The Cyclicality of Sales, Regular and Effective Prices: Comment

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Cyclicality of Sales, Regular and Effective Prices: Comment Etienne Gagnon, David Lopez-Salido, and Jason A. Sockin 2015-052 Please cite this paper as: Gagnon, Etienne, David Lopez-Salido, and Jason A. Sockin (2015). “The Cyclicality of Sales, Regular and Effective Prices: Comment,” Finance and Economics Discussion Series 2015-052. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2015.052. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

The Cyclicality of Sales, Regular and E⁄ective Prices: Comment (cid:3) Etienne Gagnon David L(cid:243)pez-Salido Federal Reserve Board Federal Reserve Board Jason Sockin Federal Reserve Board July 9, 2015 Abstract Coibion, Gorodnichenko, and Hong (2015) argue that the CPI underestimates the deceleration in consumer prices during economic downturns because the index fails to account for the reallocation of consumer spending from high- to low-price stores. We show that these authors(cid:146)measures of in(cid:135)ation with and without store switching su⁄er from several methodological de(cid:133)ciencies, including an excessive truncation of price adjustments and the lack of a treatment for missing observations. When we address these de(cid:133)ciencies, the authors(cid:146)key regression results no longer suggest that greater store switching during downturns is a statistically or economically signi(cid:133)cant phenomenon. JEL Codes: D12, E31, E32. Keywords: Outlet substitution bias, e⁄ective prices, in(cid:135)ation measurement. The views in this paper are solely the responsibility of the authors and should not be interpreted as (cid:3) re(cid:135)ecting the views of the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System. We are grateful to Information Resources Inc. (IRI) for providing the scanner data. All estimates and analyses in this paper are by the authors and not by IRI. Comments and suggestions can be directed to etienne.gagnon@frb.gov and david.lopez-salido@frb.gov. 1

1 Introduction Coibion, Gorodnichenko, and Hong (2015, henceforth (cid:147)CGH(cid:148)) argue that the U.S. CPI understates the response of consumer prices to economic downturns because the index(cid:151)which collects information on the prices posted by (cid:133)rms but not on the quantities sold(cid:151)fails to account for the reallocation of consumer spending from high-price to low-price stores as labor market conditions deteriorate. Using retail data, CGH show that the di⁄erence in sensitivity to labor market slack between in(cid:135)ation ignoring quantity movements ((cid:147)posted price in(cid:135)ation(cid:148)) and in(cid:135)ation taking those movements into account ((cid:147)e⁄ective price in(cid:135)ation(cid:148)) is (cid:147)quantitatively large: a 2 percentage point rise in the unemployment rate lowers in(cid:135)ation in e⁄ective prices by 0.2(cid:150)0.3 percentage points relative to in(cid:135)ation in posted prices for a given UPC.(cid:148)Applying their range of estimates to the 5-percentage-point jump in the U.S. unemployment rate during the Great Recession suggests that o¢ cial in(cid:135)ation might have overestimatedactualin(cid:135)ationby0:4(cid:150)0:7 percentagepoint. These(cid:133)guresarenotablebecause they indicate, for the (cid:133)rst time, that the severity of what is known as (cid:147)outlet substitution bias(cid:148)in the price measurement literature (cid:135)uctuates in an economically signi(cid:133)cant manner with the business cycle.1 They also shed light on a potential contributor to the remarkable stability of U.S. nonenergy in(cid:135)ation during and after the Great Recession despite large increases in resource slack.2 Our paper shows that CGH(cid:146)s conclusions are unwarranted because their measures of posted and e⁄ective price in(cid:135)ation su⁄er from several methodological de(cid:133)ciencies that, on net, bias the inference toward (cid:133)nding a cyclical role for store switching. One key de(cid:133)ciency is CGH(cid:146)s overly severe truncation of price movements prior to calculating in(cid:135)ation, a procedure presumably employed to control for outliers, but that, ultimately, dampens cyclical movements in posted price in(cid:135)ation more than in e⁄ective price in(cid:135)ation. In a nutshell, CGH obtain their measure of posted price in(cid:135)ation by aggregating price movements at the lowest possible level of disaggregation(cid:151)the item level, where an item corresponds to a universal product code ((cid:147)UPC(cid:148)) sold in a speci(cid:133)c store. Prior to aggregating, they truncate all monthly item price movements that exceed, in absolute terms, 100 percent on an annualized basis, that is, only 8:3 percent on a monthly basis. Most promotional discounts and many 1An outlet substitution bias has been known to a⁄ect the CPI for several decades but its e⁄ects have typically been discussed in the context of structural transformations in the retail industry(cid:146)s competitive landscape unfolding over decades. See, for example, Denison (1962), Oi (1990), and Reinsdorf (1993). The outletsubstitutionbiasisakintothe(cid:147)sourcingsubstitutionbias(cid:148)discussedinthetradeandproducerprices literature. For recent reviews of this related bias, see Houseman et al. (2011) and Nakamura et al. (2014). 2See Robert E. Hall(cid:146)s 2011 presidential address to the American Economic Association, in which he documents this stability and invites macroeconomists to reconsider the long-held view that producers (cid:133)nd it desirable to expand output by cutting prices in times of extreme slack. 2

regular price movements meet that threshold, so truncation greatly reduces the amplitude of movements in their posted price in(cid:135)ation series. CGH derive their measure of e⁄ective price in(cid:135)ation in a similar manner, with the crucial di⁄erence being that they apply their truncation procedure at a higher level of aggregation for which the threshold is less binding. Because CGH dampen movements in posted price in(cid:135)ation(cid:151)including cyclical responses(cid:151) more than movements in e⁄ective price in(cid:135)ation, they overestimate the importance of store switching. When we substitute CGH(cid:146)s aggressive truncation procedure with a less invasive method to control for outsize price adjustments, we (cid:133)nd that the di⁄erence in sensitivity to slack between posted and e⁄ective price in(cid:135)ation loses much of its statistical and economic signi(cid:133)cance. Notably, CGH(cid:146)s weighted panel regressions, which are arguably the best benchmarks for the size of the cyclical outlet substitution bias in o¢ cial statistics, have point estimates of the sensitivity to slack with the wrong ordering. The only cases for which we still (cid:133)nd a signi(cid:133)cantly larger sensitivity of e⁄ective price in(cid:135)ation to labor market slack are those placing relatively large weights on small markets and sparsely traded items. This latter pattern is revealing of the e⁄ects of a second source of bias in CGH(cid:146)s analysis: the treatment of missing observations. Missing item prices account for over a third of all observations in CGH(cid:146)s sample of weekly scanner data. When computing posted price in(cid:135)ation, CGH systematically (cid:133)ll in most missing monthly item price adjustments with zeros (possibly unintentionally). As was the case with CGH(cid:146)s truncation method, their imputation of missing item price adjustments arti(cid:133)cially lowers the cyclical response of posted price in(cid:135)ation relative to that of e⁄ective price in(cid:135)ation, with the consequence that the importance of store switching is further overstated during downturns. To address this second problem, we follow an imputation procedure for missing item pricessimilartothatemployedbytheBLSfortheCPI.Theprocedureensuresthatitem-level in(cid:135)ation sums up to the actual changes in item prices over long horizons even when missing observations are pervasive. In the process, we also (cid:133)x a number of other unsatisfactory aspects of CGH(cid:146)s methodology, including an improper stitching of the 2001(cid:150)2007 and 2008(cid:150) 2011 subsamples, the lack of a treatment for clearance sales, and an error in the calculation of e⁄ective price in(cid:135)ation for months with (cid:133)ve weeks. Together, our data (cid:133)lters result in posted and e⁄ective price series that are better behaved than those originally derived by CGH. In particular, our price indexes are much less subject to spurious level jumps or implausibly large divergences between the level of posted and e⁄ective prices over the sample period. Importantly for our question of interest, the economic and statistical signi(cid:133)cance of the di⁄erence in sensitivity between posted and e⁄ective price in(cid:135)ation to local labor market conditions vanishes from all panel regressions considered by CGH. We thus conclude 3

