“Relative Price Dispersion: Evidence and Theory,” with Greg Kaplan, Leena Rudanko and Nicholas Trachter, American Economic Journal: Microeconomics, Forthcoming.
We use a large dataset on retail pricing to document that a sizeable portion of the cross-sectional variation in the price at which the same good trades in the same period and in the same market is due to the fact that stores that are, on average, equally expensive set persistently different prices for the same good. We refer to this phenomenon as relative price dispersion. We show that relative price dispersion might stem from sellers’ attempts to discriminate between high-valuation buyers who need to make all of their purchases in the same store and low-valuation buyers who are willing to purchase different items from different stores. We calibrate our theory and show that it is not only consistent with the extent and sources of dispersion in the price that different sellers charge for the same good, but also with the extent and sources of dispersion in the prices that different households pay for the same basket of goods.
“The (Q,S,s) Pricing Rule,” with Kenneth Burdett, Review of Economic Studies, 2018, 85 (2), 892-928.
We introduce menu costs in the search-theoretic model of imperfect competition of Burdett and Judd (1983). When menu costs are not too large, the equilibrium is such that sellers follow a (Q,S,s) pricing rule. According to the rule, a seller lets inflation erode the real value of its nominal price until it reaches some point s. Then, the seller pays the menu cost and resets the real value of its nominal price to a point randomly drawn from a distribution with support [S,Q], where s<S<Q. A (Q,S,s) equilibrium differs with respect to a standard (S,s) equilibrium: (i) In a (Q,S,s) equilibrium, sellers sometimes keep their nominal price constant to avoid paying the menu cost, other times because they are indifferent to changes in the real value of their price. An exploratory calibration reveals that menu costs account less than half of the observed duration of nominal prices. (ii) In a (Q,S,s) equilibrium, higher inflation leads to higher real prices, as sellers pass onto buyers the cost of more frequent price adjustments, and to lower welfare.
“Equilibrium Price Dispersion Across and Within Stores,” with Nicholas Trachter, Review of Economic Dynamics, 2018, 28 (2), 205-220.
We develop a search-theoretic model of the product market that generates price dispersion across and within stores. Buyers differ with respect to their ability to shop around, both at different stores and at different times. The fact that some buyers can shop from only one seller while others can shop from multiple sellers causes price dispersion across stores. The fact that the buyers who can shop from multiple sellers are more likely to be able to shop at multiple times causes price dispersion within stores. Specifically, it causes sellers to post different prices for the same good at different times in order to discriminate between different types of buyers.
“The (Q,S,s) Pricing Rule: A Quantitative Analysis,” with Kenneth Burdett, Research in Economics, 2017, 71 (4), 784-797.
Are nominal prices sticky because menu costs prevent sellers from continuously adjusting their prices to keep up with inflation or because search frictions make sellers indifferent to any real price over some non-degenerate interval? The paper answers the question by developing and calibrating a model in which both search frictions and menu costs may generate price stickiness and sellers are subject to idiosyncratic shocks. The equilibrium of the calibrated model is such that sellers follow a (Q,S,s) pricing rule: each seller lets inflation erode the effective real value of the nominal prices until it reaches some point s and then pays the menu cost and sets a new nominal price with an effective real value drawn from a distribution with support [S,Q], with s<S<Q. Idiosyncratic shocks short-circuit the repricing cycle and may lead to negative price changes. The calibrated model reproduces closely the properties of the empirical price and price-change distributions. The calibrated model implies that search frictions are the main source of nominal price stickiness.
“Shopping Externalities and Self-Fulfilling Unemployment Fluctuations,” with Greg Kaplan, Journal of Political Economy, 2016, 124 (3), 771-825.
