Jan Eeckhout

Gibrat's Law for (All) Cities

Two empirical regularities concerning the size distribution of cities have repeatedly been established: Zipfs law holds (the upper tail is Pareto), and city growth is proportionate. Census 2000 data are used covering the entire size distribution, not just the upper tail. The nontruncated distribution is shown to be lognormal, rather than Pareto. This provides a simple justification for the coexistence of proportionate growth and the resulting lognormal distribution. An equilibrium theory of local externalities that can explain the empirical size distribution of cities is proposed. The driving force is a random productivity process of local economies and the perfect mobility of workers.

Knowledge Spillovers and Inequality

We develop a dynamic model with knowledge spillovers in production. The model contains two opposing forces. Imitation of other firms helps followers catch up with leaders, but the prospect of doing so makes followers want to free ride. The second force dominates and creates permanent inequality. We show that the greater are the average spillovers and the easier they are to obtain, the greater is the free-riding and inequality. More directed copying raises inequality by raising the free-riding advantages of hanging back. Using Compustat and patent-citation data we find that copying is highly undirected.

Sorting and Decentralized Price Competition

We investigate the role of search frictions in markets with price competition and how it leads to sorting of heterogeneous agents. There are two aspects of value creation: the match value when two agents actually trade and the probability of trading governed by the search technology. We show that positive assortative matching obtains when complementarities in the former outweigh complementarities in the latter. This happens if and only if the match-value function is root-supermodular, that is, its nth root is supermodular, where n reflects the elasticity of substitution of the search technology. This condition is weaker than the condition required for positive assortative matching in markets with random search.

On the uniqueness of stable marriage matchings

Abstract A sufficient condition for uniqueness is identified on the preferences in the marriage problem, i.e. two-sided one-to-one matching with non transferable utility. For small economies this condition is also necessary. This class of preferences is broad and they are of particular relevance in economic applications.

Indeterminacy and directed search

The directed search approach assumes each seller posts a fixed price and, ex post, randomly allocates the good should more than one buyer desire the good. This paper assumes sellers can post prices which are contingent on ex post realized demand; e.g. an advertisement might state the Bertrand price should there be more than one buyer, which corresponds to an auction outcome. Competition in fixed prices and ex post rationing describes equilibrium behavior. There is also real market indeterminacy: a continuum of equilibria exists which are not payoff equivalent. Sellers prefer the equilibrium in auctions.

Bilateral Search and Vertical Heterogeneity

The Two-Sided Perfect Matching model is generalised to an Imperfect Matching model with search frictions. A search model is proposed which is characterised by bilateral search and vertical heterogeneity and allows for a generally specified utility function. The fundamental result is that with common beliefs about the evolving population, a unique Imperfect Matching equilibrium exists in iterated strict dominance. This holds independent of the characteristics of the utility function. The properties of equilibrium are analysed for different pay-off specifications. It is shown that for multiplicatively separable pay-offs both Steady State distributions are endogenously partitioned into classes. This fails to hold however out of Steady State. With search frictions disappearing, the limit case of the search model is the Gale-Shapley-Becker Perfect Matching model.

Sorting versus screening: search frictions and competing mechanisms

In a market where sellers compete by posting trading mechanisms, we allow for a general search technology and show that its features crucially affect the equilibrium mechanism. Price posting prevails when meetings are rival, i.e., when a meeting by one buyer reduces another buyers meeting probability. Under price posting buyers reveal their type by sorting ex-ante. Only if the meeting technology is sufficiently non-rival, price posting is not an equilibrium. Multiple buyer types then visit the same sellers who screen ex-post through auctions.

Heterogeneity as a coordination device

A model of directed search with a finite number of buyers and sellers is considered, where sellers compete in direct mechanisms. Buyer heterogeneity and Nash equilibrium results in perfect sorting. The restriction to complementary inputs, that the match value function Q is supermodular, in addition coordinates the sellers’ strategies. In that case, equilibrium implements positive assortative matching, which is efficient and consistent with the stable (cooperative equilibrium) outcome. This provides a non-cooperative and decentralized solution for the Assignment Game. Conversely, if buyers are identical, no such coordination is possible, and there is a continuum of equilibria, one of which exhibits price posting, another yields competition in auctions.

Competitive bargaining equilibrium

In a simple exchange economy we propose a bargaining procedure that leads to a Walrasian outcome as the agents become increasingly patient. The competitive outcome therefore obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. Our bargaining procedure involves bargaining over prices and maximum quantity constraints, and it guarantees convergence to a Walrasian outcome for any standard exchange economy. In contrast, without quantity constraints we show that equilibrium is generically inefficient.

Common value experimentation

In many economic environments, agents often continue to learn about the same underlying state variable, even if they switch action. For example, a workers ability revealed in one job or when unemployed is informative about her productivity in another job. We analyze a general setup of experimentation with common values, and show that in addition to the well-known conditions of value matching (level) and smooth pasting (first derivative), this implies that the second derivatives of the value function must be equal whenever the agent switches action. This condition holds generally whenever the stochastic process has continuous increments. The main appeal of our approach is its applicability, which is demonstrated with two applications featuring common value experimentation: strategic pricing, and job search with switching costs.