Food, Fuel, and Facts: Distributional Effects of Global Price Shocks

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1414 July 2025 Food, Fuel, and Facts: Distributional Effects of Global Price Shocks Saroj Bhattarai, Arpita Chatterjee, and Gautham Udupa Please cite this paper as: Bhattarai, Saroj, Arpita Chatterjee, and Gautham Udupa (2025). “Food, Fuel, and Facts: Distributional Effects of Global Price Shocks,” International Finance Discussion Papers 1414. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2025.1414. NOTE: International Finance Discussion Papers (IFDPs) 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 International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Food, Fuel, and Facts: Distributional Effects of Global Price Shocks* SarojBhattarai† ArpitaChatterjee‡ GauthamUdupa§ Univ. ofTexas-Austin FederalReserveBoard CAFRAL Abstract Weestimatedistributionalimplicationsofglobalfoodandoilpriceshocksbyutilizing monthly panel data on consumption and income from India, and an IV strategy that removesvariationcomingfromglobaldemandshocks.Whilebothshocksleadtostagflationary aggregate dynamics, they differ in terms of distributional consequences. Consumptionoflowerincomedecilesisaffectedmorebyexogenousincreasesinfoodprices,while consumptionofbothtailsoftheincomedistributionisaffectedsimilarlybyexogenousincreases in oil prices. These heterogeneous negative consumption responses largely mirrorthepatternofheterogeneityinwageincomeresponses. Increasesinrelativeexpenditure of food, despite a rise in the relative local price of food, provides clear evidence for non-homotheticdemandinnon-durableconsumption. EstimatingtheslopesoftheEngel curve by impulse response matching, we find that food, compared to fuel, is a necessary consumptiongoodforallincomegroups. Comparingthemodelpredictionswiththeempirical consumption responses, we decompose the role played by wage income, relative pricechanges,andnon-homotheticityinexplainingourresults. JELclassification:E31,E32,F62,O11 Keywords: GlobalPriceshocks;Foodprices;Oilprices;Inequality;Householdheterogeneity;Householdconsumption;Necessarygood;Non-homotheticity;India *WethankOliCoibion,IppeiFujiwara,JoaquinGarcia-Cabo,XingGuo,NirJaimovich,DiegoKanzig,Matthew Klepacz,LoganLewis,GiacomoMangiante,PetrSedlacek,SanjaySingh,DanielXu,andseminarandconference participantsatFederalReserveBoard,NCStateUniversity,JHU-SAIS,CarletonUniversity,AEAAnnualMeeting, CAFRAL Conference, West Coast Workshop in International Finance, Joint Bank of Lithuania and Poland Conference, CEBRA Workshop for Commodities and Macroeconomics, IJCB Conference, Econometric Society AustralasianMeeting,RBAAnnualConference,UWA,HKU,SERIConference,UNSW,IIM-Bangalore,MidwestMacro Conference,ISI-Delhi,AshokaUniversity,AmericanUniversity,JohnsHopkinsUniversity,UCSantaCruzandANU CrawfordSchoolforhelpfulcomments. WethankSowmyaGaneshandSurajKumarforresearchassistance. This researchpresentsviewsoftheauthorsandnotthatoftheFederalReserveBoardortheFederalReserveSystem. Firstversion:July2022.Thisversion:July2025. †UniversityofTexasatAustin,U.S.A.Email:saroj.bhattarai@austin.utexas.edu. ‡FederalReserveBoard,U.S.A.Email:chatterjee.econ@gmail.com. §CAFRAL,Mumbai,India.Email:gautham.udupa@cafral.org.in.

1 Introduction We have seen large movements in relative prices globally recently, due to both sector-specific shocks(suchascommodity-specificsupplyshocks)aswellaspolicychangesthataffectspecific sectorsdirectly(suchastariffs). Aparticularlynotableexampleofsucharelativepricechange, andthefocusofthispaper,istheincreaseinglobal oilandfoodprices. Theseexternalshocks haveraisedmajorconcernsworldwide,particularlyinemergingmarkets,whoseeconomiesare oftenmoreexposedandvulnerabletoglobalshocks. Economists sometimes predict relative price increases to have little, if any, effects on aggregateconsumptionastheypresumeconsumerswillshifttheirspendingtowardsectorsthat havebecomerelativelycheaper.However,thisreasoningoverlookspotentialnegativeeffectson earningsthatcanresultfromsuchpriceshifts,whichwill,inturn,reduceoverallconsumption. Moreover,inemergingmarketeconomies(EMEs),theseshocks—particularlythoseinfoodand fuel—canhaveanout-sizedimpact,astheyaffectthelivelihoodsofalargeportionofthepopulation. Theseshocksarefurtherexpectedtoexacerbateexistinginequalityinthesecountries byhavingstrongeffectsoninflation,andleadingtodisproportionateincreasesincost-of-living forthepoorerpeopleduetothenecessarynatureoffoodand/orfuelinconsumption. InEMEs,asglobalpriceshocksarelikelytohavestagflationaryeffects–simultaneouslyslowinggrowthandfuelinginflation–whilealsoraisingsuchdistributionalconcerns,theyhaveunsurprisinglybeenattheforefrontofpolicymakers’agendas.Forinstance,intheApril2022issue oftheWorldEconomicOutlook((IMF)(2022a)),theInternationalMonetaryFund(IMF)states: Fuel and food prices have increased rapidly, with vulnerable populations–particularly in lowincome countries–most affected. Elevated inflation will complicate the trade-offs central banks facebetweencontainingpricepressuresandsafeguardinggrowth... Higherfoodpriceswillhurt consumers’purchasingpower–particularlyamonglow-incomehouseholds–andweighondomesticdemand. Moreover,withdeterioratingconditionsinfoodandenergymarkets,theIMF’s stance is more grave in the July 2022 issue of the outlook ((IMF) (2022b)): Rising food and energypricescausewidespreadhardship,famine,andunrest.Becauseenergyandfoodareessential goodswithfewsubstitutes,higherpricesareparticularlypainfulforhouseholds. Previousworkprovidesrigorousevidenceontheimpactofsuchglobalpriceshocksonthe overall macroeconomy.1 Olivi, Sterk, and Xhani (2023) and Afrouzi, Bhattarai, and Wu (2024) offerimportanttheoreticalinsightsonhowsector-specificshockscanleadtoaggregatestagflationary dynamics. However, rigorous evidence on the distributional consequences of such shocks, as well as on the channel of transmission of such shocks operating from income to 1Seeamongothers,Hamilton(2003),Kilian(2009),BaumeisterandHamilton(2019),Kanzig(2021),DeWinne andPeersman(2016),andDeWinneandPeersman(2021). 1

