困境中的定價.pdf

1、Pricing Under DistressBoragan Aruoba1Andres Fernandez2Daniel Guzmn3Ernesto Pasten4Felipe Saffie51University of Maryland and NBER2IMF3UBC and Central Bank of Chile4Central Bank of Chile5UVA(Darden)and NBERNovember 14,2024IMF Annual Research ConferenceDisclaimer:The views expressed are those of the au

2、thors and do not necessarily represent the views of the IMF,its ExecutiveBoard,or IMF management,nor those of the Central Bank of Chile or its board members.MotivationPrice-setting behavior of firms is central in macroeconomics.Monetary policy effectiveness:The more prices adjust,the smaller the rea

3、l effects.Price setting is forward looking.Uncertainty about the future matters.Fernndez-Villaverde et al.(2011,2015)aggregate uncertainty amplifies BC fluctuationsTypical model of uncertainty:time variation in dispersion of a fundamental distribution:realization vs.anticipation.Bloom(2009):volatili

4、ty effect vs.uncertainty effectVavra(2014):Realized uncertaintymore price changesMP less effective.Literature ReviewAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressIntroduction1MotivationPrice-setting behavior of firms is central in macroeconomics.Monetary policy effectiveness:The mor

5、e prices adjust,the smaller the real effects.Price setting is forward looking.Uncertainty about the future matters.Fernndez-Villaverde et al.(2011,2015)aggregate uncertainty amplifies BC fluctuationsTypical model of uncertainty:time variation in dispersion of a fundamental distribution:realization v

6、s.anticipation.Bloom(2009):volatility effect vs.uncertainty effectVavra(2014):Realized uncertaintymore price changesMP less effective.Literature ReviewAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressIntroduction1MotivationPrice-setting behavior of firms is central in macroeconomics.Mo

7、netary policy effectiveness:The more prices adjust,the smaller the real effects.Price setting is forward looking.Uncertainty about the future matters.Fernndez-Villaverde et al.(2011,2015)aggregate uncertainty amplifies BC fluctuationsTypical model of uncertainty:time variation in dispersion of a fun

8、damental distribution:realization vs.anticipation.Bloom(2009):volatility effect vs.uncertainty effectVavra(2014):Realized uncertaintymore price changesMP less effective.Literature ReviewAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressIntroduction1MotivationPrice-setting behavior of fi

9、rms is central in macroeconomics.Monetary policy effectiveness:The more prices adjust,the smaller the real effects.Price setting is forward looking.Uncertainty about the future matters.Fernndez-Villaverde et al.(2011,2015)aggregate uncertainty amplifies BC fluctuationsTypical model of uncertainty:ti

10、me variation in dispersion of a fundamental distribution:realization vs.anticipation.Bloom(2009):volatility effect vs.uncertainty effectVavra(2014):Realized uncertaintymore price changesMP less effective.Literature ReviewAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressIntroduction1Men

11、u Cost:Inaction Bands,Realized Dispersion,and MPInaction0Desired Price ChangePure realized volatility increase the mass outside the bands.More firms adjust their pricesA contemporaneous MP shock is less effective.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressIntroduction2Menu Cost:I

12、naction Bands,Realized Dispersion,and MPInaction0Desired Price ChangePure realized volatility increase the mass outside the bands.More firms adjust their pricesA contemporaneous MP shock is less effective.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressIntroduction2Menu Cost:Inaction

13、Bands,Expected Dispersion,and MPInaction0Desired Price ChangeExpected volatility next period makes future adjustments more likely.Firms delay adjustment to avoid paying the cost twice:wait and seemore inactionFewer firms adjust their pricesA contemporaneous MP shock is more effective.Aruoba,Fernande

14、z,Guzman,Pasten,and SaffiePricing Under DistressIntroduction3Menu Cost:Inaction Bands,Expected Dispersion,and MPInaction0Desired Price ChangeExpected volatility next period makes future adjustments more likely.Firms delay adjustment to avoid paying the cost twice:wait and seemore inactionFewer firms

15、 adjust their pricesA contemporaneous MP shock is more effective.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressIntroduction3Menu Cost:Inaction Bands,Expected Dispersion,and MPInaction0Desired Price ChangeExpected volatility next period makes future adjustments more likely.Firms dela

