically differentiated markets. Since the outcome of each director depends on his own effort and on a random variable representing market conditions, the problem takes the form of a principal multi-agent model. We first provide appropriate extensions of the MLR and CDF conditions that ensure the validity of the first-order approach in the single agent case. Then, we show that affiliation of the random variables is a necessary and sufficient condition for the compensation of one director to negatively and monotonically depend on the performance of the other.Received: 23 July 2004, Revised: 18 February 2005, JEL Classification Numbers: D23, D82.I thank Ray Rees and an anonimous referee for helpuful comments and suggestions. Support from CES (Center for Economic Studies), University of Munich is gratefully aknowledged.     

Market Power and Buffer Stocks

The first-order conditions for a monopolist inventory holder are found under more general conditions than previously. It is found that monopolist storers facing inelastic demand will carry over more stock than they would with competition unless the elasticity of demand b increasing as price decreases or is constant. The competitive stocks equilibrium is identified and found to be Pareto optimal and hence Sams' result that there will be no losers from a rent-maximizing buffer stock policy is shown to be wrong.     

On the moral hazard problem without the first-order approach

We study the moral hazard problem without the first-order approach or other common structure. We present sufficient conditions under which the shadow value of simultaneously tightening the minimum payment and individual rationality constraints has a simple and intuitive expression. We then show how this expression can be used to perform comparative statics exercises in which we study (i) the effect of a change in the agent?s wealth on the well-being of the principal; and (ii) the effects of the outside option and minimum payment on the effort level optimally implemented.     

Do downturns cause desperation? The effect of economic conditions on suicide rates in Canada

There is conflicting evidence concerning the impact of macroeconomic conditions on suicide rates. To help resolve this pertinent question, we present evidence using Canadian data. We estimate feasible generalized least squares models of annual gender-specific suicide rates in the working age population (aged 25–64) using data from each of the 10 Canadian provinces over the period 1982 to 2007. We allow for heteroscedasticity across provinces and first-order autocorrelation common to all provinces. We posit that suicide rates in this population are a function of macroeconomic conditions (current and lagged unemployment rates and real per capita GDP) and other determinants that might be correlated with macro conditions, such as physician supply. We find that different factors affect suicide rates across genders and that some of the results are sensitive to the specification of the model we use and the regressors included. Generally, economic conditions affect men more than women; suicide rates are counter-cyclical and a higher supply of psychiatrists in a province is correlated with lower suicide rates.     

Heterogeneity of First-order Risk Aversion and the Equity Premium

I show that stockholders and non-stockholders can coexist in equilibrium even if securities markets are perfect and complete. This is due to a heterogeneous safety inclination, which is defined as heterogeneity in first-order risk aversion (Segal and Spivak, 1990). A static two-security market model is analysed by the mean–standard deviation approach, where safety inclination is described by the degree of the marginal rate of substitution between the mean and the standard deviation at a certain point. In equilibrium, aggregate shocks may be concentrated on stockholders, which may lead to a high equity premium.
JEL Classification Numbers: D81, E44.     

Limited knowledge of demand and oligopoly equilibria

In a standard model of oligopoly with differentiated products, the existence of an equilibrium at which the first-order conditions for profit maximisation are simultaneously satisfied for all firms is proved and this is done without imposing any restrictions on the demand functions. This is an equilibrium in the following sense: although some firms may not necessarily be maximising their profits, nevertheless if each firm's knowledge of demand is limited to the linear approximation of its own demand curve, then it will believe that it is indeed maximising its profits.     

Alternative approach to determine the common cycle time for a multi-item production system with discontinuous deliveries and failure in rework

This study employs an alternative approach to determine common production cycle time for a multi-item production system with discontinuous deliveries and failure in rework. A straightforward approach using algebraic derivation is proposed here to reexamine a specific common cycle time problem studied by Chiu et al. (2013a,b), where they used the conventional method with the need of applying first-order and second-order differentiations to system cost function for proof of convexity before deriving the optimal common cycle time. The result of this study is confirmed to be identical to that was obtained in Chiu et al. (2013a,b). This alternative approach enables practitioners who may not have sufficient knowledge of differential calculus to manage the real-life multi-item production systems more effectively.     

Shadow directional distance functions with bads: GMM estimation of optimal directions and efficiencies

Because of its greater flexibility, the directional distance function (DDF) has been employed with increasing frequency to estimate multiple-input and multiple-output production, where inputs and outputs can be good or bad. However, typically researchers make three restrictive assumptions. First, they assume a direction of movement of firm production toward the frontier. Second, they assume that actual quantities of inputs and outputs are allocatively or price efficient. Third, they assume exogeneity of all inputs and all outputs, except for the normalized one. The first contribution of this paper is to include parameters to estimate optimal directions which correspond to the firm’s profit-maximizing (PM) position. The second contribution is to generalize the DDF to a shadow-quantity DDF. This entails adding distortion parameters to each input and output quantity of the DDF, creating shadow quantities. To estimate the shadow quantities and the structural parameters, we form the shadow DDF system, which includes the shadow DDF and all the first-order price equations from the shadow-PM problem. These include prices for bad inputs and bad outputs, where we approximate their missing prices for use in their first-order price equations. The third contribution is that we estimate the shadow DDF system using a Generalized Method of Moments approach, where all variables are potentially endogenous. This approach is simpler than the Bayesian one employed in Atkinson et al. (Estimating efficient production with bad inputs and outputs using latent prices and optimal directions. Working paper, University of Georgia, Athens, 2016), which estimated shadow prices and optimal directions. Using the same data set, both sets of results are qualitatively very similar, although they differ somewhat quantitatively.     

Dynamic factor demands under imperfect competition: the Greek manufucturing industry 1958–1981

The intertemporal maximization problem of the firm under adjustment costs for its factors of production and imperfect competition in the output market is considered. The first-order conditions, with respect to capital and labour, the production function and the demand equation have been jointly estimated using Greek manufacturing data and values for the structural parameters have been obtained. The estimates are plausible and most of them significant. Tests of the overidentifying restirctions are unable to reject the overall specification of the model at conventional levels of significance.     

Trade and transport connectivity: a spatial approach

This article aims to analyse whether transport connectivity affects trade flows using a spatial approach. We consider first-order contiguity and incorporate logistics network structure dependence in a spatial autoregressive model. The results provide evidence regarding the role of the location of logistics platforms for satisfying existing demand for transport structure in Spain.