that CGH(cid:146)s regressions do not o⁄er conclusive evidence, as they claim, (cid:147)that e⁄ective price in(cid:135)ation is [...] more cyclically sensitive than in(cid:135)ation in posted prices.(cid:148) The paper is organized as follows. Section 2 presents the data and methodology used by CGH. Section 3 discusses the main de(cid:133)ciencies of CGH(cid:146)s methodology and our strategies to remedy them. Section 4 presents our corrected panel regression results. Section 5 concludes with some general remarks on the cyclical importance of the outlet substitution bias and on the challenges researchers face when using high-frequency scanner data. 2 Dataset, de(cid:133)nitions, and methodology 2.1 Description of the IRI dataset and terminology CGH(cid:146)sscannerdatasetismadeavailabletoresearchersbyInformationResourcesInc.((cid:147)IRI(cid:148)). Thedatasetcontainsweeklypriceandquantityinformationfrom2001through2011onitems belonging to 29 personal care, housekeeping, and food product categories, as well as cigarettes and photographic supplies. The data come from a sample of over 2;000 supermarkets and drugstores operating in 50 U.S. markets. The content of the dataset is detailed in Bronnenberg, Kruger, and Mela (2008). For clarity of exposition, we de(cid:133)ne an (cid:147)item(cid:148)as a UPC sold in a speci(cid:133)c store. An (cid:147)observation(cid:148)corresponds to the information collected by IRI on an item in a particular week; this information includes the number of units sold and total revenues, along with characteristics such as the presence of a promotional display. We call the history of an item(cid:146)s price in the sample its (cid:147)price trajectory.(cid:148)We refer to the combination of a product category and a market as a (cid:147)stratum.(cid:148)Because our focus is on store switching, we drop all observations pertaining to private labels (that is, to UPCs that are speci(cid:133)c to a retail chain), as CGH also do. 2.2 Posted and e⁄ective price in(cid:135)ation All posted and e⁄ective price in(cid:135)ation series used in CGH(cid:146)s key regressions are computed at the stratum level and are aggregated to a monthly frequency. The concept of posted price in(cid:135)ation seeks to capture changes in the prices posted by (cid:133)rms ignoring contemporaneous movements in quantities, whereas the concept of e⁄ective price in(cid:135)ation seeks to take these quantity movements into account. In principle, a true cost of living index should factor in quantity changes in order to account for substitution over time and across outlets (see, for example, Diewert (1999)). In practice, the use of quantities in the construction of o¢ cial price indexes is an exception rather than the norm. One reason is that the process of 4

gathering quantity information is often challenging or even impossible, in part because some retailers are reluctant to disclose sales volumes or lack the technology to track those volumes in real time.3 Even if statistical agencies could observe quantities along with item prices, the computationofane⁄ectivepriceindextrackingsubstitutionacrossoutletswouldnecessitate, for each market, the gathering of many observations of items with identical characteristics, which under current data collection methods would be onerous. The IRI dataset is largely immune to the above shortcomings because it tracks the prices and quantities of identical items sold at multiple retailers in each market, with the data collection done electronically rather than in person at the stores. However, its product and outlet coverage is far more limited than that of the CPI.4 Following CGH, we de(cid:133)ne the (cid:147)posted price,(cid:148)P , as the price paid for an item in mscj;t week t , where m, s, c, and j are indices for markets, stores, product categories, and UPCs, respectively. The posted price is calculated as the item(cid:146)s total revenue that week, TR , mscj;t divided by the item(cid:146)s total number of units sold, TQ . We de(cid:133)ne the (cid:147)e⁄ective price(cid:148)of mscj;t UPC c in market m as TR Peff = s 2 S(m) mscj;t ; mcj;t TQ Ps S(m) mscj;t 2 where S(m) is the set of participating Pstores in market m. This e⁄ective price can be alternatively expressed as a weighted sum of prices paid at the stores in market m, where store weights are proportional to the number of units sold by each store for that UPC. E⁄ective price in(cid:135)ation at the stratum level is obtained by aggregating the log changes in Peff across UPCs sold in the stratum, mcj;t Peff (cid:25)eff = w log mcj;t ; mc;t mcj;t Peff ! j J(m;c) mcj;t 1 2X (cid:0) whereJ (m;c)isthesetofUPCssoldatparticipatingstoresinthestratum. Theaggregation uses some relative weights w to be discussed shortly. In(cid:135)ation in posted prices is de(cid:133)ned mcj;t similarly, with the distinction that the aggregation takes place at the item level rather than 3To be sure, the BLS gathers information on household consumption patterns every other year, updates the sample of visited stores frequently based on an on-going point-of-sale survey, and works with sampled stores to assess the relative importance of items joining the CPI basket. However, the quantity information thus gathered is unsatisfactory for the purpose of computing a monthly e⁄ective price index because it is collected too infrequently and made available with too substantial a lag. 4IRI censors the identity of retailers but the dataset is known to exclude independent stores, online retailers, and Wal-Mart. 5

at the UPC level, P (cid:25)pos = w log mscj;t ; mc;t mscj;t P (s;j) X2 I(m;c) (cid:18) mscj;t (cid:0) 1(cid:19) where I(m;c) is the set of items sold in the stratum and w is an item(cid:146)s relative weight. mscj;t Both the UPC-level weights, w , and the item-level weights, w , are assumed to mcj;t mscj;t change infrequently, so that the reallocation of consumer spending from high-price stores to low-price stores is captured by (cid:25)eff (through changes in Peff ) but not by (cid:25)pos . mc;t mcj;t mc;t 2.3 UPC and item weights Like CGH, we consider three sets of weights to aggregate changes in Peff to stratum-level mcj;t e⁄ective price in(cid:135)ation. (cid:147)Uniform(cid:148)UPC weights assign equal weights to all UPCs in a market. (cid:147)Market-speci(cid:133)c(cid:148)UPC weights are proportional to total spending across stores in each market for all UPCs in a calendar year. (cid:147)Common(cid:148)UPC weights are proportional to total spending across all stores in the IRI sample of UPCs during the year. Similarly, we consider three kinds of weights to aggregate changes in P to stratum-level posted price mscj;t in(cid:135)ation. (cid:147)Uniform(cid:148)item weights give equal weights to all items in a stratum. (cid:147)Marketspeci(cid:133)c(cid:148)item weights are the product of the market-speci(cid:133)c UPC weights de(cid:133)ned above and a store(cid:146)s yearly market share in the stratum. Likewise, (cid:147)common(cid:148)item weights are the product of the above common UPC weights and a store(cid:146)s share of total annual sales in the product category in the IRI sample.5 We make a couple observations regarding these weighting schemes. First, if we had a balanced panel of items, then the item-level market-speci(cid:133)c and common weights used for posted price in(cid:135)ation would aggregate to the corresponding UPC-level market-speci(cid:133)c and common weights used for e⁄ective price in(cid:135)ation. In practice, basket turnover and missing observations may create some di⁄erences in UPC-level weights between the two in(cid:135)ation measures, especially if no treatment of missing observations is employed. Second, even if we had a balanced panel of items, CGH(cid:146)s uniform item weights used for posted price in(cid:135)ation (which depend on the number of items in a market) would generally not aggregate up to the uniform UPC weights used for e⁄ective price in(cid:135)ation (which depend on the number of UPCs in a market). For this reason, and because uniform weights treat sparsely-traded items and UPCs on the same basis as big sellers, we see the regression results associated with uniform weights as less reliable than those derived for market-speci(cid:133)c and common weights for gauging the in(cid:135)ation bias due to store switching. 5CGH(cid:146)spaperandtechnicalappendixdiscusstheaggregationofUPCpricestothestratumlevelbutnot the aggregation of item prices to the UPC level or higher. Our description of the item weights is based on our reading of their computer code. 6