16、y adjustment to avoid paying the cost twice:wait and seemore inactionFewer firms adjust their pricesA contemporaneous MP shock is more effective.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressIntroduction3DataBusiness to Business(B2B)VAT Invoices from Chilean Tax Authority provided t

17、o theCentral Bank of ChileDaily Frequency from 2015 to 2019.Universe of B2B transactions.Description of product,buyer,seller,price and quantityFocus on supermarkets1.Well-defined input and output prices2.Traditionally used when studying pricing in the literatureUnit of observation:supermarket-locati

18、on-productPrice:Intra-day maximum price.Continuity.Remove short-lived fluctuations.ExamplesBaseline Dataset:39,829 products across 183 supermarkets at 768 locations(14M+observations)Matched Subsample:Supplier prices for a subset of the products analyzed in thebaseline dataset using fuzzy matching,6,

19、540 products across 94 supermarkets at 491locations(2M+observations)DetailsDescriptive Statictics*SAMPLE DETAILS SLIDE NEED UPDATING*Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressDataset4DataBusiness to Business(B2B)VAT Invoices from Chilean Tax Authority provided to theCentral Bank

20、 of ChileDaily Frequency from 2015 to 2019.Universe of B2B transactions.Description of product,buyer,seller,price and quantityFocus on supermarkets1.Well-defined input and output prices2.Traditionally used when studying pricing in the literatureUnit of observation:supermarket-location-productPrice:I

21、ntra-day maximum price.Continuity.Remove short-lived fluctuations.ExamplesBaseline Dataset:39,829 products across 183 supermarkets at 768 locations(14M+observations)Matched Subsample:Supplier prices for a subset of the products analyzed in thebaseline dataset using fuzzy matching,6,540 products acro

22、ss 94 supermarkets at 491locations(2M+observations)DetailsDescriptive Statictics*SAMPLE DETAILS SLIDE NEED UPDATING*Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressDataset4DataBusiness to Business(B2B)VAT Invoices from Chilean Tax Authority provided to theCentral Bank of ChileDaily Fr

23、equency from 2015 to 2019.Universe of B2B transactions.Description of product,buyer,seller,price and quantityFocus on supermarkets1.Well-defined input and output prices2.Traditionally used when studying pricing in the literatureUnit of observation:supermarket-location-productPrice:Intra-day maximum

24、price.Continuity.Remove short-lived fluctuations.ExamplesBaseline Dataset:39,829 products across 183 supermarkets at 768 locations(14M+observations)Matched Subsample:Supplier prices for a subset of the products analyzed in thebaseline dataset using fuzzy matching,6,540 products across 94 supermarket

25、s at 491locations(2M+observations)DetailsDescriptive Statictics*SAMPLE DETAILS SLIDE NEED UPDATING*Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressDataset4DataBusiness to Business(B2B)VAT Invoices from Chilean Tax Authority provided to theCentral Bank of ChileDaily Frequency from 2015

26、 to 2019.Universe of B2B transactions.Description of product,buyer,seller,price and quantityFocus on supermarkets1.Well-defined input and output prices2.Traditionally used when studying pricing in the literatureUnit of observation:supermarket-location-productPrice:Intra-day maximum price.Continuity.

27、Remove short-lived fluctuations.ExamplesBaseline Dataset:39,829 products across 183 supermarkets at 768 locations(14M+observations)Matched Subsample:Supplier prices for a subset of the products analyzed in thebaseline dataset using fuzzy matching,6,540 products across 94 supermarkets at 491locations

28、(2M+observations)DetailsDescriptive Statictics*SAMPLE DETAILS SLIDE NEED UPDATING*Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressDataset4DataBusiness to Business(B2B)VAT Invoices from Chilean Tax Authority provided to theCentral Bank of ChileDaily Frequency from 2015 to 2019.Universe

29、 of B2B transactions.Description of product,buyer,seller,price and quantityFocus on supermarkets1.Well-defined input and output prices2.Traditionally used when studying pricing in the literatureUnit of observation:supermarket-location-productPrice:Intra-day maximum price.Continuity.Remove short-live

30、d fluctuations.ExamplesBaseline Dataset:39,829 products across 183 supermarkets at 768 locations(14M+observations)Matched Subsample:Supplier prices for a subset of the products analyzed in thebaseline dataset using fuzzy matching,6,540 products across 94 supermarkets at 491locations(2M+observations)

