Hedi Kallal

Growth in Cities

Recent theories of economic growth, including those of Romer, Porter, and Jacobs, have stressed the role of technological spillovers in generating growth. Because such knowledge spillovers are particularly effective in cities, where communication between people is more extensive, data on the growth of industries in different cities allow us to test some of these theories. Using a new data set on the growth of large industries in 170 U.S. cities between 1956 and 1987, we find that local competition and urban variety, but not regional specialization, encourage employment growth in industries. The evidence suggests that important knowledge spillovers might occur between rather than within industries, consistent with the theories of Jacobs.

Viability and equilibrium in securities markets with frictions

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive linear pricing rule on the entire space of contingent claims - an underlying frictionless linear pricing rule - that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches - a generalization of opportunities of arbitrage. When a market for a non marketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule - the supremum of the underlying frictionless linear pricing rules - for which the original equilibrium does not collapse, when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules.

Arbitrage and Viability in Securities Markets with Fixed Trading Costs

This paper studies foundational issues in securities markets models with fixed costs of trading, i.e. transactions costs that are bounded regardless of the transaction size, such as fixed brokerage fees, investment taxes, operational, and processing costs or opportunity costs. We show that the absence of free lunches in such models is equivalent to the existence of a family of absolutely continuous probability measures for which the normalized securities price processes are martingales. This is a weaker condition than the absence of free lunch in frictionless models, which is equivalent to the existence of an equivalent martingale measure. We also show that the only arbitrage-free pricing rules on the set of attainable contingent claims are those that are equal to the sum of an expected value with respect to any absolutely continuous martingale measure and of a bounded fixed cost functional. Moreover, these pricing rules are the only ones to be viable as models of economic equilibrium.

Minimal returns and the breakdown of the price-volume relation

Abstract We look at stock-market prices and transaction volume on the day of minimal (the minimum for that year) daily returns, from 1885 to 1990. We find that large (in absolute terms) minimal returns show little correlation with transaction volume.

General equilibrium with producers and brokers : Existence and regularity

In this paper we prove the existence of general equilibrium with transaction costs generalizing Hahns (Review of Economic Studies, 1973, 40, 449-461) model by introducing producers and nonconvexities (in particular we allow for increasing returns in transaction sets). We also recover any exchange economy as a special case and this allows us to analyze the effects of small frictions on bid-ask prices, consumption vectors and utilities. We prove that, generically, the induced perturbations are of the same order as the frictions.