2.4 The cyclicality of posted and e⁄ective prices To assess the cyclicality of price changes with respect to economic conditions, CGH (cid:133)rst aggregate the micro data to a monthly frequency and calculate monthly (cid:25)pos and (cid:25)eff mc;t mc;t series(ournextsectiondetailsthesesteps). Theythenadoptthefollowingbaselineempirical speci(cid:133)cation for their panel regressions, Y = (cid:12) U +(cid:21) +(cid:18) +error ; mc;t m;t t mc mc;t where Y is the 12-month rate of either posted or e⁄ective price in(cid:135)ation, U is the mc;t m;t seasonally-adjusted unemployment rate prevailing in month t and market m, and (cid:21) and t (cid:18) are month and stratum (cid:133)xed e⁄ects, respectively. To the extent that local in(cid:135)ation mc slows when local labor market conditions deteriorate relative to those in the sample, the point estimates of (cid:12) should be negative. And to the extent that consumers reallocate their expenditures toward cheaper stores at a faster pace during downturns, then, as CGH (cid:133)nd, the estimate of (cid:12) should be smaller (that is, more negative) for (cid:25)eff than for (cid:25)pos .6 mc;t mc;t FollowingCGH,weconsidereightvariationsoftheabovebaselinespeci(cid:133)cation. Arguably the two most important variations use the market-speci(cid:133)c and common weights to aggregate price changes into monthly (cid:25)eff and (cid:25)pos series at the stratum level, and then use the mc;t mc;t stratums(cid:146)respective expenditure shares as panel weights.7 By accounting for the importance of items, UPCs, and stratums, these regressions come closest to measuring the bias in o¢ cial statistics, which use importance weights at all these levels. Another two variations similarly use market-speci(cid:133)c and common weights to derive the (cid:25)eff and (cid:25)pos series, but then treat mc;t mc;t each panel equally, so that small stratums (for example, razors in Eau Claire, WI) receives the same weights as large ones (for example, carbonated beverages in Chicago, IL) in the estimation of (cid:12). The last four variations considered by CGHuse uniformweights to compute (cid:25)eff and (cid:25)pos at the stratum level, along with equal panel weights; by over-emphasizing mc;t mc;t sparsely-traded items and UPCs as well as small markets, they provide, in our view, less reliable estimates of the bias a› icting o¢ cial in(cid:135)ation statistics than the aforementioned four variations.8 Like CGH, we account for possible sectoral and cross-sectional correlation 6Asmallerestimateof(cid:12) for(cid:25)eff thanfor(cid:25)pos isalsoconsistentwithretailershavingagreaterrecourse mc;t mc;t to sales, or households being more responsive to sales, during economic downturns. CGH rule out these alternative explanations by showing that the frequency and depth of sales, as well as the share of goods bought on sale, are insensitive to local labor market conditions in the IRI sample. 7We follow CGH in using panel weights proportional to each stratum(cid:146)s median monthly share of total expenditures in the sample. 8Oneofthesefourregressionsusesnomonthandstratum(cid:133)xede⁄ects,anotheronlystratum(cid:133)xede⁄ects, andyetanotherbothmonthandstratum(cid:133)xede⁄ects. Theremainingvariationkeepsthestratum(cid:133)xede⁄ects but replaces the month (cid:133)xed e⁄ects with stratum-speci(cid:133)c linear time trends. 7

in all eight speci(cid:133)cations by computing Driscoll and Kraay (1998) standard errors. 3 Shortcomings of CGH(cid:146)s implementation and our solutions 3.1 Truncation of monthly item and UPC price movements Priortocomputing(cid:25)pos ,CGHtruncateallitem-levelmonthlypriceadjustments,(cid:1)log(P ), mc;t mscj;t that exceed 100 percent on an annualized basis, or, equivalently, 8:3 percent on a monthly basis. Similarly, prior to computing (cid:25)eff , CGH truncate all e⁄ective price movements, mc;t (cid:1)log Peff , that exceed that threshold. CGH(cid:146)s paper and supporting material do not mcj;t menti(cid:16)on this(cid:17)truncation; our conjecture is that it was introduced to ensure that the regression estimates are not driven by outliers.9 Unfortunately, the thresholds misleadingly tilt the regression coe¢ cients in the direction of (cid:133)nding greater cyclical responses for (cid:25)eff than mc;t (cid:25)pos . mc;t Table 1 shows that the chosen thresholds are easily met. For posted price in(cid:135)ation (column 1), between a (cid:133)fth and a quarter of underlying monthly (cid:1)log(P ) used by CGH mscj;t are truncated. Among nonzero adjustments (not shown in the table), the proportion reaches a staggering 70 percent of raw price changes in the sample. The reason why the threshold is so easily met by item price changes is simple: Most promotional discounts and many regular price movements exceed 8:3 percent in absolute terms. The proportion of truncated item price changes is especially large in product categories for which active promotional discounting is a feature of how goods are marketed to consumers. For example, over a third of nonmissing monthly item price adjustments are truncated for carbonated beverages, frozen dinners, and frozen pizzas. For e⁄ective price in(cid:135)ation (column 4), the proportion of underlying (cid:1)log Peff that are truncated, which is around 40 percent, is even larger than mcj;t that of (cid:1)log(P (cid:16) ). (cid:17) mscj;t To explore the e⁄ects of truncation on CGH(cid:146)s (cid:133)ndings while still controlling for possible outliers, we replace CGH(cid:146)s aggressive truncation procedure with the exclusion of items that exhibit one or more outsize adjustments.10 Our trimming ensures greater uniformity in the item-level price movements that underpin the calculation of (cid:25)pos and (cid:25)eff . Dropping the mc;t mc;t a⁄ected items(cid:146)entire price histories leads to the trimming out of only about half a percent 9Our replication (cid:133)les, which are available upon request, detail where this and other possible errors occur in CGH(cid:146)s computer code. 10Inparticular,wedropfromoursampleanitem(cid:146)sentirepricetrajectorywheneverP =P <0:15 mscj;t mscj;t 0 or P =P > (1=0:15) for some week t, where t t 1 is the item(cid:146)s previous nonmissing price mscj;t mscj;t 0 0 (cid:20) (cid:0) observation. 8

of observations accounting for a similarly modest fraction of store revenues. Table1showsthatCGH(cid:146)struncationproceduredramaticallylowersthevolatilityoftheir (cid:25)pos and (cid:25)eff series (expressed on a 12-month rate basis), with the e⁄ect being more promc;t mc;t nounced for posted price in(cid:135)ation. Absent truncation, the expenditure-weighted standard deviations of posted and e⁄ective price in(cid:135)ation are similar, at 4:5 percentage points and 4:6 percentage points, respectively.11 This tiny di⁄erence suggests that the e⁄ects of swings in quantities on e⁄ective prices, which may be important at the UPC-market level, tend to cancel each other as the data are aggregated to the product-category or higher levels. Truncation more than halves the standard deviation of (cid:25)pos , to 1:9 percentage points, whereas mc;t it only cuts that of (cid:25)eff by about a third, to 3:1 percent. mc;t The relatively large reduction in the volatility of posted price in(cid:135)ation is crucial for understanding why truncation might bias the analysis toward (cid:133)nding a counterfactually important role for store switching. Intuitively, in a univariate context, a linear regression of (cid:25) on U produces a coe¢ cient (cid:12) = cov((cid:25) ;U )=var(U ). Roughly speaking, CGH(cid:146)s t t t t t aggressive truncation scales down (cid:25) to (cid:21)(cid:25) , with 0 < (cid:21) < 1, so that the standard deviation t t of (cid:21)(cid:25) , the covariance term cov((cid:21)(cid:25) ;U ), and the estimate of (cid:12) are also scaled down by the t t t samefactor(cid:21) relativetotheirtruevalue.12 Becauseitiseasierforitempricechangestomeet CGH(cid:146)s truncation threshold than for e⁄ective price adjustments at the UPC-market-level, CGH end up scaling down (cid:25)pos by a factor (cid:21)pos that is smaller than the factor (cid:21)eff a⁄ecting mc;t (cid:25)eff . As a result, CGH(cid:146)s estimates of (cid:12)pos are more severely biased toward zero than those mc;t for (cid:12)eff, thereby leading to an overstatement of the incidence of store switching. 3.2 Treatment of missing observations CGH do not discuss the presence of missing observations but table 2 shows that they are pervasive in their sample. On average, 39:0 percent of raw observations in the IRI dataset are missing each week. A majority of weekly observations are missing for 9 out of the 31 product categories, with a proportion as high as 68:0 percent for razors.13 Unfortunately, IRI provides no information that would allow us to ascertain the nature of each missing 11These statistics use market-speci(cid:133)c item and UPC weights to derive stratum-level in(cid:135)ation series. The standard deviations of the resulting in(cid:135)ation series are then aggregated to the product-category and sample levels using as weights the stratums(cid:146)spending shares over the full sample period. 12A similar line of reasoning applies to CGH(cid:146)s multivariate panel regressions, with the complications that the estimates of (cid:12) further depend on the covariance between the local unemployment rate and the month and stratum (cid:133)xed e⁄ects, as well as, in the case of weighted regressions, how the incidence of truncation varies with the panel weights. 13These statistics are lower bounds because IRI only reports an item(cid:146)s information if a transaction occurs duringtheweekandthestoretransmitsitsdata;therefore,thestatisticscountobservationsthataremissing between the (cid:133)rst and last recorded transactions in the sample but not those outside of that period. 9