overall consumption, is limited. The emerging literature on distributional consequences of gas/oil prices or carbon pricing (Gelman, Gorodnichenko, Kariv, Koustas, Shapiro, Silverman, and Tadelis (2023), Kanzig (2023), Pallotti, Paz-Pardo, Slacalek, Tristani, and Violante (2024)) focusesonadvancedeconomiesand(explicitlyorimplicitly)assumesenergytobeessentialin consumptionsuchthatfluctuationsinoilpricecanbetreatedasunexpectedincomeshocks. Inthispaper,weexaminethecausal connectionbetweenincreasesinglobalfoodandfuel pricesandconsumptioninequalityinIndia, amajoremergingeconomythathasexperienced significantinflationarypressuresinthesesectorsrecently.Critically,wedonotassume,ex-ante, thateitherfoodorfuelarenecessaryconsumptiongoods,andratheruseourempiricalresults andanon-homotheticdemandstructuretoeconometricallyinferwhetherfoodand/orfuelare indeednecessitiesintheconsumptionbasket.2 We find clear distributional consequences in India due to a rise in global food prices. An exogenous increase in global food price leads to a statistically significant, and economically meaningful,increaseinconsumptioninequality,aswefindmonotonicallylargeradversetotal (real) consumption effects on poorer income groups. While an exogenous rise in global fuel pricesalsoclearlyhasadverseeffectsonconsumption, thepatternofheterogeneity, andconsequentlytheimpactoninequality,ismoresubtleasthepoorestandthetworichesthousehold groupsaresimilarlyaffected.Weshowthatakeytransmissionmechanismthroughwhichoverallconsumptionfallsisthroughlowerwageincome. Thisexplainswhytotalconsumptionand variouscategory-specificconsumptiondisplayacommonpatternofheterogeneityinresponse to global price shocks. Finally, matching dynamic impulse responses of consumption expendituresharesandpriceresponsesthroughthelensofanon-homotheticdemandstructure,we estimatedifferencesinslopesofEngelcurvestoestablishthatfoodisindeedanecessaryconsumptiongoodforallhouseholdsinIndia. For our empirical analysis, we utilize a comprehensive monthly household panel dataset from India that spans 2014-2019. Leveraging the panel dimension of the data, in a local projectionframeworkatthehouseholdlevel,weinvestigatewhetherthedynamiceffectson(real) consumptionofglobaloilandfoodpricefluctuationsdifferalongtheincomedistribution. Our analysisinvolvescategorizinghouseholdsintofiveincomebracketsandestimatinginteraction effectsbetweenthesegroupsandtheglobalpriceshocks.3 To ensure a causal interpretation of our findings, we devise an instrumental variable (IV) 2Weusethetermsnon-homotheticdemandandanecessaryconsumptiongoodasinclassicalconsumertheory. Non-homotheticdemandimpliesanincomeeffectonexpendituresharesandanecessary(luxury)consumption goodhasanincomeelasticityofdemandthatisless(greater)thanone.Incommonuse,agoodwithalowpriceelasticityofdemandisreferredtoasanessentialgood.Formally,anessentialgoodisonesuchthatzeroconsumption ofthatgoodimpliesazeromarginalutilityofallothergoods. 3Werefertotheseincomegroupsaslowest,low,low-middle,upper-middle,andhigh-incomegroups. 2