31、DetailsDescriptive Statictics*SAMPLE DETAILS SLIDE NEED UPDATING*Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressDataset4DataBusiness to Business(B2B)VAT Invoices from Chilean Tax Authority provided to theCentral Bank of ChileDaily Frequency from 2015 to 2019.Universe of B2B transacti

32、ons.Description of product,buyer,seller,price and quantityFocus on supermarkets1.Well-defined input and output prices2.Traditionally used when studying pricing in the literatureUnit of observation:supermarket-location-productPrice:Intra-day maximum price.Continuity.Remove short-lived fluctuations.Ex

33、amplesBaseline Dataset:39,829 products across 183 supermarkets at 768 locations(14M+observations)Matched Subsample:Supplier prices for a subset of the products analyzed in thebaseline dataset using fuzzy matching,6,540 products across 94 supermarkets at 491locations(2M+observations)DetailsDescriptiv

34、e Statictics*SAMPLE DETAILS SLIDE NEED UPDATING*Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressDataset4The Riots in Chile:An Unexpected EventOct 6,2019:Santiago subway fare is raised by approximately USD$0.05(4%).Oct 18:Disruptions in Santiago subway,wide-spread unrest ensued for a m

35、onth.TimelineKey characteristic:Unexpected,yet relatively short-lived(quasi natural experiment)020406080100Index2018-012018-042018-072018-102019-012019-042019-072019-102020-012020-042020-07DateOct-Nov 2019Google trend for protestasGoogle trend for“protestas”Police Reports of“desrdenes”Aruoba,Fernand

36、ez,Guzman,Pasten,and SaffiePricing Under DistressThe Riots5The Riots in Chile:An Unexpected EventOct 6,2019:Santiago subway fare is raised by approximately USD$0.05(4%).Oct 18:Disruptions in Santiago subway,wide-spread unrest ensued for a month.TimelineKey characteristic:Unexpected,yet relatively sh

37、ort-lived(quasi natural experiment)020406080100Index2018-012018-042018-072018-102019-012019-042019-072019-102020-012020-042020-07DateOct-Nov 2019Google trend for protestasGoogle trend for“protestas”Police Reports of“desrdenes”Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressThe Riots5T

38、he Riots in Chile:An Unexpected EventOct 6,2019:Santiago subway fare is raised by approximately USD$0.05(4%).Oct 18:Disruptions in Santiago subway,wide-spread unrest ensued for a month.TimelineKey characteristic:Unexpected,yet relatively short-lived(quasi natural experiment)020406080100Index2018-012

39、018-042018-072018-102019-012019-042019-072019-102020-012020-042020-07DateOct-Nov 2019Google trend for protestasGoogle trend for“protestas”Police Reports of“desrdenes”Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressThe Riots5The Riots in Chile:An Unexpected EventOct 6,2019:Santiago sub

40、way fare is raised by approximately USD$0.05(4%).Oct 18:Disruptions in Santiago subway,wide-spread unrest ensued for a month.TimelineKey characteristic:Unexpected,yet relatively short-lived(quasi natural experiment)020406080100Index2018-012018-042018-072018-102019-012019-042019-072019-102020-012020-

41、042020-07DateOct-Nov 2019Google trend for protestasGoogle trend for“protestas”Police Reports of“desrdenes”Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressThe Riots5The Riots in Chile:An Unexpected EventOct 6,2019:Santiago subway fare is raised by approximately USD$0.05(4%).Oct 18:Disr

42、uptions in Santiago subway,wide-spread unrest ensued for a month.TimelineKey characteristic:Unexpected,yet relatively short-lived(quasi natural experiment)020406080100Index2018-012018-042018-072018-102019-012019-042019-072019-102020-012020-042020-07DateOct-Nov 2019Google trend for protestasGoogle tr

43、end for“protestas”Police Reports of“desrdenes”Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressThe Riots5The Riots in Chile:Spike in Uncertainty1002003004005002018m12018m42018m72018m102019m12019m42019m72019m102020m12020m3InflationReal Activity IndexUncertainty as Proxied by Standard De

44、viation Across ForecastersAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressThe Riots6Raw DataFraction of Prices That ChangeAverage Size of Price ChangeFrequency of price changes drops during the Riots.The size of price changes increases during the Riots.Aruoba,Fernandez,Guzman,Pasten,a

