Common Shocks and Relative Compensation Schemes

This paper studies qualitative properties of an optimal contract in a multi-agent setting in which agents are subject to a common shock. We derive a necessary and sufficient condition for the optimal reward of an agent to be a decreasing (increasing) function of the outputs of the other agents, under the assumption that the agents' outputs are informative signals of the value of the common shock. The condition is that the likelihood ratio of a given outcome with high versus low effort be a decreasing (increasing) function of the common shock. We derive conditions on the way the common shock affects the marginal product of effort under which the likelihood ratio is decreasing for all output levels, or increasing for some output levels and decreasing for others.optimal incentive contracts, common shocks, multi agents, monotone likelihood ratio

NORMATIVE PROPERTIES OF STOCK MARKET EQUILIBRIUM WITH MORAL HAZARD

This paper presents a model of stock market equilibrium with a finite number of corporations and studies its normative properties. Each firm is run by a manager whose effort is unobservable and influences the probabilities of the firm’s outcomes. The Board of Directors of each firm chooses an incentive contract for the manager which maximizes the firm’s market value. With a finite number of firms, the equilibrium is constrained Pareto optimal only when investors are risk neutral and firms’ outcomes are independent. The inefficiencies which arise when investors are risk averse, or when firms are influenced by a common shock, are studied and it is shown that under reasonable assumptions there is under investment in effort in equilibrium. The inefficiencies exist when the firms are not completely negligible, as is typical of the large corporations with dispersed ownership traded on public exchanges in the US. In the idealized case where firms of each type are replicated and replaced by a continuum of firms of each type with independent outcomes, the inefficiencies disappear.market, economics, stock

An Equilibrium Model of Managerial Compensation

This paper studies a general equilibrium model with two groups of agents, investors (shareholders) and managers of firms, in which managerial effort is not observable and influences the probabilities of firms' outcomes. Shareholders of each firm offer the manager an incentive contract which maximizes the firm's market value, under the assumption that the financial markets are complete relative to the possible outcomes of the firms. The paper studies two sources of inefficiency of equilibrium. First, when investors are risk averse and effort influences probability, market-value maximization differs from maximization of expected utility. Second, because the optimal contract exploits all sources of information for inferring managerial effort, when firms' outputs are correlated the contract of a manager depends on the outcomes of other firms. This leads to an external effect of the effort of one manager on the compensation of other managers, which market-value maximization ignores. We show that under typical conditions these two effects lead to an under-provision of effort in equilibrium. These inefficiencies disappear however if each firm is replicated, and in the limit there is a continuum of firms of each type.general equilibrium, incentive contracts, inefficiencies

WHICH IMPROVES WELFARE MORE: NOMINAL OR INDEXED BOND?

Despite economists'' long standing arguments in favor of systematic indexation of loan contracts to remove the risks associated with fluctuations in the purchasing power of money (Jevons (1875), Marshall (1887, 1923), F~lsher (1922), Friedman (1991)), surprisingly few loan contracts are indexed in most Western Eclonomies. fin the United States even thirty year corporate and government bonds are not indexed. The situation is however different in many Latin American countries where indexing is widely used as a way of coping with high and variable inflation rates. What seems difiicult to eicplain is that it takes lvgh variability in inflation rates before private sector agents shift from lmindexed to indexed contracts. In practice, indexing a loan contract m.eans linking its payoff to the value of an officially computed price index such as the Consumer Price Index (CPI). Such an index is always an imperfect measure of the purchasing power of money: in particular, it fluctuates not only with variations in the general level of prices but also varies with changes in the relative prices of goods. This paper formalizes the idea that the imperfections of indexing may serve tal explain why agents prefer nominal bonds in economies with a low variability in purchasing power of money and only resort to indexing when the variability becomes sufficiently high. The model is a variant of the two-period general equilibrium model with incomplete markets (GEI) in which the purchasing power of money depends on a (broadly defined) measure of the amount of money available in the economy and on an index of real output. The objective of the analysis is to compare two second-best situations, in which in addition to a given security structure, there is either a nominal bond which has the risks induced by fluctuations in the purchasing power of money or an indexed bond which has the risks induced by relative price fluctuations. Adding a bond to an existing market structure has two effects: the first is the direct effect of increasing the span of the fmancial markets i.e. increasing the opportunity sets of agents for transferring income; the second is the indirect effect of changing spot and security prices, which can either increase or decrease agents'' welfare. This paper only compares direct effects, all indirect effects being absent by virtue of the specification of agents'' preferences. The direct effects are always present, even with more general preferences, but some of the results that we

THE PROBABILITY APPROACH TO GENERAL EQUILIBRIUM WITH PRODUCTION

We develop an alternative approach to the general equilibrium analysis of a stochastic production economy when firms’ choices of investment influence the probability distributions of their output. Using a normative approach we derive the criterion that a firm should maximize to obtain a Pareto optimal equilibrium: the criterion expresses the firm’s contribution to the expected social utility of output, and is not the linear criterion of market value. If firms do not know agents utility functions, and are restricted to using the information conveyed by prices then they can construct an approximate criterion which leads to a second-best choice of investment which, in examples, is found to be close to the first best.equilibrium, production

The Stock Market in the Overlapping Generations Model with Production

This paper studies a simple OLG model with production under the assumption that capital investment is completely irreversible: installed capital cannot be transformed back into consumption good nor transferred from one firm to another. Since firms cannot be dismantled at each generational change without loosing their value, their ownership is transmitted from generations to generations through a stock market. The paper shows that the financial price of a firm can be lower than the replacement value of its capital without creating arbitrage or dampening the incentives to invest. This possibility changes the long-run behavior of the equilibrium, but only for economies with under-accumulation. In the stock market dynamics these economies have two steady states, the Diamond steady state and the Golden Rule. The Diamond steady stable is locally saddle-point stable and can be reached by only one trajectory on which the financial price and replacement value of firms coincide at all times. All other trajectories on which there is a discount on equity converge (when they converge) to the Golden Rule which is locally stable: the discount on equity has the same effect as an increase of the savings of the young, which lowers the interest rate, and increases investment and wages at the next generation, a virtuous cycle which leads to the efficient long-run steady state. On all these trajectories the equity prices are larger than the fundamental value of future dividends and thus include a bubble component.

Demography and the Long-run Predictability of the Stock Market

Stock market price/earnings ratios should be influenced by demography. Since demography is predictable, stock returns should be as well. We provide a simple stochastic OLG model with a cyclical structure that generates cyclical P/E ratios. We calibrate the model to roughly fit the cyclical features of historical P/E ratios.Demography, Price earnings ratio, Returns, Efficient markets, Baby-boom, Savings