strategy. The key concern with OLS estimation is that of omitted variable bias arising due to global demand shocks. As the literature on the macroeconomic impact of oil shocks emphasizes, separating the effects of global demand shocks from those of supply shocks is essential foraclearinterpretationoftheresults. Usingchangesinglobaloilandfoodpricesasameasure ofshockwouldthusproduceOLSestimatesthatataminimumconflatetheeffectsofbothtypes ofshocks. Inoursetting,however,theywouldalsoleadtobiasedestimates. Specifically,global demandshocksarewell-knowndriversofglobalcommoditypricesandtheydirectlyalsoaffect Indianhouseholdconsumptionthroughmanychannelsofexposure.Thisbiasisexpectedtobe positive,whichmeansweanticipatetheOLSestimatestobelessnegativethantheIVestimates. Totacklethischallenge,weemployanIVapproachthatistailoredtoremovingthevariation coming from global demand shocks, using supply-side instruments for the change in global oil and food prices. For the global oil price change, we use the oil supply shock estimated in BaumeisterandHamilton(2019)asanIV,whilefortheglobalfoodpricechange,weconstruct our own IV. The latter is based on residuals of food commodity prices, after extracting an aggregatecommonfactorasaproxyofglobaldemand,estimatedbyimposingsignrestrictionsin adynamicfactormodeltocapturecomovementofallcommoditypriceswithglobaldemand. Withthedynamicfactormodel,wealsofurtherextractafood-specificfactorthatcapturescomovementofonlyfoodcommodityprices.4 Our main findings in more detail are as follows. First, global food and oil price increases are stagflationary for India. We reach this conclusion from estimates based on aggregate data aswellasestimatesofaverageeffectsbasedonthehouseholdconsumptionandregionalconsumerpricedata. Second, thenegativeconsumptioneffectsoftheseshocksshowrobustheterogeneityalongtheincomedistribution. Anexogenousincreaseinfoodpricesaffectshouseholdsinthelowerincomedecilesmore,andthenegativeconsumptioneffectsbecomeprogressively less severe as we move up the income distribution. In contrast, an exogenous increase in fuel prices decreases consumption of both the lowest and the two highest income groups similarly. Moreover, consumption of the low-income group decreases the most for food price shocks, while it decreases the least for oil price shocks. These differential effects are not only statisticallysignificant,butalsoeconomicallymeaningful.5 4UsinganIValsohelpsaddressanyreversecausalityconcerns.IfoneassumesIndiatobeasmallopeneconomy withnoeffectsoperatingfromlocalconditionstoglobalcommodityprices,thenreversecausalityisnotmuchof aconcern. ButsinceIndiaisgrowingfast,itmightbemorecrediblenottoassumeitex-anteandratheruseanIV thatisolatesvariationcomingfromthesupply-sideoutsideIndia. 5Themaximumimpactofaone-standarddeviationfoodpriceshockaccountsfor10%oftheunconditional volatility in non-durable consumption for the low-income group, while it explains only 5% of the volatility for thehighestincomegroup. Incontrast,themaximumimpactofaone-standarddeviationoilpriceshockexplains 5.5%oftheunconditionalvolatilityinnon-durableconsumptionforthepoorestincomegroup,5%forthehighest incomegroup,andjust3.2%forthelow-incomegroup. 3

WethenutilizetheIVframeworktofurtherinvestigatethemechanismsthatcausesuchheterogeneouseffectsinconsumption. Wedevelopaparsimoniousandtractablemodeltomotivatethetransmissionmechanisms, butevenwithoutgoingintodetailsofthemodel, theeconomicsbehindthetransmissionmechanismscanbeexplainedwellintuitively. Aswefindthat notjustown-categorycategoryconsumption, butalsocross-categoryandoverallmeasuresof consumption fall in response to increases in food and fuel prices, it already strongly suggests wageincomedeclines. Therefore,wefirstestimatetheheterogeneouswageearningseffectsof the global price shocks. Our analysis reveals that food price shocks lead to a consistent negativeeffectonrealwageincomes,withtheeffectsmonotonicallydecreasingaswemoveupthe incomedistribution. Thissuggeststhatfoodpriceshocksaffectconsumptionheterogeneously through their differential effects on real wage income. For oil price shocks, there are consistently negative wage income effects on the lowest and highest income groups, which is also alignedwiththenegativeconsumptioneffectsforthesegroups. OurIVestimatesrevealsubstantivedifferencesfromthecorrespondingOLSestimates. For instance,whileOLSresultsindicateanincreaseinrealearningsforthehigh-incomegroupfollowinganoilpriceincrease,theIVresultsexhibitadecreaseinstead. Thisfindingofapositive biasinOLSestimatesisintuitive,aspositiveglobaldemandshocks,whichareapartoftheOLS results,andwhichincreaseoilprices,arelikelytobenefithigh-incomehouseholds. Moreover, foroilshocks,OLSestimatesofconsumptioneffectsarenotconsistentlyandpersistentlynegative for any income group. Finally, for consumption effects, the OLS estimates are robustly biasedupwardsforfoodshocksaswell. Second, state-level panel local projection IV results show that both global shocks “passthrough”tolocalpricesinIndia, affectingnotjustown-categorypricesbutalsooverall(headline) prices. Both these shocks also affect relative prices: global food price shocks elevate the relativepriceoffood,whileglobaloilpriceshocksdriveuptherelativepriceoffuelinIndia. Conventional homothetic demand functions predict expenditure-switching effects followingsucharelativepricechange. We,however,findstrongevidencetothecontrary. Specifically, we show that in response to the global food price shock, the food expenditure ratio (e.g., the ratioofnominalfoodexpendituretonominalfuelexpenditure)increasesforthelowerincome groups, which is not consistent with expenditure switching as the only force determining expenditure shares. In fact, given that the relative price of food increases with the global food priceshock, theseconsumptionshareresponsesunambiguouslysuggestaroleforincomeeffects in relative demand and expenditure shares. With this finding as motivation, we proceed further econometrically. Using the dynamic impulse responses of relative food prices, relative food expenditures, and real non-durable consumption expenditure together, we estimate the difference in Engel curve slopes for food and fuel and infer econometrically that food is a 4