45、nd SaffiePricing Under DistressThe Riots7Raw DataFraction of Prices That ChangeAverage Size of Price ChangeFrequency of price changes drops during the Riots.The size of price changes increases during the Riots.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressThe Riots7Baseline Specific

46、ationyit=Fixed Effects+Dt+1X1it+2X2t+yitTwo dimensions of pricing behavior captured in yit:Occurrence and Sign of price change(break)in product i in day tSize and Sign of price change(size)in product i in day tDt:Riots Dummy,Oct.18-Nov.17Fixed Effects:1.Product(supermarket-branch-category):Must be s

47、old before and during riots.2.Week day(17),Month(112),Number of the week(15),and Holidays.Other Controls:product-specific time-varying pricing dynamics and economicactivity controlsErrors are clustered at seller-location levelAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressEmpirical a

48、nalysis8Baseline Specificationyit=Fixed Effects+Dt+1X1it+2X2t+yitTwo dimensions of pricing behavior captured in yit:Occurrence and Sign of price change(break)in product i in day tSize and Sign of price change(size)in product i in day tDt:Riots Dummy,Oct.18-Nov.17Fixed Effects:1.Product(supermarket-b

49、ranch-category):Must be sold before and during riots.2.Week day(17),Month(112),Number of the week(15),and Holidays.Other Controls:product-specific time-varying pricing dynamics and economicactivity controlsErrors are clustered at seller-location levelAruoba,Fernandez,Guzman,Pasten,and SaffiePricing

50、Under DistressEmpirical analysis8Baseline ResultsSupermarket Pricing Behavior(1)(2)(3)(4)VariablesPositive BreaksNegative BreaksSize PositiveSize NegativeD-0.00300*-0.00305*0.0313*0.0462*(0.000298)(0.000270)(0.0121)(0.00927)Observations14,135,65014,135,65081,43964,648Adjusted R-squared0.0020.0030.42

51、60.472ControlsYesYesYesYesEconomic Activity ControlsYesYesYesYesFEYesYesYesYesMean of Dependent Variable0.006470.005230.1150.124Note:Clustered Std.Errs.in parentheses.*p0.01,*p0.05,*p0.1Identification:more than 6,000 daily products sold before and during the Riots.During the Riots the frequency of p

52、ositive price changes decreased by around 46%and negative price changes by 58%relative to unconditional mean.The size of price changes increased by around 30%.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressEmpirical analysis9Were Supermarkets responding to changes in suppliers behavi

53、or?Regression using pricing data of supermarkets suppliers.Supermarkets Suppliers Pricing Behavior:Matched Sample(1)(2)(3)(4)VariablesPositive BreaksNegative BreaksSize PositiveSize NegativeD-0.000457-0.001050.00979-0.00790(0.000658)(0.000824)(0.0117)(0.0196)Observations857,519857,5195,2663,005Adjus

54、ted R-squared0.0280.0270.3460.362ControlsYesYesYesYesEconomic Activity ControlsYesYesYesYesFEYesYesYesYesMean of Dependent Variable0.006640.003890.09450.125Note:Clustered Std.Errs.at supplier-supermarket link level in parentheses.*p0.01,*p0.05,*p0.1Suppliers did not change their pricing behavior dur

55、ing riots.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressEmpirical analysis10The Riots in Chile:Widespread&HeterogeneousChange in Frequency of Public Disorder Reports across Regions During RiotsIntensityAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressEmpirical analysis

56、11Taking StockChilean Riots decreased the frequency(50-60%)and increased the size of pricechanges(30%)in supermarkets relative to pre-Riots period.Supply factors cannot explain these changes:No change in behavior of suppliers.Supermarkets seem not to react to something happening contemporaneously:Su

57、permarkets that were not directly affected by Riots exhibit the same behavior.Disagreement among professional forecasters(proxy for uncertainty)increasesdrastically in the months that follow the Riots.Turn to the structural model to show that news about future dispersion inidiosyncratic demand can e

58、xplain these empirical results.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressEmpirical analysis12ModelBuilds on off-the-shelf menu-cost model(Vavra,2014).Intermediate producers setting prices subject to a fixed adjustment cost,facingleptokurtic idiosyncratic TFPMatched to suppliers

59、changing prices occasionally in the dataThey face persistent idiosyncratic demand shocks.Kimball(1995)demand systemDemand shocks affect pricesModel DetailsAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressModel13CalibrationTo the extent possible we use calibration targets from the Chile