observation. One aspect we can infer, though, is that only a small proportion of missing observations are due to a failure of stores to report data to IRI. As column 4 indicates, only about 2 percent of the sample(cid:146)s observations come from stores for which all (or essentially all) observations are missing during the week. The vast majority of missing observations are thus attributable to other factors, which include stockouts, out-of-season items, and the absence of weekly transactions. CGH derive item-level monthly posted price in(cid:135)ation by summing weekly price changes during the month. If all weekly (cid:1)log(P ) are missing in a month, then CGH(cid:146)s computer mscj;t code overwrites the missing monthly entry with a zero.14 This handling of missing observations is unsatisfactory on several levels. First, a monthly price change may be missing even if the price is observed on occasion during the month, so that there is a loss of information. Second, there is no guarantee that the sum of weekly changes will coincide with the actual change in an item(cid:146)s price over the month. For example, suppose that an item is discounted in the (cid:133)nal week of the previous month, stocked out in the (cid:133)rst week of the current month, then sold at its original regular price over the remainder of the month. The price changes for the (cid:133)rst and second weeks of the month are missing because either the current or previous weekly pice is not observed, so that the price increase at the end of the promotional sale is never registered; CGH would thus record that the price is unchanged during the entire month, as if it had stayed at its promotional level. To the extent that there are systematic patterns inthewayweeklyobservations aremissing(cid:151)saybecauseitems arelikelytobemissing after sales because of stockouts and satiated consumer demand(cid:151)then CGH(cid:146)s handling could create systematic biases in the measurement of posted and e⁄ective price in(cid:135)ation. Moreover, because item prices are more likely to be missing than market-wide UPC e⁄ective prices, any bias is likely to a⁄ect (cid:25)pos and (cid:25)eff to di⁄ering degrees. Third, and perhaps mc;t mc;t most consequential for CGH(cid:146)s analysis, the systematic imputation of missing monthly item price changes with zeros arti(cid:133)cially dampens movements in the posted price in(cid:135)ation series. As a consequence, these imputations are likely to tilt the inference toward (cid:133)nding smaller cyclical responses for posted price in(cid:135)ation than for e⁄ective price in(cid:135)ation, leading to the (cid:133)nding of a counterfactually large role for store switching. To control for selection biases due to missing weekly prices and to undo CGH(cid:146)s zeroimputations of missing monthly price changes, we handle missing prices using a procedure similar to that used by the BLS for the CPI. For as long as an item price is missing, our imputation method imputes the last observed price using the in(cid:135)ation rate in the stratum, 14ItisuncleartousifCGHintendedtohavethisoverwritingofmissingmonthlypricechangeswithzeros. The overwriting of missing observations with zeros is a feature of the particular Stata function called by CGH to aggregate weekly data to a monthly frequency. 10

but then corrects any imputation errors by e⁄ectively linking the next observed weekly item priceswiththepreviousnonmissingweeklyprices. Asanillustration, supposethatanitemis heavily discounted in week t 1, stocked out in week t, then transacted at its earlier regular (cid:0) price in period t + 1. We impute the (cid:133)rst missing price change, (cid:1)p , by the average mscj;t amountofin(cid:135)ationinthestratum, (cid:25)pos . Inperiodt+1, wecomputethechangeintheitem(cid:146)s mc;t pricefromitsimputedlevelinperiodt, (cid:1)p = log(P ) log(P )+(cid:25)pos . mscj;t+1 mscj;t+1 mscj;t 1 mc;t (cid:0) (cid:0) This approach ensures that the sum of (cid:1)p and (cid:1)p equals the actual change in mscj;t mscj;t+1 (cid:0) (cid:1) the item(cid:146)s price from week t 1 to week t+1.15 When item prices are missing for several (cid:0) consecutive periods, we keep imputing the level of the item(cid:146)s price with posted price in(cid:135)ation in the stratum until the item(cid:146)s price is available again. For consistency, we follow the same imputation strategy for missing monthly e⁄ective prices, which, as we noted earlier, are less likely to be missing than weekly item prices. pos eff 3.3 Incorrect time aggregation of (cid:25) and (cid:25) mc;t mc;t CGH(cid:146)s aggregation of weekly e⁄ective price in(cid:135)ation to a monthly frequency contains a mistake for months that have (cid:133)ve weeks. To compute monthly e⁄ective price in(cid:135)ation, they (cid:133)rst create a weekly variable that contains the average paid price over the entire month by dividing total revenues that month by total quantities sold that month. They next calculate the four-week change in this weekly variable and then take, for each month, the average of those weekly four-week changes to obtain a measure of monthly e⁄ective price in(cid:135)ation. A problem arises for months that have (cid:133)ve weeks because the four-week change in the monthly average price is always zero for the (cid:133)fth week of the month. As a result, CGH(cid:146)s measure of monthly e⁄ective price in(cid:135)ation understates actual in(cid:135)ation by a (cid:133)fth in months with (cid:133)ve weeks. This time aggregation mistake dampens the measured response of e⁄ective prices. As a result, it may actually lead CGH to understate the (cid:135)exibility of e⁄ective prices, and thus to underestimate the bias in posted price in(cid:135)ation due store switching. Table 3 provides an illustration of this error. This issue aside, the monthly aggregation of e⁄ective prices requires at least one pair of weekly observations(cid:151)one observation in each month(cid:151)separated by exactly four weeks; otherwise the four-week change will be missing for the month, resulting in a loss of information. Relatedly, thetimeaggregationofweeklypostedpricein(cid:135)ationisalsounsatisfactorybecause of CGH(cid:146)s treatment of missing weekly and monthly price observations noted earlier. Our imputation procedure for missing observations allows us to circumvent this problem. We de(cid:133)ne an item(cid:146)s monthly posted price as the average weekly price(cid:151)observed or imputed(cid:151)during 15GagnonandL(cid:243)pez-Salido(2014)followthesameapproach,withthedistinctionthattheyonlyuseprices for frequently-traded items to compute in(cid:135)ation. 11

the month, and then compute monthly (cid:25)pos by aggregating changes in those item-level mc;t monthly averages. 3.4 Spurious index jumps due to clearance sales Table4showsthat, onaverage, 2:3percentofitemsintheIRIdatasetdisappeareverymonth and do not return. A slightly larger proportion of items (about 2:4 percent) join the sample eachmonth, consistentwithmodestgrowthinstores(cid:146)producto⁄eringsovertime.16 Selection e⁄ects associated with the entry and exit of items are a well known source of bias in the o¢ cial CPI over long horizons.17 A number of authors have also explored how such selection e⁄ects distort the dynamic response of price indexes to shocks(cid:151)in our case, the response to variation in local labor market conditions.18 A fully satisfying treatment of biases due to basket turnover is beyond the scope of this paper because it would require the judgmental linking of millions of entering and exiting items. That said, there is one major source of downward bias in CGH(cid:146)s price indexes that we can readily address and that potentially creates a wedge in the cyclical response of posted and e⁄ective price in(cid:135)ation. (cid:147)Clearance sales(cid:148)is the phenomenon by which retailers sometimes o⁄er extra discounts on items about to permanently disappear from the shelves. In this case, a failure to link the disappearing item(cid:146)s price with that of its replacement(cid:151)even when no quality adjustment is required(cid:151)can lead to a downward bias in the index over time because the index fails to capture the rise in the price as consumers reallocate theirspendingtoneworexistingitems. The disappearance ofanitemafteraclearancesalepermanentlylowersthepostedpriceindexbut, iftheUPCto which the item belongs remains in the sample, e⁄ective price in(cid:135)ation will remain anchored by the prices of continuing items.19 Table 4 shows that clearance sales are a material concern in the IRI dataset. On average, the price of an exiting item is over 8 percent lower than the price that prevailed a quarter before the item(cid:146)s exit (that is, 14 to 26 weeks earlier), with a majority of product categories having a price drop of over 10 percent.20 The probability 16Incomputingthesestatistics,weexcludeallobservationsinthe(cid:133)rstandlast13weeksofastore(cid:146)spresence in the sample to reduce the risk of confounding store and item turnover. Some of the growth in product o⁄ering likely re(cid:135)ects a broadening of some product category de(cid:133)nitions around sample enlargements. 17Notably,a(cid:147)newgoodbias(cid:148)anda(cid:147)qualitychangebias(cid:148)areknowntoslantupwardmeasuredchangesin the CPI, leading to an underestimation of the rise in living standards over long periods. See, among many contributors, the edited volume by Boskin et al. (1996), Bresnahan and Gordon (1996), Gordon (2006) and the conference summaries of the Ottawa Group on Price Indices. 18Broda and Weinstein (2010) provide evidence of cyclical creation of destruction of barcodes in scanner data. See also Berger et al. (2009), Nakamura and Steinsson (2012), and Gagnon, Mandel, and Vigfusson (2014) for some related evidence and theory on the response of trade prices to exchange rate movements. 19Note that incorrect imputations of missing market-wide e⁄ective price changes can similarly create spurious shifts in the level of the e⁄ective price indexes. 20We identify promotional sales using the IRI(cid:146)s sales (cid:135)ag, which is extracted from price records using a proprietary algorithm. This sales (cid:135)ag is not directly comparable to the BLS sales (cid:135)ag, which is based on 12

