通货膨胀、价格分散和福利：消费者搜索的作用

Federal Reserve Board, Washington, D.C.ISSN 1936-2854 (Print)ISSN 2767-3898 (Online) Inflation, Price Dispersion, and Welfare: The Role of ConsumerSearch Francisca Sara-Zaror 2024-047 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminarymaterials circulated to stimulate discussion and critical comment.The analysis and conclusions set forthare those of the authors and do not indicate concurrence by other members of the research staff or theBoard of Governors. References in publications to the Finance and Economics Discussion Series (other thanacknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Inflation, Price Dispersion, and Welfare:The Role of Consumer Search Francisca Sara-Zaror∗†‡ May 21, 2024 Abstract In standard macroeconomic models, the costs of inflation are tightly linkedto the price dispersion of identical goods.Therefore, understanding how pricedispersion empirically relates to inflation is crucial for welfare analysis.In thispaper, I study the relationship between steady-state inflation and price disper-sion for a cross section of U.S. retail products using scanner data. By comparingprices of items with the same barcode, my measure of relative price dispersioncontrols for product heterogeneity, overcoming an important challenge in the lit-erature.I document a new fact:price dispersion of identical goods increasessteeply around zero inflation and becomes flatter as inflation increases, display-ing aΥ-shaped pattern.Current sticky-price models are inconsistent with thisfinding. I develop a menu-cost model with idiosyncratic productivity shocks andsequential consumer search that reproduces the new fact and exhibits realisticprice-setting behavior. In the model, inflation-induced price dispersion increasesshoppers’ incentives to search for low prices and thus competition among retailers.The positive welfare-maximizing inflation rate optimally trades off the efficiencygains from lower markups and the resources spent on search.JELCodes: E31, E50, L11, L16. 1Introduction A salient feature of micro-level data is that the prices of identical goods vary acrosssellers. In current macroeconomic models, inflation is a crucial determinant of price dis-persion, and the costs of inflation mainly arise from inflation-induced price dispersion.In this paper, I address three questions: What is the empirical relationship betweeninflation and price dispersion? What does this relationship imply for current monetarytheories? What do we learn for the welfare analysis of inflation? Studying how price dispersion empirically relates to inflation imposes several chal-lenges. The first is to measure price dispersion accurately. For this, we need to observethe prices different sellers charge foridentical goods.Typically, granular datasetswhich have been essential to establish facts on micro-price rigidity do not satisfy thisrequirement. For instance, quotes in the micro-data underlying the CPI are groupedinto product categories with limited information about the specific product being mea-sured or the ability to link identical products across sellers. Thus, the comparison ofprices across sellers, even within narrow product categories, would not take productheterogeneity into account (Nakamura et al., 2018). I overcome this challenge using highly detailed scanner data for retail products inthe U.S. The dataset contains prices and quantities of products sold in over 35,000stores across the country between 2006 and 2020. The observations are identified bythe product barcode, the week, and the retailer where the transaction was carried out.More than 3 million barcodes are available, each of them sold by 50 stores on average.Each retailer belongs to one of over a thousand geographically dispersed counties.With these data, I can compare prices of products with identical barcodes sold acrossdifferent retailers on the same date and county. Hence, my measure of relative pricedispersion controls for several sources of heterogeneity which a priori are unrelated toinflation. A shortcoming of this dataset is that it is only available for a relatively low andstable aggregate inflation period.Therefore, the variation in aggregate inflation isinsufficient to statistically identify its time-series comovement with price dispersion.In contrast, the variation in product-level inflation rates across markets and productcategories is substantial.While aggregate inflation fluctuated between -1% and 7%over the sample period, product-level inflation ranged between -30% and 30%. Thus,my approach is to study the relationship between inflation and price dispersion byexploiting cross-sectional variation and derive implications of aggregate inflation using a multi-product model calibrated to match the disaggregate evidence.1 I contribute to the literature by documenting a new fact:in the cross section,small deviations from zero inflation sharply