Working papers

Extreme Value Theory with Heterogeneous Agents conditionally accepted at Econometrica

Abstract: Extreme value processes feature in any economic model in which agents receive a number of draws from some distribution and we examine the behavior of the maximum in the limit as the number of draws becomes large. This paper asks: Do the average outcomes of such processes change when different agents receive a different number of draws? To answer this, we allow the number of draws an agent receives from the underlying distribution (e.g. of productivities, ideas, or utility shocks) to be given by a search technology, which reflects heterogeneity in the expected number of draws across different types of agents. We derive a new class of extreme value distributions that generalize the three standard distributions (Fréchet, Gumbel, Weibull) by incorporating heterogeneity across agent types. We generalize a result from Gabaix, Laibson, Li, Li, Resnick, and de Vries (2016) regarding extreme value outcomes and consider applications to aggregate productivity, markups, and social networks.

Private and Social Learning in Frictional Product Markets (with Guido Menzio)

Abstract: We introduce dynamic learning in the static search-theoretic framework of imperfect competition of Butters (1977), Varian (1980) and Burdett and Judd (1983). We consider two forms of learning: memory and word of mouth. In the model with memory, long-lived buyers not only learn about some new sellers in every period, but they also remember some of the sellers about which they learned in the past. In the model with word of mouth, short-lived buyers not only learn about sellers through search, but they also learn about sellers by talking to previous buyers, which refer them to the best seller of which they are aware. Both models are tractable. We establish the existence and uniqueness of equilibrium and characterize the dynamics of the product market. Memory increases the quantity of information available to buyers and, for this reason, leads to higher concentration and competition. Word of mouth increases the quality of information available to buyers and, for this reason, leads to higher concentration, but does not increase competition as much as memory.

Consumer Choice, Market Power, and Inflation (with A. Bajaj) R&R at European Economic Review

Abstract: We introduce consumer choice into a search-theoretic model of monetary exchange. In contrast to standard search models featuring bilateral meetings, consumers can meet multiple sellers and choose a seller with whom to trade. Market power is endogenized through competitive search and it is influenced by the degree of consumer choice. We consider the effects of greater consumer choice on both market power and the welfare cost of inflation. Surprisingly, we find that greater consumer choice can have a nonmonotonic effect on market power. At lower levels of consumer choice, an increase in the degree of consumer choice tends to increase firms' market power, while the opposite is true at higher levels. When we calibrate the model to U.S. data, we find that despite greater consumer choice having a positive effect on welfare overall, it can also amplify the negative welfare effects of inflation, making it significantly more costly.

Work in progress

Personalized Pricing and Competitive Dispersion

Abstract: This paper examines the effects of competitive dispersion on both personalized pricing and uniform pricing in an environment where the number of competing firms varies across consumers. We define an increase in competitive dispersion as a mean-preserving spread in the distribution of the number of competing firms. We provide conditions under which greater competitive dispersion decreases the average markup under uniform pricing, but increases the average markup under personalized pricing. We find that the degree of competitive dispersion has a significant effect on markups even in the competitive limit where the expected number of competing firms becomes large. Relative to uniform pricing, personalized pricing may either benefit or harm consumers depending on the degree of competitive dispersion. If competitive dispersion is relatively low, personalized pricing benefits consumers and harms firms relative to uniform pricing. However, if competitive dispersion is sufficiently high, personalized pricing harms consumers and benefits firms.

Consumer Choice and Nonlinear Pricing in Competitive Search Equilibrium

Abstract: We study the effects of competition on nonlinear pricing in a competitive search model where the distribution of buyer types is endogenous. In the first stage (i.e. competitive search), a large number of sellers compete by offering price-quantity schedules that attract buyers to their submarket. In the second stage (i.e. imperfect competition), buyers contact a finite number of sellers within a submarket and choose a seller from this choice set. The type of a consumer is their valuation of their chosen seller’s good, which is private information. The distribution of types depends on both the underlying distribution of valuations, the endogenous seller-buyer ratio, and properties of the search technology (i.e. the distribution of the size of buyers’ choice sets). We find that greater competition leads to a decrease in the extent of nonlinear pricing, lower quantity distortions, and wider market coverage, i.e. more consumers purchase. In the competitive limit, the effects of private information are eliminated by consumers’ choice of seller and competitive search delivers the first best.

Publications

When is Competition Price-increasing? The Impact of Expected Competition on Prices RAND Journal of Economics,, 55 (4), pp 627-657, 2024

Abstract: We examine the effect of expected competition on markups in a random utility model where the number of competing firms may differ across consumers. Firms observe consumers’ utility shocks and set prices using “limit pricing” or Bertrand competition. We derive a precise condition under which the expected markup across consumers can be represented by a simple expression involving consumers’ expected utility and the expected demand. This simple expression delivers a general condition under which greater expected competition is price-increasing. The behavior of markups depends on the distribution of utility shocks, consumers’ outside option, the expected number of competing firms, and the distribution of the number of competing firms.

Efficiency in Search and Matching Models: A Generalized Hosios Condition (with B. Julien) Journal of Economic Theory, 193, April 2021 PDF file

Abstract: When is entry efficient in markets with search and matching frictions? This paper generalizes the well-known Hosios condition to dynamic environments where the expected match output depends on the market tightness. Entry is efficient when buyers' surplus share is equal to the matching elasticity plus the surplus elasticity (i.e. the elasticity of the expected match surplus with respect to buyers). This ensures agents are paid for their contribution to both match creation and surplus creation. For example, vacancy entry in the labor market is efficient only when firms are compensated for the effect of job creation on both employment and labor productivity.

Unemployment and the Labor Share (with Petr Sedlacek) Journal of Monetary Economics, 94, pp 41-59, 2018 PDF file

Abstract: The labor share fluctuates over the business cycle. To explain this behavior, we develop a novel model featuring direct competition between heterogeneous firms to hire workers. This simultaneously endogenizes both average match productivity and the division of output between workers and firms. In existing matches, wages partly reflect labor market conditions at the time of hiring. A positive TFP shock therefore reduces the aggregate labor share, making it counter-cyclical. However, greater competition and lower unemployment increase labor’s share among new firms. As more firms enter, the aggregate labor share rises and eventually overshoots its initial level, as in the data.