necessaryconsumptiongood(thatis,foodhasanincomeelasticityofdemandlessthanone), comparedtofuel,forallincomegroupsinIndia.6 Ourfinalsetofresultscomefromacomparisonofempiricalimpulsestothosepredictedby themodel. Asafirstexercise,wetakeasgiventheestimatedtotalconsumptionresponsesand relativepriceoffoodresponsestoafoodpriceshockandpredictthenon-durableconsumption responseaccordingtothemodel’sdemandstructure.Weshowthatthismodelpredictioniswell alignedtotheempiricalresponseofnon-durableconsumption.Thisdecompositionshowsthat justtherelativepriceoffoodgoingupexplainsverylittleofthenon-durableconsumptiondrop. Thisthenmotivatesustoexplorewhatdrivesthetotalconsumptiondecline. Aswediscussed above, our theoretical framework shows wage income as a common driver of all categories of consumption. We constructa measure of present discounted value of wage income using the empirical wage income response and show that using it instead of total consumption in the exerciseabovecontinuestopredictadropinnon-durableconsumptionthatisclosetotheempiricalresponse. Thisexercisethusclearlydepictstherolesofwageincomeandrelativeprice channelsinexplainingnon-durableconsumptionresponsestotheglobalfoodpriceshock. Ourpaperisrelatedtoseveralstrandsoftheliterature. Thetwo-wayrelationshipbetween globaloilpricesandtheU.S.macroeconomyhasbeenstudiedextensivelybyHamilton(2003), BarskyandKilian(2004),andKilian(2009). Wefirstdemonstratestagflationaryaggregateoutput and price effects in India of oil supply shocks using the Baumeister and Hamilton (2019) supplyshocksdirectlyasameasureofexternalshocks. Asourmaincontribution,wethenestimate distributional effects of global oil prices on household consumption, an area that has only recently garnered empirical attention (see, for example, Gelman et al. (2023), Peersman andWauters(2022),Kanzig(2023),andPallottietal.(2024)). Ourresultsareconsistentinsome important substantive fronts with those in Kanzig (2023). First, our findings that at least part of the heterogeneous response in consumption to oil shocks can be traced to heterogeneous response in wage income is similar to the results in Kanzig (2023) for carbon tax/energy price shocks. Second,likeinKanzig(2023),wealsofindevidenceconsistentwith“leaning-in"monetarypolicyasshort-terminterestratesintheeconomyriseinresponsetosuchshocks. These channels are even stronger for food price shocks in our paper. We illustrate the stagflationary effects of the global food price shocks onthe Indian macroeconomy that go together with a rise in short-term interest rates. In two-sector sticky-price models, if external 6As we discuss later, the class of preferences that align well with our results are iso-elastic non-homothetic constantelasticityofsubstitutionpreferencesbetweenfoodandfuel.Thesegiverisetolog-linearEngelcurvesfor foodandfuel,similartoBanks,Blundell,andLewbel(1997).Ourtheoreticalframeworkandeconometricanalysis use this class of preferences. In these preferences, distinct parameters govern separately the price elasticity of demand(whichwillcapturethestandardexpenditureswitchingchannel)andtheincomeelasticityofdemand (whichwillcapturethenon-homotheticitychannel).SeeMatsuyama(2022)foradiscussion. 5

commoditypriceshocksleadtoaggregateinflation,thenbyactinglike“cost-push”shocksthat introduce a policy trade-off for central banks, they can cause a recession and lead to a fall in wage earnings domestically. The possibility of oil price shocks as negative aggregate supplyshockshastraditionallyreceivedmoreattentioninadvancedeconomies(seeAfrouzietal. (2024)forarecentexample),wherethekeymechanismarisestheoreticallyduetooil’sroleasan intermediateinput. However,foodpriceshockscanalsohavesimilareffectsduetofoodbeing anecessaryconsumptiongood. Forinstance,Olivietal.(2023)showtheoreticallythatasupply shock in a sector that produces a necessary consumption good, which we show empirically is foodintheIndiancontext,canactasanaggregatecost-pushshock.7 Empirically, De Winne and Peersman (2021) have previously established how global food price shocks, driven by adverse weather shocks, can negatively impact real economic activity inmiddle-incomecountries. Theliteratureonthemacroeconomiceffectsofglobalfoodprice shocks,suchasDeWinneandPeersman(2016)andPeersman(2022),hasexaminedtheaggregate or sectoral effects of food price shocks. We contribute by estimating regressive distributionaleffects,atthehouseholdlevel,ofariseinglobalfoodprices. WeusetheoilsupplyshockestimatedinBaumeisterandHamilton(2019)asaninstrument inourpanelIVspecificationstoisolatetheroleofexternalsupplyshocks.InourIVspecification fortheglobalfoodpricechange,theinstrumentwedevelopisnovelasweestimateadynamic factormodelwithsignrestrictionsusingdatafromabroadcross-sectionofcommodityprices toisolateaggregatedemandandfood-specificfactorsfromglobalfoodpricedynamics. Inthis context, for both global price changes, one of our contributions is to show a positive omitted variablebiasinOLSestimates. Thisholdsbothintermsofaverageeffects,connectingwiththe literatureonoilpriceshocks,aswellasthedistributionaleffects. In one important difference from the recent literature on distributional effects of energy pricechanges,wedonotassumeex-antethatfuelisanecessarygood,andratherinferstatisticallywhetherfoodandfuelarenecessities. Ourinferencereliesonestimateddifferencesinthe slopesoftheEngelcurvesforfoodandfuel. Combininghouseholdpaneldataandtimeseries shocks,aswementionedabove,wedevelopanovelmethodthatreliesondynamicvariationto estimateslopesoftheEngelcurveusingexternalinstruments.Onthismethodologicalfront,we complementworkthatestimatesEngelcurvesusinginternalinstrumentsinaGMMsetting.8 Onthesubstantivefront,ourestimationrevealsthatfood,relativetofuel,isanecessarycon- 7Bergman, Jaimovich, and Saporta-Eksten (2024) provides a general framework for understanding distributionalimplicationsofsectoraldemandandsupplyshocksinthepresenceofnonhomotheticityindemandina flexiblepricesetting.Inthepresenceofnominalrigidities,inpractice,centralbanksmightalsorespondtosectorspecificcommoditypriceshocksduetotheirout-sizedeffectsoninflationexpectations(see, forexample, Malmendier,Ospina,andWeber(2021)andCoibionandGorodnichenko(2015)). 8SeeDeaton(2019)andLewbel(2008)forcomprehensivereviews. 6