that an item is on sale in its (cid:133)nal week in the sample is higher, at 30:5 percent (column 3), than for the typical item in the sample, at 23:4 percent (column 4), contributing to these relatively lower prices upon exiting. We limit the incidence of clearance sales on our price indexes through a simple (cid:133)x: We drop the last quarter (that is, 13 weeks) of every item(cid:146)s price trajectory in the sample. This trimming out horizon is chosen to be long enough that it encompasses the vast majority of clearance sales. 3.5 Incorrect stitching of subsamples In November 2012, the IRI dataset(cid:146)s sample coverage was extended through the end of 2011 with the release of data for the years 2008 to 2011. The inclusion of these latter years in the analysis is important because these years witnessed the largest swings in unemployment rates. We note that CGH improperly stitched the 2001(cid:150)2007 and 2008(cid:150)2011 subsamples. In short, CGH create item identi(cid:133)ers for each subsample, mapping each item to a unique integer. They then aggregate the two subsamples using those item identi(cid:133)ers. Because the two subsamples do not contain the same number of items, the price history of, say, item n in the (cid:133)rst subsample is typically stitched with the price history of a di⁄erent item in the second subsample that had been attributed the n-th identi(cid:133)er. Our implementation corrects for this error. 4 Corrected regression results The upper panel of table 5 reproduces CGH(cid:146)s original panel regression estimates from their table 1 for the eight speci(cid:133)cations they consider. They emphasize the last four columns because these regressions control for the relative importance of items and UPCs in the computation of the (cid:25)pos and (cid:25)eff series. The statistical object of interest is the di⁄erence mc;t mc;t between the regression coe¢ cients on the local unemployment rate for 12-month posted price in(cid:135)ation and the corresponding coe¢ cient for 12-month e⁄ective price in(cid:135)ation. Across CGH(cid:146)s regressions using either market-speci(cid:133)c or common weights (columns 5 through 8), this di⁄erence is statistically signi(cid:133)cant, ranging from 0:084 to 0:130, implying that a 5percentage point rise in the local unemployment rate is associated with an extra fall in in-store observations by price collectors. Nonetheless, we take some comfort in that the fraction of items exiting the IRI sample (2:3 percent) multiplied by the fraction for which the IRI price-reduction (cid:135)ag is one upon exit (30:5 percent) is, at 0:7 percent, similar to the fraction of items subject to a clearance sale in the (cid:147)processed food(cid:148)and (cid:147)other goods(cid:148)categories of the U.S. CPI, at 0:6 percent, as reported by Nakamura and Steinsson (2008) in table 7 of their supplementary materials. 13

e⁄ective price in(cid:135)ation of 0:4(cid:150)0:7 percentage point. A similar set of regressions are presented in the (cid:133)rst four columns for which CGH use uniformly weighted items and UPCs in the computation of 12-month posted and e⁄ective price in(cid:135)ation series. Again, the di⁄erence in sensitivity to slack between posted and e⁄ective price in(cid:135)ation is economically large and statistically signi(cid:133)cant. The middle panel of table 5 shows our regression results once we replace CGH(cid:146)s severe truncation of price changes with our more standard treatment of outliers.21 As expected, removing CGH(cid:146)s severe truncation of observations boosts the measured sensitivity of both posted and e⁄ective price in(cid:135)ation to local slack. The only two point estimates that do not increase in absolute size relative to their values in the upper panel pertain to e⁄ective price in(cid:135)ation when we use the stratum-level expenditure shares as panel weights (columns 7 and 8); these measures are arguably the least susceptible to CGH(cid:146)s truncation because large marketstendtohavelessvolatilee⁄ectivepricesbecauseoftheaveragingofitempricesacross large sets of stores. Importantly for assessing the relevance of store switching, the regression estimates that aggregate across stratums using their relative weights (columns 7 and 8)(cid:151) which provide the most reliable estimate of the bias a⁄ecting o¢ cial statistics(cid:151)nowhave the wrong ordering, with posted price in(cid:135)ation being marginally more cyclically responsive than e⁄ective price in(cid:135)ation (although not statistically or economically so). Moreover, when the stratums are given the same weights in the panel regression (columns 5 and 6), the di⁄erence in coe¢ cients is a third smaller than reported by CGH and we can no longer reject that the regression coe¢ cients are the same at standard signi(cid:133)cance levels. An arguably more direct statistical test for the presence of a cyclical store switching bias hypothesizes that the response to the local unemployment rate of e⁄ective price in(cid:135)ation is larger (that is, less negative) than that of posted price in(cid:135)ation. The data do not reject this hypothesis for the weighted panel regressions but do reject it at the 10 percent and 5 percent level of statistical signi(cid:133)cance for market-speci(cid:133)c and common weights, respectively, when the panels are uniformly weighted. Our results illustrate that, to some degree, CGH(cid:146)s (cid:133)ndings of an economically large di⁄erence in the cyclical response to slack between the two in(cid:135)ation measures is driven by their severe truncation procedure. That said, given the methodological de(cid:133)ciencies noted in the previous section that, in addition to severe truncation, plague CGH(cid:146)s estimates, the coe¢ cients reported in the middle panel of table 5 do not yet provide satisfactory estimates of the cyclical sensitivity of in(cid:135)ation to labor market slack. Indeed, a number of patterns apparent in the middle panel are worrisome. We note that the estimated cyclical biases 21These regressions results also correct for CGH(cid:146)s improper stitching of the 2001(cid:150)2007 and 2008(cid:150)2011 subsamples, which only has a limited e⁄ect on the regression coe¢ cients at the margin. 14

are much larger for the panel regressions that apply uniform item and UPC weights in the calculation of (cid:25)pos and (cid:25)eff (columns 1 through 4) than for those that use expenditure mc;t mc;t shares (columns 5 through 8). By placing infrequently-traded items and UPCs on the same footing as big sellers, the (cid:133)rst four regressions might be more susceptible to selection e⁄ects associated with sparse data, which could explain the contrasting results. Likewise, the fact that the di⁄erence in cyclical sensitivity for the panel regressions that use market-speci(cid:133)c or common item and UPC weights retains some signi(cid:133)cance when the stratums are equally weighted (columns 5 and 6) but not when the stratums are weighted by expenditures shares (columns 7 and 8) also worries us that biases other than truncation could be a⁄ecting small stratums. We are further motivated to explore other methodological de(cid:133)ciencies because, whenwecumulateCGH(cid:146)spostedande⁄ectivepricein(cid:135)ationseries, we(cid:133)ndthattheresulting price indexes are plagued with large jumps in their levels. Notably, even after controlling for truncation and proper sample stitching, we (cid:133)nd that a majority of stratums saw e⁄ective prices increase by more than posted prices over the sample period despite the large rise in unemployment, a fact that is inconsistent with consumers taking advantage of lower prices. Before discussing the regression estimates with all our corrective (cid:133)lters, we note that the application of our (cid:133)lters results in posted and in(cid:135)ation price indexes that are substantially better behaved than those derived using CGH(cid:146)s original methodology.22 Although we cannot ascertain that all methodological issues have been addressed(cid:151)for instance, we do not have a formalwayofaccountingforsampleentryandexitbesidesoursimpleprocedureforclearance sales(cid:151)we nonetheless see our in(cid:135)ation series as considerably more likely to provide reliable estimates than those produced by CGH. The bottom panel of table 5 shows our regression results after implementing all of our corrections, thatis, includingastandardtreatmentofoutsizeitempricemovements, arobust imputation procedure for missing observations, comparable de(cid:133)nitions of monthly posted and e⁄ective price in(cid:135)ation, a proper stitching of the subsamples, and our simple control for clearance sales. There are two main take-away messages. The (cid:133)rst is that the signi(cid:133)cance of the di⁄erence in cyclical responses between posted and e⁄ective price in(cid:135)ation has vanished fromall speci(cid:133)cations considered by CGH. The coe¢ cients pertaining to the weighted panels with in(cid:135)ation series constructed using either market-speci(cid:133)c or common weights (columns 7 and8)changesonlymoderatelywithrespecttothecasewithnotruncation,butinadirection that makes it even less likely that e⁄ective price in(cid:135)ation is more cyclically sensitive than posted price in(cid:135)ation. The corresponding unweighted panel regressions (columns 5 and 6) now also have point estimates with posted price in(cid:135)ation that are marginally more sensitive 22Stratum-level posted and e⁄ective price indexes are available on our replication page, along with the corresponding indexes consistent with CGH(cid:146)s original methodology. 15