We propose a novel theory of self-fulfilling unemployment fluctuations. When a firm increases its workforce, it increases the demand facing other firms—as employed workers spend more than unemployed workers—and decreases the extent of competition facing other firms—as employed workers have less time to search for low prices than unemployed workers. In turn, the increase in demand and the decline in competition induces other firms to hire more labor in order to scale-up their presence in the product market. The feedback between employment and product market conditions generates multiple equilibria—and the possibility of self-fulfilling fluctuations—if the differences in the shopping behavior of employed and unemployed workers are large enough. Empirical evidence on spending, shopping and prices paid suggests that this is the case.
“Equilibrium Price Dispersion with Sequential Search,” with Nicholas Trachter, Journal of Economic Theory, 2015, 160 (6), 188-215.
The paper studies equilibrium pricing in a product market for an indivisible good where buyers search for sellers. Buyers search sequentially for sellers, but do not meet every sellers with the same probability. Specifically, a fraction of the buyers’ meetings lead to one particular large seller, while the remaining meetings lead to one of a continuum of small sellers. In this environment, the small sellers would like to set a price that makes the buyers indifferent between purchasing the good and searching for another seller. The large seller would like to price the small sellers out of the market by posting a price that is low enough to induce buyers not to purchase from the small sellers. These incentives give rise to a game of cat and mouse, whose only equilibrium involves mixed strategies for both the large and the small sellers. The fact that the small sellers play mixed strategies implies that there is price dispersion. The fact that the large seller plays mixed strategies implies that prices and allocations vary over time. We show that the fraction of the gains from trade accruing to the buyers is positive and non-monotonic in the degree of market power of the large seller. As long as the large seller has some positive but incomplete market power, the fraction of the gains from trade accruing to the buyers depends in a natural way on the extent of search frictions.
“The Morphology of Price Dispersion,” with Greg Kaplan, International Economic Review, 2015, 56 (4), 1165-1206.
This paper is a study of the shape and structure of the distribution of prices at which an identical good is sold in a given market and time period. We find that the typical price distribution is symmetric and leptokurtic, with a standard deviation between 19% and 36%. Only 10% of the variance of prices is due to variation in the expensiveness of the stores at which a good is sold, while the remaining 90% is due, in approximately equal parts, to differences in the average price of a good across equally expensive stores and to differences in the price of a good across transactions at the same store. We show that the distribution of prices that households pay for the same bundle of goods is approximately Normal, with a standard deviation between 9% and 14%. Half of this dispersion is due to differences in the expensiveness of the stores where households shop, while the other half is mostly due to differences in households’ choices of which goods to purchase at which stores. We find that households with fewer employed members pay lower prices, and do so by visiting a larger number of stores, rather than by shopping more frequently.
“Sticky Prices: A New Monetarist Approach,” with Allen Head, Lucy Qian Liu and Randall Wright, Journal of the European Economic Association, 2012, 10 (5), 939-973 (Lead article).
Why do some sellers set prices in nominal terms that do not respond to changes in the aggregate price level? In many models, prices are sticky by assumption. Here it is a result. We use search theory, with two consequences: prices are set in dollars since money is the medium of exchange; and equilibrium implies a nondegenerate price distribution. When money increases, some sellers keep prices constant, earning less per unit but making it up on volume, so profit is unaffected. The model is consistent with the micro data. But, in contrast with other sticky-price models, money is neutral.
“A Search Theory of Rigid Prices,” PIER Working Paper 07-031 (2007).
This paper studies price dynamics in a product markets characterized by: (a) search frictions—in the sense that it takes time for a buyer to find a seller that produces a version of the good he likes; (b) anonymity—in the sense that sellers cannot price discriminate between first-time buyers and returning costumers; (c) asymmetric information—in the sense that sellers are subject to idiosyncratic shocks to their marginal cost of production and privately observe the shocks’ realizations. I find that the joint dynamics of costs and prices may be very different than in a standard Walrasian market. When shocks are i.i.d., the price remains constant in the face of fluctuations in a seller’s marginal cost. When shocks are moderately persistent, the price adjusts slowly and imperfectly in response to changes in a seller’s cost. Finally, when shocks are sufficiently persistent, the price adjusts instantaneously and efficiently as soon as a seller’s production cost varies.