sumption good for all income groups. We then show how non-homothetic preferences affect thedynamicresponseoffoodconsumptionorthefoodconsumptionsharewhenshocksaffect income. Thus,forinstance,whenfoodisanecessaryconsumptiongood,weshowinamodelbased exercise that real food consumption falls by less (than under homothetic preferences) whenincomedeclines,andweprovideevidencethatthefoodexpenditureratioincreaseswhen foodbecomesrelativelymoreexpensive.9 Our empirical framework assessing the impact of macro shocks using micro panel data alsorelatestotheliteraturethathasexaminedthedistributionaleffectsofdomesticmonetary policy shocks. On the theoretical front, Auclert (2019) develops a general model that encompassesvariousredistribution-basedchannelsformonetarypolicytransmission. Ontheempiricalfront, Coibion, Gorodnichenko, Kueng, andSilvia(2017)studytheeffectsofUSmonetary policy shocks on inequality, while Holm, Paul, and Tischbirek (2021), Amberg, Jansson, Klein, andPicco(2022)andAndersen,Johannesen,Jørgensen,andPeydró(2023)estimatetheheterogeneous household effects of monetary policy shocks along the liquid asset or income distributioninNorway, SwedenandDenmark. Inbuildingonthisbodyofwork, ourpaperfocuses on the distributional implications of an external sector-specific shock that leads to a contractionary monetary policy response in the context of an emerging market. We tailor our theoretical model to understanding responses of various categories of consumption under a wage incomechangeandarelative-pricechange,andfocusonhowtheseresponsesdifferalongthe incomedistributionbyusingdetailedhouseholdpanelconsumption,income,andexpenditure sharesdataatamonthlyfrequency. 2 Data and Stylized Facts Wenowdiscussourdataandpresentsomestylizedfacts. 2.1 DataDescription Our paper studies implications of macro shocks, captured by global commodity price movements, on micro level household consumption. Our household data is from the Consumer Pyramid Household Survey (CPHS) dataset, a survey conducted by the Centre for Monitoring IndianEconomy(CMIE).10CPHShassurveyedover232,000uniquehouseholdssince2014and ituniquelyprovidesdetailedconsumptionandincome/earningsathouseholdlevelinasingle 9Aswediscussindetaillater,ourfocusinthepaperisnotonaverage/steady-statedifferencesinfoodexpenditureshareorenergyexpenditureshareacrossincomegroups,whichisalsoatypeofnon-homotheticity. 10CMIEdatawasobtainedbyGauthamUdupaunderthepurviewofCAFRALlicenses.ArpitaChatterjeeorSaroj Bhattaraididnothaveanyunauthorizedaccesstothisdatawhileworkingonthispaper. 7

longitudinaldataset. Moreover,itisavailableatthemonthlyfrequency,whichallowsananalysisofthedynamiceffectsofglobalfoodandoilpricesinastraightforwardway,withouthaving to impute data due to frequency mismatch between the shock and the consumption/income data. OuranalysisusesdatafromJanuary2014toDecember2019.11 Toemphasizehowuniquelypositionedthisdatasetisforustoanswerthekeyresearchquestions,wenotethatadministrativetaxreturnsdata,oftenusedintheliteratureoneffectsofmonetarypolicyoninequality, isannualandcontainslittleinformationonconsumption; datasets suchastheConsumerExpenditureSurveyareextraordinarilyrichbuthavearotatingpanel;the longest running (since 1968) panel income dataset, the Panel Study of Income Dynamics, has consumptiondataavailableonlyfrom1999andonlyatabi-annualfrequency;andthescanner datastudiedintheinflationinequalityliteraturedoesnotcontainhouseholdlevelpanelinformation on earnings/ income. It is indeed rare to have a monthly panel of detailed household consumptionandearningsforsuchalargesampleofhouseholds. Weconstructconsumption,income,andearningsmeasuresfollowingthemethodofCoibion, Gorodnichenko,Kueng,andSilvia(2017). Consumptionexpenditurecomprises153categories. The total consumption measure we construct is the sum of non-durable consumption (food, cooking fuel, electricity, transport, communication, and intoxicants), durable consumption (appliances,furniture,jewelry,clothing,electronics,toys,cosmetics),andserviceconsumption (entertainment, beauty services, fitness services, restaurants, etc). We present results on totalconsumptionandnon-durableconsumptionseparatelyinallouranalysis. Wedenotetotal consumptionofcookingfuel,electricity,transport,andcommunicationasfuelconsumption.12 Totalconsumptionisdeflatedusingmonthlystate-regionlevelConsumerPriceIndex(CPI) -Combinedseries(2012base)availablefromtheMinistryofStatisticsandProgramImplementation(MoSPI),GovernmentofIndia.Theremainingconsumptioncategoriesaredeflatedusing theirrespectiveCPIsasfollows. FoodconsumptionisdeflatedbytheindexavailablefromMo- SPI.Fuelconsumption,whereweincludenotjustthecookingfuelandelectricityexpenditure for which the deflator is given directly by MoSPI, but also expenditure on transportation and communication, is deflated using a weighted average of the two categories with the weights provided by MoSPI. Non-durable consumption is deflated using a weighted average of food, cooking fuel and electricity, and transport and communication price indices with the weights providedbyMoSPI.13Thisdetailedstate-regionlevelmonthlypanelofpricedataalsoallowsus 11Thedataisavailabletill2024.InordertoavoidCovid-relateddisruptionsinconductingthehouseholdsurvey, weperformedouranalysisusingdatauntiltheendof2019. 12Theaverageshareofnon-durableconsumptionintotalconsumptionis89%andtheaverageshareofearnings intotalincomeis75%inourdataset. 13Weusethemostdetailedstate-region(urbanorrural)levelmonthlydeflatoravailableforIndiaatamonthly frequency,followingthesuggestionsinDeaton(2019). Thereare35statesandunionterritories(regionsadministeredbythecentralgovernment)inourdataset. WhileheadlineandfoodCPIisavailableforeachstate-region, 8