60、an micro dataSupplier prices used for calibration firm-level TFP process.Average product-level markup(supermarket prices over supplier prices)Pass-through of changes in supplier prices to supermarket pricesFrequency and size of price changesCalibration DetailsAruoba,Fernandez,Guzman,Pasten,and Saffi

61、ePricing Under DistressModel14News ShockStart at the steady state and receive an unanticipated news shockWith probabilityP,dispersion of idiosyncratic demand shock will increase by a factor ofD in the next period.log?nit+1?=nlog?nit?+vt+1nn,it+1vt+1=(Dwith prob.P1with prob.1 PToday firms learn that

62、shocks to idiosyncratic demand tomorrow may become moredispersed,prompting a wait-and-see effect on price adjustment.Decision RulesA news shock today in the model leads to a decrease in price adjustment frequencyand increase in the average size of adjustments immediately.Solution MethodAruoba,Fernan

63、dez,Guzman,Pasten,and SaffiePricing Under DistressModel15Pricing Responses to the News Shock(Various D andP)Data(Monthly)FrequencySizeData0.107*0.020*(0.0172)(0.00605)Model:FrequencyDP0.50.751.020.0170.0250.03230.0200.0310.04240.0220.0320.045Model:SizeDP0.50.751.020.0060.0090.01230.0060.0110.01440.0

64、070.0110.015Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressModel16Pricing Responses to the News Shock(Various D andP)Data(Monthly)FrequencySizeData0.107*0.020*(0.0172)(0.00605)Model:FrequencyDP0.50.751.020.0170.0250.03230.0200.0310.04240.0220.0320.045Model:SizeDP0.50.751.020.0060.009

65、0.01230.0060.0110.01440.0070.0110.015Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressModel16Policy ImplicationsNews shock arrives in period t=1.(D=3 andP=0.75)Shock to nominal expenditure(monetary policy)in period t=1 or t=2.Output response as a fraction of the shock(CIR:cumulative re

66、sponse)t=1t=2CIRNo NewsMP in t=10.400.160.11News(realized in t=2)MP in t=10.60-0.010.12News(not realized in t=2)MP in t=10.600.280.21News(realized in t=2)MP in t=20.000.050.00News(not realized in t=2)MP in t=20.000.420.12MP in t=1:Effectiveness increases by 50%on impact and persistent if no realizat

67、ion.MP in t=2:If realized very little effect(Vavras result),if not as effective as normaltimes.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressModel17Policy ImplicationsNews shock arrives in period t=1.(D=3 andP=0.75)Shock to nominal expenditure(monetary policy)in period t=1 or t=2.Ou

68、tput response as a fraction of the shock(CIR:cumulative response)t=1t=2CIRNo NewsMP in t=10.400.160.11News(realized in t=2)MP in t=10.60-0.010.12News(not realized in t=2)MP in t=10.600.280.21News(realized in t=2)MP in t=20.000.050.00News(not realized in t=2)MP in t=20.000.420.12MP in t=1:Effectivene

69、ss increases by 50%on impact and persistent if no realization.MP in t=2:If realized very little effect(Vavras result),if not as effective as normaltimes.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressModel17Policy ImplicationsNews shock arrives in period t=1.(D=3 andP=0.75)Shock to n

70、ominal expenditure(monetary policy)in period t=1 or t=2.Output response as a fraction of the shock(CIR:cumulative response)t=1t=2CIRNo NewsMP in t=10.400.160.11News(realized in t=2)MP in t=10.60-0.010.12News(not realized in t=2)MP in t=10.600.280.21News(realized in t=2)MP in t=20.000.050.00News(not

71、realized in t=2)MP in t=20.000.420.12MP in t=1:Effectiveness increases by 50%on impact and persistent if no realization.MP in t=2:If realized very little effect(Vavras result),if not as effective as normaltimes.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressModel17Policy Implications

72、News shock arrives in period t=1.(D=3 andP=0.75)Shock to nominal expenditure(monetary policy)in period t=1 or t=2.Output response as a fraction of the shock(CIR:cumulative response)t=1t=2CIRNo NewsMP in t=10.400.160.11News(realized in t=2)MP in t=10.60-0.010.12News(not realized in t=2)MP in t=10.600