to slack than e⁄ective price in(cid:135)ation, although not in a statistically signi(cid:133)cant manner. Similarly, the coe¢ cients using in(cid:135)ation measures without regards to item and UPC weights (columns1through4)eitherhavethewrongcoe¢ cientorderingforstoreswitchingtomatter or have no signi(cid:133)cance. These latter results di⁄er markedly from those shown in the upper and middle panels, and suggest that CGH(cid:146)s original results were driven to some degree by the lack of a proper treatment for sparsely traded items and UPCs. The second message is that the application of our (cid:133)lters points to in(cid:135)ation(cid:151)both posted and e⁄ective(cid:151)being more responsive to local labor market conditions than estimated by CGH. Our preferred estimates suggest that a one-percentage point increase in the local unemployment rate lowers 12-month in(cid:135)ation by about 0:15 percentage point, a (cid:133)gure roughly two to three times larger than the range of estimates originally reported by CGH in columns 5 through 8. Of note, these estimates are nearly identical to those presented by Beraja, Hurst, and Ospina (2015) using the Nielsen scanner database, which has a broader coverage of the retail sector than the IRI database. These authors estimate that a one percentage point increase in the local unemployment rate lowers retail prices (measured on a posted basis) by 0:46 percentage point over a three-year period, a (cid:133)gure is almost exactly three times as large as our point estimate for yearly posted price in(cid:135)ation. 5 Conclusion We have identi(cid:133)ed several methodological de(cid:133)ciencies in the way CGH calculate posted and e⁄ective price in(cid:135)ation that, when addressed, make their (cid:133)nding of e⁄ective prices(cid:146)relatively large cyclical response to slack disappear. It could be tempting to conclude from our analysis that the cyclical bias due to store switching in o¢ cial price indexes is an economically unimportant phenomenon. However, we are reluctant to draw such a conclusion for a number of reasons. Most importantly, the IRI sample is not representative of the universe of outlets, notably excluding online retailers and the largest U.S. brick-and-mortar retailer, Wal-Mart, which pursued competitive pricing strategies and saw their market shares rise over the sample period. The IRI sample(cid:146)s product coverage is also limited and might thus not be representative the extent of cyclical outlet substitution occurring in other economic sectors. Furthermore, anumberof studieshaveuncoveredrelatedevidencethatstoresadjust prices and households respond to them in a manner that correlates with the business cycle (see Kryvtsov and Vincent (2015) and Nevo and Wong (2014)). Whilesomemethodological de(cid:133)ciencies werespeci(cid:133)ctoCGH(cid:146)s study, others serveas cautionary tales that large scanner datasets can be a mixed blessing compared with the smaller datasets of consumer prices collected by statistical agencies for the production of o¢ cial 16

price indexes. On the one hand, scanner datasets such as IRI(cid:146)s promise to enable research that would be impossible with the micro datasets behind o¢ cial indices such as the CPI. For example, the high frequency of data collection allows the study of short-lived economic phenomenons (see, for example, Gagnon and L(cid:243)pez-Salido (2015)) while the extensive store coverage, coupled with multiple UPC-level observations across stores, permits the study of price dispersion (for example, Kaplan and Menzio (forthcoming)) and retail competition for particular products. Ultimately, the availability of quantity information along with prices could bring us closer to computing satisfactory cost-of-living indexes. On the other hand, high-frequency scanner data present some important challenges to users relative to micro CPI databases. One challenge is the large size of the datasets, which makes access to a computer cluster a must for computationally intensive operations, such as the (cid:133)ltering out of promotional sales. Another challenge is the high proportion of missing observations, which is partly due to the granularity of the data. Whereas price collectors working for statistical agencies may observe why an item is missing, there is typically no such information stored in scanner dataset. Our implementation of an imputation procedure similar to that used by the BLS reduces some of the potential biases caused by missing observations. Finally, another challenge is sample turnover. The BLS devotes signi(cid:133)cant resources toward linking departing and entering items in order to reduce the extent of the new goods and quality change biases in the U.S. CPI. In doing so, it collects information on whether the item was discounted prior to leaving the sample, and can make judgmental adjustments. Such an approach is more di¢ cult to implement in large scanner datasets for which millions of item prices would possibly need to be linked on a judgmental basis. That said, it seems possible to avoid some signi(cid:133)cant downward bias in price indexes by trimming out the last several observations of each item(cid:146)s price trajectory, as we have done with our sample. References [1] Beraja, Martin, Erik Hurst, and Juan Ospina (2015). (cid:147)The Aggregate Implications of Regional Business Cycles,(cid:148)mimeo, University of Chicago. [2] Berger, David, Jon Faust, John H. Rogers, and Kai Steverson (2009). (cid:147)Border Prices and Retail Prices,(cid:148)International Finance Discussion Papers 972, Board of Governors of the Federal Reserve System. [3] Bresnahan, TimothyF., andRobertJ.Gordon(1997).(cid:147)TheEconomicsofNewGoods,(cid:148) Studies in Income and Wealth, Volume 58, National Bureau of Economic Research. 17

[4] Boskin, Michael J., Ellen R. Dulberger, Robert J. Gordon, Zvi Griliches, and Dale Jorgenson (1996). (cid:147)Toward a More Accurate Measure of the Cost of Living,(cid:148)Final Report to the Senate Finance Committee. [5] Broda, Christian, and David E. Weinstein (2010). (cid:147)Product Creation and Destruction: Evidence and Price Implications,(cid:148)American Economic Review, vol. 100(3), pages 691(cid:150) 723. [6] Bronnenberg, Bart J., Michael W. Kruger, and Carl F. Mela (2008). (cid:147)Database Paper: The IRI Marketing Data Set,(cid:148)Marketing Science, vol. 27(4), pages 745(cid:150)748. [7] Bureau of Labor Statistics, Handbook of Methods, Washington DC, 2009. [8] Coibion, Olivier, Yuriy Gorodnichenko, and Gee Hee Hong (2015). (cid:147)The Cyclicality of Sales, Regular and E⁄ective Prices: Business Cycle and Policy Implications,(cid:148)American Economic Review, vol. 105(3), pages 993(cid:150)1029. [9] Denison, Edward (1962). (cid:147)The Sources of Economic Growth in the United States and the Alternatives before Us,(cid:148)New York: Committee for Economic Development. [10] Diewert,W.Erwin(1999).(cid:147)AxiomaticandEconomicApproachestoInternationalComparisons,(cid:148)NBER Chapters, in: International and Interarea Comparisons of Income, Output, and Prices, pages 13(cid:150)107, National Bureau of Economic Research, Inc. [11] Driscoll, JohnC., andAartC.Kraay(1998).(cid:147)ConsistentCovarianceMatrixEstimation with Spatially Dependent Panel Data.(cid:148)Review of Economics and Statistics, vol. 80(4), pages 549(cid:150)60. [12] Fabiani, Silvia, Martine Druant, Ignacio Hernando, Claudia Kwapil, Bettina Landau, Claire Loupias, Fernando Martins, Thomas Math(cid:228), Roberto Sabbatini, Harald Stahl, and Ad Stokman (2006). (cid:147)What Firms(cid:146)Surveys Tell Us about Price-Setting Behavior in the Euro Area.(cid:148)International Journal of Central Banking, vol. 2(3), pages 3(cid:150)48. [13] Gagnon, Etienne and David L(cid:243)pez-Salido (2014). (cid:147)Small Price Responses to Large Demand Shocks,(cid:148)Finance and Economics Discussion Series 2014-18, Board of Governors of the Federal Reserve System. [14] Gagnon, Etienne, Benjamin R. Mandel, and Robert J. Vigfusson (2014). (cid:147)Missing Import Price Changes and Low Exchange Rate Pass-Through.(cid:148)American Economic Journal: Macroeconomics, vol. 6(2), pages156(cid:150)206. 18