toexaminethedegreetowhichglobalpriceshockspass-throughtolocalconsumerpricesina keytestofourtransmissionmechanism. Incomeisthesumofvariouscomprehensivesourcesofhouseholdincomesuchaswageand rental income. Our earnings measure is constructed using income from wages and overtime bonuses. To construct real values of these nominal income and earnings variables we use the state-regionlevelCPI-Combinedseries(2012base). Finally,weuseIMF’sGlobalPriceofFood Index(Nominal,USDollar)andtheBrentcrudeoilprices(USDollarperbarrel)asourmeasure of global food and oil prices respectively.14 The Global Price of Food Index is an index of 28 differentfoodcommodityprices,wheretheweightsareglobalimportshares. 2.2 SummaryStatisticsAlongtheIncomeDistribution Ourkeyresearchquestionisregardingdistributionalimplicationsofglobalpriceshocks.Toanswerthisquestion,forcontext,itisimportanttounderstandhowhouseholdconsumptionand earnings on average differ along the income distribution in our data. To this end, we present several summary statistics from our household panel data, along the deciles of the initial period (2014) real household income, in Appendix B. Most importantly, we present in Table A1 summarystatisticsonaverage(acrosshouseholdsandmonths)monthlyincome,monthlyconsumption, share of non-durable consumption, share of earnings in income and share of food andfuelconsumptionbyvariousincomedeciles. Thepoorestincomegroupisbelowthepovertylineandiscomposedofnetborrowerswith ahighshareofnon-durableandfoodinconsumption.Thesavingsrateriseswhilenon-durable andfoodsharesdeclinewithincome. Thetopincomedecilehasnearlya70%savingsrateand a relatively low share of food in total consumption. No significant variation in fuel share is observedacrossincomegroups. 15 These statistics motivate us to divide households in five income groups when we estimate heterogeneous consumption effects of global commodity price shocks. In these regressions whereweestimateinteractioneffects,weconsiderfiveincomegroups:verylowincome(decile 1),lowincome(deciles2and3),lowermiddleincome(deciles4,5and6),uppermiddleincome (deciles 7, 8 and 9), and high income (decile 10). We determine the cut-offs for deciles based nondurableCPIhastobeconstructed.Weovercomethischallengebyconstructingstate-region(urbanandrural) levelnon-durableCPIusingstate-regionlevelheadlineCPIaswellasstate-regionlevelfoodandenergyconsumptionsharesintheCPIbasket.WeprovidefurtherdetailsinAppendixA. 14We downloaded the global food price index and the brent crude oil price index from the St. Louis Fed FRED data base. The links, respectively, are https://fred.stlouisfed.org/series/PFOODINDEXM and https://fred.stlouisfed.org/series/POILBREUSDM. 15Wedonotincludeexpendituresonrent,EMIs,health,andeducationinourmeasureoftotalconsumption. Also,notethatwhileoverallfuelsharedoesnotvaryacrossincomedistribution,typeoffuelusevary. 9

onrealincomein2014andassigneachhouseholdtoagroupbasedonthosecutoffs.16 Various characteristicsofthebaselineincomegroupsaresummarizedinTableA2. 2.3 GlobalCommodityPricesandAggregateConsumptionInequality In this Section, we present evidence from the raw data on comovement between global commoditypricesandconsumptioninequalityinIndia,whereweconstructthemeasuresofaggregateinequality fromtheunderlyinghouseholddata. Thisservesasmotivationforoureconometricexercise. Figure1: ChangesinGlobalFoodandFuelPrices Notes:ThisfigureplotsthelogchangeinIMF’sGlobalPriceofFoodIndex(USDollar)andBrentCrudeOilPrices(USDollarperbarrel). WefirstplotthelogchangesinglobalfoodandoilpricesinFigure1. Asexpected,theaverageofthechangesisclosetozerowhilethestandarddeviationisapproximately2.4%forfood pricesandnearly8.7%foroilprices, confirmingahigheroilpricevolatility. AR(1)coefficients oftheestimatedprocessesforthesechangeinpricesareverylow, indicatingthatthechanges are largely transitory in nature. Finally, changes in the two series are positively correlated but notveryhighlyso,henceimplyingindependentsourcesofvariation.17 16Notethatthesamehouseholdmaybelongtodifferentincomegroupsatdifferentpointsintimedependingon theircurrentrealincome.ThisisanissueweaddressinsensitivityanalysisinAppendixE.3.Wehaveconducteda broadsetofrobustnessanalysisregardinghowhouseholdsareassignedtoincomegroups. 17Correlationbetweenthetwoseriesis0.34inoursample. Someco-movementsuchasthisistobeexpected 10

