Working papers

Extreme Value Theory with Heterogeneous Agents (with Louis Becker) R&R at Econometrica

Abstract: Extreme value processes are widespread in economics. Typically, 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 outcomes of such processes change when different agents may 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 can be interpreted as representing either search frictions or heterogeneity across different types of agents. We derive a general expression for the extreme value distribution and show that it need not assume any of the three standard types. We generalize a result from Gabaix et al. (2016) regarding extreme value outcomes and consider some 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 and Private Information in Monetary Exchange

Abstract: We introduce consumer choice into a competitive search model of monetary exchange. In contrast to standard search models featuring bilateral meetings, there is a general meeting technology which allows consumers to meet multiple sellers and choose a seller with whom to trade. Consumer choice is influenced by random utility shocks which are private information. Competitive search equilibrium delivers the efficient allocation at the Friedman rule, but it cannot decentralize the first-best allocation due the presence of private information, which distorts the quantities traded in equilibrium. Our main insight is that greater seller entry and more competition between sellers to attract consumers can alleviate the quantity distortion due to private information, bringing the economy closer to the first-best. In fact, in the competitive limit, we find that consumer choice eliminates the effects of private information and competitive search can deliver the first-best allocation at the Friedman rule.

Consumer Choice, Market Power, and Inflation (with A. Bajaj)

Abstract: Consumers today have access to a large amount of online information prior to making purchases, enabling a greater degree of informed choice in retail trade. This paper develops a search-theoretic model of retail trade that features both monetary exchange and the possibility of informed choice by consumers. Market power is endogenized through competitive search and it is influenced by the degree of consumer choice. We consider the effects of greater informed choice by consumers on both market power and the welfare cost of inflation. Surprisingly, we find that greater informed choice by consumers can have a non-monotonic effect on market power. At lower levels of informed 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 choice having a positive effect on welfare overall, it can also amplify the negative 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.

Publications

When is Competition Price-increasing? The Impact of Expected Competition on Prices RAND Journal of Economics (accepted)

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.