[15] Gordon, Robert J. (2006). (cid:147)The Boskin Commission Report: A Retrospective One DecadeLater,(cid:148)International Productivity Monitor, CentrefortheStudyofLivingStandards, vol. 12, pages 7(cid:150)22. [16] Greenlees, John S., and Robert McClelland (2011), (cid:147)New Evidence on Outlet Substitution E⁄ects in Consumer Price Index Data,(cid:148)Review of Economics and Statistics, vol. 93(2), pages 632(cid:150)646. [17] Hall, Robert E. (2011). (cid:147)The Long Slump,(cid:148)American Economic Review, vol. 101(2), pages 431(cid:150)69. [18] Houseman, Susan, Christopher Kurz, Paul Lengermann, and Benjamin Mandel (2011). (cid:147)O⁄shoring Bias in U.S. Manufacturing,(cid:148)Journal of Economic Perspectives, vol. 25(2), pages 111(cid:150)32. [19] Kaplan, Greg and Guido Menzio (forthcoming). (cid:147)The Morphology of Price Dispersion,(cid:148) with Greg Kaplan, International Economic Review. [20] Klenow, Peter J. and Oleksiy Kryvtsov (2008). (cid:147)State-Dependent or Time-Dependent Pricing: Does It Matter for Recent U.S. In(cid:135)ation?(cid:148)Quarterly Journal of Economics, vol. 123 (3), pages 863(cid:150)904. [21] Klenow, Peter J. and Benjamin A. Malin (2011). (cid:147)Microeconomic Evidence on Price- Setting.(cid:148)Handbook of Monetary Economics, Volume 3, Chapter 6, in B. M. Friedman and M. Woodford (editors), pages 231(cid:150)284. North Holland: Elsevier. [22] Kryvtsov, Oleksiy and Nicolas Vincent (2014). (cid:147)On the Importance of Sales for Aggregate Price Flexibility,(cid:148)Working Papers 14-45, Bank of Canada. [23] Nakamura, Alice O., W. Erwin Diewert, John S. Greenlees, Leonard I. Nakamura, and Marshall B. Reinsdorf (2014). (cid:147)Sourcing Substitution and Related Price Index Biases,(cid:148) mimeo, University of British Columbia. [24] Nakamura, Emi and J(cid:243)n Steinsson (2008). (cid:147)Five Facts about Prices: A Reevaluation of Menu Cost Models,(cid:148)Quarterly Journal of Economics, vol. 123(4), pages 1415(cid:150)1464. [25] Nakamura, Emi and J(cid:243)n Steinsson (2012). (cid:147)Lost in Transit: Product Replacement Bias and Pricing to Market,(cid:148)American Economic Review, vol. 102(7), pages 3277(cid:150)3316. [26] Nevo, Aviv and Arlene Wong (2015). (cid:147)The Elasticity of Substitution Between Time and Market Goods: Evidence fromthe Great Recession,(cid:148)NBERWorking Papers 21318, National Bureau of Economic Research, Inc. 19

[27] Oi, Walter Y. (1992). (cid:147)Productivity in the Distributive Trades: The Shopper and the Economies of Massed Reserves,(cid:148)in Output Measurement in the Service Sectors, Zvi Griliches, editor, NBER Books, National Bureau of Economic Research, Inc. [28] Reinsdorf, Marshall (1993). (cid:147)The E⁄ect of Outlet Price Di⁄erentials on the U.S. Consumer Price Index,(cid:148) in Price Measurements and Their Uses, Murry Foss, Marylin Manser, and Allan Young, editors, NBER Books, National Bureau of Economic Research, Inc. 20

Table 1: Incidence of CGH(cid:146)s truncation and its dampening e⁄ect on in(cid:135)ation Posted prices E⁄ective prices share of share of (cid:27) (cid:25)pos (cid:27) (cid:25)eff (cid:1)p mc;t (cid:1)peff mc;t mscj;t mcj;t Product category truncated untrunc(cid:0). t(cid:1)runc. truncated untrunc(cid:16). t(cid:17)runc. (percent) (percent) (percent) (percent) (percent) (percent) (1) (2) (3) (4) (5) (6) Beer 14:4 1:9 1:2 21:2 1:7 1:5 Blades 10:6 1:7 0:9 44:1 1:9 1:5 Carb. beverages 33:4 5:2 2:1 34:6 5:1 3:6 Cigarettes 4:1 6:2 3:5 36:1 7:4 5:7 Co⁄ee 18:3 6:4 2:9 43:0 7:5 4:4 Cold cereal 26:7 3:9 1:4 46:3 3:8 2:0 Condiments 11:6 4:4 1:9 38:8 5:0 3:3 Deodorant 13:4 2:0 0:6 54:1 2:5 1:7 Diapers 14:7 3:3 1:8 39:7 4:3 3:9 Facial tissue 27:4 6:3 2:5 44:7 5:8 3:7 Frozen dinners 34:2 4:5 1:5 43:3 4:3 2:6 Frozen pizza 36:4 5:1 1:9 41:1 4:8 3:2 Hot dogs 37:5 6:0 1:9 39:9 5:8 3:3 Household cleaners 15:7 2:9 1:3 42:5 3:1 2:1 Laundry detergent 25:4 3:8 1:5 48:2 4:2 2:6 Margarine/butter 26:3 7:5 3:6 30:8 7:3 5:0 Mayonnaise 18:9 7:9 3:5 32:5 8:2 5:3 Milk 16:7 5:7 3:8 18:2 5:9 5:0 Paper towels 23:5 4:7 2:1 43:5 5:0 3:2 Peanut butter 19:1 5:9 2:9 29:7 6:3 4:3 Photography 10:7 7:0 1:7 66:0 6:3 3:8 Razors 10:9 3:3 1:3 65:8 4:1 2:8 Salty snacks 26:1 4:0 1:6 34:5 3:9 2:7 Shampoo 14:6 2:1 0:7 77:7 2:6 1:8 Soup 20:5 4:6 1:8 45:5 5:1 3:1 Spaghetti sauce 25:4 4:7 2:0 49:9 4:8 3:1 Sugar/substitutes 10:3 3:0 1:6 29:4 3:0 2:5 Toilet tissue 25:8 4:5 2:2 43:6 5:1 3:3 Tooth brushes 12:2 2:7 0:8 61:6 3:3 2:0 Tooth paste 19:1 2:7 1:0 51:0 3:1 1:9 Yogurt 30:0 4:8 2:1 31:4 4:1 2:9 Mean Unweighted 20:5 4:5 1:9 42:9 4:7 3:2 Expenditures-weighted 23:6 4:5 2:0 37:5 4:6 3:1 Observations-weighted 22:0 n:a: n:a: 42:7 n:a: n:a: Source: Authors(cid:146)calculations using IRI data. Notes: The statistics exclude private labels. We pool raw observations across markets and months to derive the shares of truncated posted and e⁄ective price changes at the product-category level. Stratumlevel in(cid:135)ation is measured on a 12-month basis. The averaging of statistics across product categories uses either uniform weights ((cid:147)Unweighted(cid:148)), sample expenditures weights ((cid:147)Expenditures-weighted(cid:148)), or raw observations weights ((cid:147)Observations-weighted(cid:148)). 21

Table 2: Statistics on missing weekly item observations in the IRI sample Mean weekly Mean weekly Missing observations Product category sales observations (percent of sample obs.) (thousands of $) (thousands) Total Reporting issues (1) (2) (3) (4) Beer 10;833 302 31:4 2:0 Blades 952 120 57:4 2:0 Carb. beverages 14;209 433 27:0 2:1 Cigarettes 6;017 410 61:7 1:9 Co⁄ee 3;270 238 43:1 2:1 Cold cereal 7;588 312 24:4 2:1 Condiments 792 88 42:3 2:5 Deodorant 1;029 433 61:3 1:9 Diapers 1;518 118 55:3 2:2 Facial tissue 946 44 25:7 1:8 Frozen dinners 6;641 505 25:0 2:0 Frozen pizza 3;364 166 28:3 2:2 Hot dogs 945 132 40:3 2:2 Household cleaners 1;978 62 21:3 2:3 Laundry detergent 3;640 171 35:1 1:9 Margarine/butter 1;532 73 13:0 2:2 Mayonnaise 1;276 54 24:4 2:7 Milk 4;631 118 23:5 2:1 Paper towels 2;106 43 22:5 1:9 Peanut butter 931 51 24:1 2:6 Photography 229 33 64:9 5:1 Razors 144 29 68:0 6:0 Salty snacks 9;039 502 27:9 1:9 Shampoo 1;127 432 64:4 1:9 Soup 4;056 432 33:3 2:2 Spaghetti sauce 1;919 175 32:4 2:5 Sugar/substitutes 410 37 36:0 3:2 Toilet tissue 3;483 60 20:2 1:8 Tooth brushes 602 214 63:7 2:1 Tooth paste 1;284 266 49:7 1:9 Yogurt 4;350 248 15:5 2:1 Total 100;842 6;299 n:a: n:a: Mean Unweighted n:a: n:a: 37:5 2:4 Expenditures-weighted n:a: n:a: 31:5 2:1 Observations-weighted n:a: n:a: 39:0 2:1 Source: Authors(cid:146)calculations using IRI data. Notes: The statistics exclude private labels. We pool raw observations across markets and months to obtain product-category (cid:133)gures. We categorize a missing observation under (cid:147)Reporting issues(cid:148)whenever over 95 percent of its store(cid:146)s weekly observations for the product category are missing. The averaging of statisticsacrossproductcategoriesuseseitheruniformweights((cid:147)Unweighted(cid:148)),sampleexpendituresweights ((cid:147)Expenditures-weighted(cid:148)), or raw observations weights ((cid:147)Observations-weighted(cid:148)). 22