We construct various aggregate measures of consumption inequality from the underlying microhouseholddata:Ginicoefficient,SD(standarddeviation)oflogchangesinconsumption, andthe90th-10thand75th-25thmeasuresofdispersion. InTable1,wepresentcorrelationsof variousmeasuresofconsumptioninequalitywithoneperiodlaggedvaluesofglobalfoodand oil price changes. The correlations are positive, and are higher for global food price changes thanforoilpricechanges. Ourraw datathusrevealsapositivecorrelationbetweenaggregate consumptioninequalityandexternalcommoditypricechanges. Doesthis“smelltest”passan econometricexamination? Thisisthekeyfocusofourpaper. Table1: CorrelationsofConsumptionInequalitywithGlobalFoodandOilPriceChanges Gini SD 90th-10th 75th-25th FoodPrice 0.111 0.051 0.049 0.052 OilPrice 0.044 0.046 0.044 0.032 Notes:Thistableshowscorrelationsofone-periodlagofglobalfoodandoil pricechangeswithvariousinequalitymeasuresforconsumptionthatare constructedusingthemicrohouseholdpaneldata. 3 Distributional Effects of Global Commodity Price Shocks InthisSection,weestablisheconometricallyasetoffactsregardingthedistributionaleffectsof globalfoodandoilshocksonhouseholdconsumption. Weuseahouseholdpanellocalprojectionframeworktoestimateheterogeneousdynamiceffectsofglobaloilandfoodpriceshocks, after we purge out the impact of global demand shocks on global commodity prices using instrumentalvariables.Wefirstdocumenttheaverageeffectsofglobalpriceshocksonhousehold consumption,andthenturntothedistributionalimplications. giventheroleofenergyasinputintheproductionoffoodaswellasthepossibleroleofglobaldemandindriving bothcommodityprices. 11

3.1 PanelLocalProjectionFramework Ourhousehold-levelpanellocalprojectionmodelwithinteractioneffectsis: J c i,t+h −c i,t−1 =β 0 g , , f h ood ext t food×1 i∈g(t) +β 0 g , , o h il ext t oil×1 i∈g(t) + (cid:88) αh(c i,t−j −c i,t−j−1 ) j=1 K K D + (cid:88) βh k,food ext t fo − o k d+ (cid:88) βh k,oil ext t o − il k + (cid:88) δhD t−d +γg,hX t ×1 i∈g(t) k=1 k=1 d=0 +1 i∈s ×1 year +1 i∈s ×1 month +ϵ i,t+h (3.1) Here,c isthelogofrealconsumptionforhouseholdi forvariousmeasuresofconsumption i (namely,total,non-durable,foodandfuelconsumption). Realconsumptionisobtainedbydeflatingnominalconsumptionexpendituresofvariouscategoriesbythecorrespondingdeflators (specifictototal, non-durable, foodandfuelCPI)forthestateandregioninwhichhousehold i resides. extfood andextoil standformeasuresoftheglobalfoodandoilpriceshocksrespectively; 1 i∈s ×1 year and 1 i∈s ×1 month areasetofhouseholdi’sresidencestatebycalendaryearand residencestatebycalendarmonthfixedeffectstoaccountforstate-regionspecifictrendsand regional variation in seasonality respectively (which control for, among others, local weather conditions); and D is the dummy for the Indian government’s demonetization policy, which is allowed to have lagged effects for up-to three periods. For the AR and MA coefficients, we choose J =3,K =3. We estimate the above specification separately for each horizon ranging from h =0 to h = 12. In all the regressions, the observations are weighted using sampling weights provided by CMIE,whichtakesintoaccountthenon-responsefactor. Thestandarderrorsareclusteredat thestate-regionlevelwhereregiondenotesurbanorrural.18 A critical aspect of this specification is that we allow the consumption effects to differ by theincomeofthehousehold. Thatis, g(t)denotestheincomegroupofhouseholdi attime t constructedusingcutoffsfrom2014realincomedata. Theeffectsofexternalshocksarethus, allowed to vary by income groups. As mentioned previously, we consider five income groups: verylowincome(decile1),lowincome(deciles2and3),lowmiddleincome(deciles4,5,and 6), upper middle income (deciles 7, 8, and 9), and high income (decile 10). Here βg,h is the 0,food coefficient of interest that captures the impact of global food price shock at time t on householdsofgroup g athorizonh; βg,h issimilarlytheestimatefortheglobaloilpriceshock. We 0,oil reportcumulativeimpulseresponsesbelow. X denotescontrolsforaggregateworldconditions: worldindustrialproductionasaproxy 18Ourspecificationleadstorobustinferenceinthemicropanellocalprojectionframeworkwithheterogeneous effectofmacroeconomicshocks(AlmuzaraandSancibrián(2024)). 12

