Hugo A. Hopenhayn

Job Turnover and Policy Evaluation: A General Equilibrium Analysis

Recent empirical work indicates that job creation and destruction rates are large, implying significant amounts of job reallocation across firms. This paper builds a general equilibrium model of this reallocation process, calibrates it using data on firm-level dynamics, and evaluates the aggregate implications of policies that interfere with this process. We find that a tax on job destruction at the firm level has a sizable negative impact on total employment: a tax equal to 1 years wages reduces employment by roughly 2.5 percent. More striking, however, are the welfare consequences: the cost in terms of consumption of this same tax is greater than 2 percent. The mechanism through which this welfare loss arises is apparently a decrease in average productivity, since this policy results in a decrease in average productivity of over 2 percent.

Optimal Unemployment Insurance

This paper considers the design of an optimal unemployment insurance system. The problem is modeled as a repeated principalagent problem involving a risk‐averse agent‐the unemployed worker‐and a risk‐neutral principal, which cannot monitor the agents search effort. The optimal long‐term contract subject to the associated incentive constraints is characterized. This contract involves a replacement ratio that decreases throughout the unemployment spell and a wage tax after reemployment that, under some mild regularity conditions, increases with the lenght of the unemployment spell. Some numerical results are presented that suggest that the gains from switching to this optimal unemployment insurance scheme could be quite large. The performance of this optimal contract is also compared to alternative liquidity provision mechanisms.

Vintage Human Capital, Growth, and the Diffusion of New Technology

We develop a model of vintage human capital in which each technology requires vintage-specific skills. We examine the properties of a stationary equilibrium for our economy. The stationary equilibrium is characterized by an endogenous distribution of skilled workers across vintages. The distribution is shown to be single-peaked. Under general conditions, there is a lag between the appearance of a technology and its peak usage, a phenomenon known as diffusion. An increase in the rate of exogenous technological change shifts the distribution of human capital to more recent vintages, thereby increasing the diffusion rate.

Stochastic Monotonicity and Stationary Distributions for Dynamic Economies

The existence and stability of invariant distributions for stochastically monotone processes is studied. The Knaster-Tarski fixed point theorem is applied to establish existence of fixed points of mappings on compact sets of measures that are increasing with respect to a stochastic ordering. Global convergence of a monotone Markov process to its unique invariant distribution is established.under an easily verified assumption. Topkiss theory of supermodular functions is applied to stochastic dynamic optimization, providing conditions under which optimal stationary decisions are monotone functions of the state and induce a monotone Markov process. Applications of these results to investment theory, stochastic growth and industry equilibrium dynamics are given. Copyright 1992 by The Econometric Society.

Tacit collusion in repeated auctions

Abstract This paper considers the question of tacit collusion in repeated auctions with independent private values and with limited public monitoring. McAfee and McMillan show that the extent of collusion is tied to the availability of transfers. Monetary transfers allow cartels to extract full surplus. A folk theorem proved by Fudenberg et al. (Econometrica 62 (1994) 997–1039) shows that transfers of future payoffs are almost as good if players are patient and communicate before auctions. We ask how the scope of collusion is affected if players dispense with explicit communication and their monitoring is limited. Collusion better than bid rotation is still feasible, but full surplus cannot be extracted. This constraint becomes less severe with more players and large cartels can become asymptotically efficient even with very limited monitoring.

Rewarding Sequential Innovators: Prizes, Patents and Buyouts

This paper presents a model of cumulative innovation where firms are heterogeneous in their research ability. We study the optimal reward policy when the quality of the ideas and their subsequent development effort are private information. The optimal assignment of property rights must counterbalance the incentives of current and future innovators. The resulting mechanism resembles a menu of patents that have infinite duration and fixed scope, where the latter increases in the value of the idea. Finally, we provide a way to implement this patent menu by using a simple buyout scheme: The innovator commits at the outset to a price ceiling at which he will sell his rights to a future inventor. By paying a larger fee initially, a higher price ceiling is obtained. Any subsequent innovator must pay this price and purchase its own buyout fee contract.

Innovation Variety and Patent Breadth

When innovations are heterogeneous, it may be advantageous to provide a variety of patents. By trading off patent breadth for length, it is possible that fees are not needed in the optimal policy. We present two examples. The first is a quality-ladder model, in which innovations benefit society directly as well as through their use as building blocks to future inventions, and the rate of arrival for the future innovation is unobserved. More fertile innovations get more breadth for a shorter time. Menus may also be useful in the case of horizontal product differentiation.

Exit, selection, and the value of firms

Abstract This paper studies a competitive dynamic model with firm level uncertainty and derives implications for the distribution of firm values and Tobins q. Allowing for entry and exit, the model determines endogenously the degree of selection. A consequence of this selection is that average industry q values are biased above one. As parameters describing the technology and firm level uncertainty are changed, the equilibrium distribution for q values changes. This comparative statics is developed in the paper.

Labor-market flexibility and aggregate employment volatility

Abstract Recent empirical work for the Spanish Economy indicates that after 1984, when the rules for temporary employment were significantly relaxed, aggregate employment increased but has become highly volatile. The counterpart of this in the labor microevidence is a significant increase in the hazard rates for match destruction. This paper develops a model of job creation and destruction with dismissal costs and analyses the effect of introducing a rule by which all jobs terminated within a given period of time are exempt from these costs. The model is calibrated using microevidence on registered social-security job matches for the Spanish economy.

Optimal Dynamic Lending Contracts with Imperfect Enforceability

In this paper we have developed a general model of borrowing constraints based on the idea of limited enforcement. I our model, borrowing constraints arise as part of the optimal borrowing and lending contract. Our model extends previous theories of borrowing and lending , such as Hart and Moore (1994) allowing for uncertainty and dynamic effects of the resulting credit constraints.