73、.280.21News(realized in t=2)MP in t=20.000.050.00News(not realized in t=2)MP in t=20.000.420.12MP in t=1:Effectiveness increases by 50%on impact and persistent if no realization.MP in t=2:If realized very little effect(Vavras result),if not as effective as normaltimes.Aruoba,Fernandez,Guzman,Pasten,

74、and SaffiePricing Under DistressModel17Conclusion1.We use microdata from Chile to identify the effect of Riots on price dynamics.Frequency of price changes both positive and negative decreasedConditional on changing prices,the size of price changes increased,for both positive andnegative changesSupp

75、ly shocks cannot explain the empirical patterns2.Using a quantitative menu cost model we show that news about future demandvolatility can rationalize the effect of Riots on price dynamics3.In periods of anticipation of uncertainty(without realization),monetary policy ismore effective,unlike when unc

76、ertainty is realized4.When pricing under distress,timing of policy is everything!Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressConclusion18AppendixAppendixAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressConclusion19Literature1.Uncertainty and firm-level decisions:Unce

77、rtainty drives business cycle fluctuations:Bloom(2009,2014)anticipated idiosyncratic volatility causes wait-and-see behavior,andFernndez-Villaverde(2011,2015)aggregate uncertainty amplify BC fluctuations.Aggregate uncertainty impacts the effectiveness of monetary policy:Vavra(2014)price changes,real

78、 policy effects,Baley and Blanco(2019),Ilut et al.(2020)price changes,real policy effects,andKlepacz(2021)aggregate uncertainty,price changes.Potential micro-foundations for firm-level decisions under uncertainty:Rotemberg(2002)consumer anger,andMackowiak et al.(2023)rational inattention.Empirical C

79、hallenge:Identifying the effects of anticipated uncertainty vs.realizedvolatility.Dew-Becker et al.(2017),Berger et al.(2019)evidence for realization effect,Drenik and Perez(2020)price dispersion,andKumar et al.(2023)survey evidence.=Quasi-natural experiment disentangles anticipation and realization

80、 channel.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix20Literature2.Menu cost model:Monetary non-neutrality due to fixed costs of changing prices is well establishedtheoretically:Barro(1972),Sheshinki and Weiss(1977),Caplin and Spulber(1987),Caballero and Engel(1993),and Do

81、tsey et al.(1999)+Kimball(1995).Quantitative models support sizable monetary non-neutralities of menu costs:Golosov and Lucas Jr(2007),Nakamura and Steinsson(2010),Midrigan(2011),and Vavra(2014)product-level data.Alvarez et al.(2016,2023)frequency of price changes crucial3.Rare events and disasters

82、in macroeconomics:Rare monetary events provide empirical insights:Hobijn et al.(2006)2022 introduction of Euro,Gagnon(2009)1995 Mexico inflation,andAlvarez et al.(2019)1990s Argentina hyper inflation.Disasters as exogenous shocks:Barro(1972),Gabaix(2012),Baskaya and Kalemli-zcan(2016)1999 Turkey ear

83、thquake,Acemoglu et al.(2018),Boehm et al.(2019)Arab Spring,andWieland(2019)2011 Japan earthquakereturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix21Riots:TimelineOct 6,2019:Santiago subway fare is raised by 30cs.Students call to demonstrate against with limited successHig

84、h Gov officials did not address the students callOct 18:Disruptions in Santiago subway;police respondedNight of Oct 18 onward:Widely spread mobs attacking,sacking and burningsupermarkets,local businesses,etc.Night of Nov 12:Mobs attacked military facilitiesNight of Nov 15:Turning point-Wide politica

85、l agreement on course of action tochange constitutionReturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix22Matched SubsampleThe baseline dataset:final prices of products sold by supermarketsThe richness of the electronic invoice data allows us to go much further:we build ana

86、dditional matched subsample dataset with suppliers prices of a subset of theproducts analyzed in the baseline sampleMatch done using non-standardized product descriptions across suppliers andsupermarketsTwo parallel methods of fuzzy matchingDetailsA product:unique triplet+suppliers id+suppliers prod

87、uct descriptionMatched Subsample:6,540 products across 94 supermarketsReturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix23A Transaction Level Dataset:Product&PricesOriginal and Filtered prices:Two products in the Dataset(a)Product X14001600180020002200Price(CLP)01jun201501