Table 3: Illustration of CGH(cid:146)s time aggregation mistake for e⁄ective prices Monthly Four-week change CGH(cid:146)s monthly Week Month e⁄ective in monthly e⁄ective price price e⁄ective price in(cid:135)ation (1) (2) (3) 1 1 1 : : 2 1 1 : : 3 1 1 : : 4 1 1 : : 5 2 1:25 0:25 0:2 6 2 1:25 0:25 0:2 7 2 1:25 0:25 0:2 8 2 1:25 0:25 0:2 9 2 1:25 0 0:2 Notes: The table illustrates CGH(cid:146)s incorrect time aggregation of weekly e⁄ective prices for months that have (cid:133)ve weeks. We suppose that a UPC(cid:146)s (cid:133)rst and second months in the sample contain four weeks and (cid:133)ve weeks, respectively. We assume that the UPC(cid:146)s e⁄ective (log) price across stores in the market is 1 in the (cid:133)rst month and 1:25 in second month (column 1), consistent with a 0:25 log increase between the two periods. Tomeasuremonthlye⁄ectivepricein(cid:135)ation,CGH(cid:133)rstcomputethefour-weekchangeintheweekly series of these monthly e⁄ective prices (column 2). For weeks 5 through 8, the four-week change coincides withtheactualmonthlye⁄ectivepricechange. Forweek9,thefour-weekchangeiszerobecauseweeks5and 9 belong to the same month. CGH then calculate the average four-week change during the month (column 3), so they report a change of only 0:2 for month 2. 23

Table 4: Item turnover and clearance sales in the IRI sample Monthly Monthly On On sale Price drop Product category exit rate entry rate sale (cid:133)nal week (cid:133)nal week (percent) (percent) (percent) (percent) (percent) (1) (2) (3) (4) (5) Beer 1:4 1:7 20:3 21:2 2:6 Blades 2:4 2:4 16:2 25:4 12:3 Carb. beverages 2:0 2:1 32:2 30:7 2:2 Cigarettes 2:3 2:0 6:8 4:0 -1:6 Co⁄ee 1:8 2:2 22:1 30:7 13:3 Cold cereal 2:1 2:2 23:0 42:1 17:0 Condiments 1:3 1:2 14:8 26:7 13:8 Deodorant 2:7 2:6 22:4 34:4 18:5 Diapers 3:9 4:2 24:6 35:0 9:6 Facial tissue 2:9 2:9 23:6 33:8 11:7 Frozen dinner 2:3 2:7 32:2 44:8 14:4 Frozen pizza 1:9 2:1 33:5 38:0 7:6 Hot dogs 1:5 1:5 27:4 28:5 3:9 Household cleaners 2:0 2:9 17:8 33:6 19:3 Laundry detergent 3:1 3:2 25:6 42:6 14:2 Margarine/butter 1:4 1:3 19:2 29:5 7:6 Mayonnaise 1:6 1:7 15:6 30:4 11:7 Milk 1:8 2:1 13:9 18:8 2:9 Paper towels 4:2 4:2 19:8 32:7 9:0 Peanut butter 1:2 1:4 16:8 31:5 12:0 Photography 3:0 2:0 21:0 18:7 13:4 Razors 3:5 3:7 24:6 28:4 15:5 Salty snacks 3:7 3:8 25:1 27:3 3:3 Shampoo 3:2 3:2 25:8 33:5 16:6 Soup 1:3 1:8 20:3 37:1 20:1 Spaghetti sauce 1:3 1:3 24:8 33:9 15:4 Sugar/substitutes 1:4 1:7 12:1 28:9 19:8 Toilet tissue 3:5 3:6 21:5 35:0 8:4 Tooth brushes 2:8 3:0 21:0 29:5 20:3 Tooth paste 2:5 2:5 23:6 36:0 18:5 Yogurt 2:3 2:6 24:5 35:8 7:6 Mean Unweighted 2:3 2:4 21:7 30:9 11:6 Expenditures-weighted 2:3 2:4 23:4 30:5 8:2 Source: Authors(cid:146)calculations using IRI data. Notes: Thestatisticsexcludeprivatelabels. Wepoolrawobservationsacrossmarketsandmonthstoobtain product-category(cid:133)gures. (cid:147)Onsale(cid:148)isthefractionofnonmissingweeklyobservationsforwhichtheIRIsales (cid:135)ag is activated. (cid:147)On sale in (cid:133)nal week(cid:148)is the corresponding fraction using only the last observation of price trajectories. (cid:147)Price drop (cid:133)nal week(cid:148)is the percent (in log changes) by which an item(cid:146)s last observed price is below its mean price over the previous 14 to 26 weeks. With the exception of (cid:147)On sale,(cid:148)all statistics exclude observations within 13 weeks of a store(cid:146)s entry in or exit from the sample. The averaging of statistics across product categories uses either uniform weights ((cid:147)Unweighted(cid:148)) or sample expenditures weights ((cid:147)Expenditures-weighted(cid:148)). 24

Table 5: Response of 12-month posted and e⁄ective price in(cid:135)ation to local unemployment rate Expenditure-weighteditemsandUPCs Market- Market- Uniformly-weighteditemsandUPCs Common Common speci(cid:133)c speci(cid:133)c (1) (2) (3) (4) (5) (6) (7) (8) CGH(cid:146)s original estimates In(cid:135)ation Posted prices 0:084 0:087 0:061 0:164 0:077 0:075 0:052 0:059 (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:041) (0:053) (0:017) (0:067) (0:021) (0:023) (0:026) (0:029) E⁄ective prices 0:120 0:126 0:219 0:288 0:201 0:205 0:136 0:146 (cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:067) (0:087) (0:024) (0:105) (0:031) (0:033) (0:027) (0:028) Testp-value (cid:12)^pos =(cid:12)^eff 0:246 0:332 <0:001 0:011 <0:001 <0:001 0:019 0:026 GLSS(cid:146)estimates without truncation In(cid:135)ation Posted prices 0:237 0:241 0:153 0:253 0:189 0:182 0:134 0:137 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:090) (0:115) (0:054) (0:139) (0:050) (0:058) (0:052) (0:063) E⁄ective prices 0:403 0:435 0:444 0:452 0:268 0:276 0:088 0:123 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:107) (0:137) (0:033) (0:154) (0:030) (0:038) (0:042) (0:048) Testp-value (cid:12)^pos =(cid:12)^eff <0:001 <0:001 <0:001 0:002 0:139 0:090 0:386 0:819 (cid:12)^pos <(cid:12)^eff <0:001 <0:001 <0:001 0:001 0:070 0:045 0:807 0:591 GLSS(cid:146)estimates with all data (cid:133)lters In(cid:135)ation Posted prices 0:067 0:058 0:223 0:428 0:256 0:253 0:142 0:157 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:120) (0:157) (0:036) (0:189) (0:044) (0:051) (0:040) (0:047) E⁄ective prices 0:083 0:072 0:236 0:416 0:222 0:210 0:090 0:098 (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3) (cid:3)(cid:3) (cid:3)(cid:3) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:100) (0:132) (0:032) (0:161) (0:034) (0:038) (0:039) (0:043) Testp-value (cid:12)^pos =(cid:12)^eff 0:486 0:633 0:507 0:718 0:284 0:193 0:084 0:045 (cid:12)^pos <(cid:12)^eff 0:243 0:317 0:254 0:641 0:858 0:904 0:958 0:978 Speci(cid:133)cation Stratum(cid:133)xed e⁄ects No Yes Yes Yes Yes Yes Yes Yes Month (cid:133)xed e⁄ects No No Yes Linear Yes Yes Yes Yes trend Weighted regressions No No No No No No Yes Yes Source: (cid:147)CGH(cid:146)s original estimates(cid:148)are reproduced from table 1 in Coibion, Gorodnichenko, and Hong (2015). All other numbers are the authors(cid:146)calculations using IRI data. Notes: The derivation of (cid:147)GLSS(cid:146)estimates without truncation(cid:148)includes a proper stitiching of the subsamples and the exclusion of price trajectories with outsize adjustments. The derivation of (cid:147)GLSS(cid:146)estimates with all data (cid:133)lters(cid:148)further includes comparable time aggregations of weekly price adjustments and treatments for missing prices and clearance sales. Driscoll and Kraay (1998) standard errors are reported in parenthesesbelowpointestimates. Statisticalsigni(cid:133)canceatthe10, 5,and1percentlevelsisindicatedwith one, two, and three stars, respectively. 25