88、jul201501aug201501sep201501oct201501nov2015dateOriginal PriceFiltered Price(b)Product Y500600700800900Price(CLP)01jul201601oct201601jan201701apr201701jul201701oct2017dateOriginal PriceFiltered PriceReturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix24Descriptive StatisticsB

89、aseline sampleMatched SampleSuppliers SampleMeanStd.DevMeanStd.DevMeanStd.DevPrice SettingTotal Breaks0.01170.10750.01260.11160.01050.1021Positive Breaks0.00650.08020.00670.08150.00660.0812Negative Breaks0.00520.07220.00590.07680.00390.0623Size Positive0.11530.12920.10060.10830.09450.1177Size Negati

90、ve0.12390.13930.10590.12000.12540.1522Sample InfoNo of Supermarkets18394-No of Suppliers-298298No of Supermarkets-locations768491-No of Product ID39,8296,5402,025No of Product Description13,7691,9311,930No of Observations14,135,6502,025,729857,519ReturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricin

91、g Under DistressAppendix25Matched SubsampleNon-standardized product descriptions across suppliers and supermarkets.Two parallel methods of fuzzy matching:cosine similarity and 1-gram distance.Strict criteria for merge validation:1.Cosine distance0.03,1-gram distance3,or Cosine distance0.05 and 1-gra

92、mdistance5.2.At least 20 weeks observed.A product:unique triplet+suppliers id.In cases with multiple suppliers,the one with the longest overlap in the observationperiod with supermarket-location prices is selected.ReturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix26Is It A

93、bout Now?Intensity of Riots-DummySupermarket Analysis and Intensity of Riots(1)(2)(3)(4)VariablesPositive BreaksNegative BreaksSize PositiveSize NegativeD-0.00310*-0.00224*0.0305*0.0652*(0.000560)(0.000461)(0.0145)(0.0253)D*Intensity0.000121-0.000906*0.000932-0.0223(0.000657)(0.000542)(0.0197)(0.027

94、3)Observations14,135,65014,135,65081,43964,648Adjusted R-squared0.0020.0030.4260.472ControlsYesYesYesYesEconomic Activity ControlsYesYesYesYesFEYesYesYesYesMean of Dependent Variable0.006470.005230.1150.124Note:Intensity is a dummy for municipalities above the median change in the number of police r

95、eports for publicdisorders in October and November 2019 relative to October and November 2018,adjusted for population.Clus-tered Std.Errs.in parentheses.*p0.01,*p0.05,*p0.1Intensity in Riots not linked to differential changes in supermarkets pricing behavior.Aruoba,Fernandez,Guzman,Pasten,and Saffie

96、Pricing Under DistressAppendix27Is It About Now?Intensity of Riots-Continuous MeasureSupermarket Analysis and Intensity of Riots(1)(2)(3)(4)VariablesPositive BreaksNegative BreaksSize PositiveSize NegativeD-0.00372*-0.00333*0.02280.0443*(0.000458)(0.000455)(0.0142)(0.0134)D*Intensity2.93e-05*1.17e-0

97、50.0003097.31e-05(1.72e-05)(9.68e-06)(0.000457)(0.000400)Observations14,135,65014,135,65081,43964,648Adjusted R-squared0.0020.0030.4260.472ControlsYesYesYesYesEconomic Activity ControlsYesYesYesYesFEYesYesYesYesMean of Dependent Variable0.006470.005230.1150.124Note:Intensity is the change in the num

98、ber of police reports for public disorders in October and November 2019relative to October and November 2018,adjusted for population.Clustered Std.Errs.in parentheses.*p0.01,*p0.05,*p0.1Intensity in Riots not linked to differential changes in supermarkets pricing behavior.ReturnAruoba,Fernandez,Guzm

99、an,Pasten,and SaffiePricing Under DistressAppendix28ModelStart with the off-the-shelf menu-cost model(Vavra,2014)Intermediate producers setting prices subject to a fixed adjustment cost,“Calvo-plus”Shocks:leptokurtic idiosyncratic TFP,aggregate TFP,aggregate volatility of TFP,nominalexpenditure.Two

100、departures:Add idiosyncratic demand shocks(nit);will introduce news laterlog?nit+1?=nlog?nit?+nn,it+1Kimball(1995)instead of CES,so idiosyncratic demand plays a role.Household standard:supply labor,consume,complete markets,own all the firms.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under Dist

101、ressAppendix29FirmsKimball(1995)aggregator to combine nityitinto Yt.R10G nityitYt!di=1G nityitYt!=1+(1+)nityitYt#1+11+nit:idiosyncratic demand shock.is related to desired markup,captures how demand elasticity changes withmarket share.Intermediate-good production:yit=zithit.CES/Dixit-Stiglitz(when=0)

102、:constant markup,nitirrelevant for pricing.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix30Exogenous ProcessesProductivity processlog?zit?=(zlog?zit1?+zz,it;z,itN(0,1)with probability pzlog?zit1?with probability 1pzDemand Processlog?nit?=nlog?nit1?+nn,itwith n,itN(0,1)Nomina

103、l expenditures StPtYtlog(St)=+log(St1)Profit Function with KimballValue FunctionReturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix31External CalibrationParameterDescriptionValueSourceDiscount Rate0.997Vavra(2014)Trend Inflation0.37%Nominal and Real GDP GrowthpzProb.change

104、in idio.TFP0.19Prob.supplier price changezIdio.TFP Process0.33Supplier price dynamicszIdio.TFP Process0.10Supplier price dynamicsLabor disutility1.0NormalizationUse direct measurements from Chilean micro data when possible.Use supplier price dynamics to calibrate the leptokurtic idiosyncratic TFP pr

105、ocess.Aruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix32Internal CalibrationParameterDescriptionValueMomentModelDataKimball elasticity1.33Avg.Markup0.370.37Kimball super-elasticity1.67Cost Pass-through0.310.31nIdio.Demand AR(1)0.76Fraction up0.550.53nIdio.Demand AR(1)0.088Size

106、0.1130.110fMenu Cost0.042Frequency0.260.26Markup from matched dataset.Pass-through estimated from matched datasetlog?pit?=log?cit?+Firm FEi+it,Match time series properties of dispersion of prices.More on CalibrationReturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix33Intern

107、al CalibrationPass-through RegressionRegress change in log-price for products on change in log-price of supplier prices betweentwo periods when the product price change to get estimated cost pass-throughRecover using=11returnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix34So

108、lution DetailsStationary equilibrium1.Initialize guesses for aggregate prices?PS,?and use VFI to solve for the pricing decision rules.2.Initialize a firm distribution H0?p1S,z,n?.Iterate forward using the law of motion of z,n and thepricing decision rules until the mass of firms at each state is sta

109、tionary.3.ComputePSand at the stationary distribution.Compute the absolute difference between theguesses and implied values.Repeat from step(1)until the differences are sufficiently small.Transition dynamics with news shock1.Set the number of periods that the transition takes denoted by T and solve

110、for the stationaryequilibrium.2.Initialize two sequences of guesses forPSand,for the case when the news shock is and is notrealized.3.Assume that in period T+1,economy is at the stationary equilibrium.Iterate backward to solve forthe value functions at each t=T,T1,.,2.Do this for the case when news

111、shock is and is notrealized4.In period t=1,solve for the value function using V()=PV(;2)+(1 P)V(;2)5.Starting from the stationary distribution,iterate the firm distribution forward using the optimaldecision rules.Compute the implied sequences of?PtSt,t?.Repeat from step(2)until the impliedsequences

112、of aggregate objects is sufficiently close to the guesses.returnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix35Kimball Profit Function-0.2-0.15-0.1-0.0500.050.10.150.200.050.10.150.20.250.3Over-pricing is more costly under Kimball demand.ModelDecision RuleAruoba,Fernandez,G

113、uzman,Pasten,and SaffiePricing Under DistressAppendix36Decision RulesDecision RuleNews about higher future demand dispersion:wait-and-see effect.ReturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix37Value FunctionV pit1St,nit,zit;PtSt,t!=max(VA?nit,zit;PtSt,t?,VN pit1St,nit,zit;PtSt,t!)VN pit1St,nit,zit;PtSt,t!=pit1St,nit,zit,PtSt,t!+Ett,t+1V pit1St1e,nit+1,zit+1;Pt+1St1e,t+1!#VA?nit,zit;PtSt,t?=fWtPt+maxpitSt(pitSt,nit,zit,PtSt,t!+Ett,t+1V pitSt1e,nit+1,zit+1;Pt+1St1e,t+1!#)Solution MethodReturnAruoba,Fernandez,Guzman,Pasten,and SaffiePricing Under DistressAppendix38