forglobaldemand(BaumeisterandHamilton(2019));USfederalfundsrate;andglobalfinancialvolatilityascapturedbytheVIXindex. Theseaggregateglobalcontrolsareinteractedwith householdincomegroupdummiestoallowsuchexternalevents,otherthanglobalcommodity prices,tohaveheterogeneousconsumptioneffects. TableA4inAppendixDlistsfulldetailsof ourhouseholdpanellocalprojectionestimation. 3.2 EndogeneityConcernsinAssessingtheDistributionalImplications Ourempiricalexerciseisanexampleofusingmicrodatatoestimateresponsestomacroshocks. Arguably,IndianhouseholdconsumptionandIndianeconomicconditionshavenodiscernible effect on global food and oil prices, thereby mitigating reverse causality concerns for the OLS estimation of the household panel local projection Equation (3.1). However, even under this assumption, OLSversionsofourestimationframeworkstillconflatetheeffectsofvariousunderlying shocks that lead to changes in world oil and food prices, leading to biased estimates duetoomittedvariablebiasproblems. Isolating global supply-side variation therefore is crucial in our exercise to guard against omitted variable bias problems. Omitted variable bias is most salient for the case of global demand shocks as Indian households are likely to have direct exposure to the global demand shocks, and the global demand shocks in turn are well-known drivers of global commodity prices. Toaddressthisissue,wetakeanInstrumentalVariable(IV)approachinwhichwefocus onremovingthevariationcomingfromglobaldemandshocks.Inparticular,weusesupplyside instrumentsforthechangeinglobaloilandfoodprices. Fortheoilpricechange,ourIVistheoilsupplyshockestimatedinBaumeisterandHamilton (2019), who estimate a Bayesian VAR using oil price, oil production, oil inventory, and world industrial production data. An oil supply shock is then identified as a movement along the downwardslopingdemandcurvebyimposingsignrestrictions. It is challenging to estimate a supply shock for the food sector in a way analogous to the oil supply shock due to two main reasons. Unlike oil, food is not a single commodity–it is a compositeofseveralcommodities. Also,whilemonthlypricedataisavailableforvariouscomponentsoffood,monthlyproductiondataisgenerallynotavailable. Therearetwoapproaches thatonecantaketocircumventtheseproblems. Thefirstistousealargecross-sectionofnonenergy commodity prices and a combination of statistical and theory-based identification to disentanglesupplyanddemandshocks(e.g., asinAlquist, Bhattarai, andCoibion(2020))and thisistheapproachwetake.Thesecondistousealimitedcross-sectionofpriceandaproxyfor monthly productiondata, as outlined in De Winne andPeersman(2016). However, the major crops of India are subject to various price regulations both on the supply and demand side in 13

the domestic market due to minimum support prices for farmers and the public distribution systemforconsumers. Hence,werelyonanapproachthatusesabroadcross-sectionofprices. Weusecommoditypricesdata(apanelof37non-energycommoditypricesincluding13industrialinputsandmetalsand24foodprices)inthetimeperiod1990-2022andestimateadynamicfactormodelusingBayesianmethods.Ourmainfocusisonestimatingacommonfactor thatcapturesthecomovementofabroadrangeofglobalcommodityprices, duetoglobaldemandconditions,byimposingsignrestrictions.Weresidualizechangesintheglobalfoodprice indexwithsuchacommonfactor,aswellasafood-specificfactorthatcapturesco-movement only among the food commodity prices, also estimated using the dynamic factor model. Our estimation method is outlined in Appendix C. With this approach, we address an important concern for omitted variable bias, as we remove the variation from global demand shocks.19 We provide several details about the IVs in Appendix C.20 We plot the changes in global commoditypricesandtheirIVs,therespectivesupplyshocks,inFigureA2intheAppendix. Themacroeconomiceffectsofanincreaseinglobalfoodpricesdrivenbysupplyshockson the Indian economy are illustrated in Figure A3 in Appendix C. Our estimation framework is a four-variable Bayesian VAR where we treat our measure of food supply shock as an external shock. The rise in global food shocks is clearly stagflationary for the Indian economy with a contractionineconomicactivityandariseinprices,leadingtoacontractionarymonetarypolicyresponse. ThesameexerciseforBaumeisterandHamilton(2019)’sadverseoilsupplyshock showssimilarmacroeconomiceffects,asillustratedinFigureA4.21 3.3 AverageConsumptionEffects: ComparisonofOLSandIVresults Beforewepresentthedistributionalimplications,itisusefulforcontexttounderstandtheaverageeffectsofglobalfoodandfuelpriceshocksonhouseholdconsumption. Theseresultsare presentedfortotal,non-durable,andown-category(fuelconsumptionforoilpriceshocksand food consumption for food price shocks) consumption in Figure 2.22 The top row of Figure 2 showstheeffectsofariseinglobaloilpricesonhouseholdconsumption,whilethebottomrow 19Omittedvariablebiascanalsoariseiflocalconditionscandriveglobalfoodpricesforcertaincommodities, especiallyrice.Weaddressthisissueinarobustnessexercisefollowingourmainresults,butwenotethatriceprice constitutesonly2%ofthefoodpriceindexweuse,whichshouldmitigatesuchconcerns. Wealsouselocationcalendarmonthandlocation-calendaryearfixedeffectstocontrolforsuchlocal,sayweather,shocks. 20Economic activity shock from the Bayesian VAR capturing the energy market dynamics in Baumeister and Hamilton(2019)andthecommonfactorestimatedfromtheBayesianestimationofcomovementinnon-energy commoditypricesinourexerciseareillustratedtogetherinFigureA1.Theyroughlycapturesimilarmovementsin globalbusinesscycles,withanaveragecorrelationof0.23. 21LakdawalaandSingh(2019)makesimilarobservationsfortheoilsupplyshockusingadifferentmethod. 22InthenotationofthehouseholdpanellocalprojectiondescribedinEquation(3.1),households’dynamicresponsesβh andβh arenotallowedtodifferbyincomegroupg whileevaluatingtheaverageeffects. food oil 14

shows the effects of a rise in global food prices. We first focus on the IV estimates of the impulseresponses(inblue)wheretheglobalpricemovementsareinstrumentedbytherespective supply shocks. The conclusion is unambiguous: rise in global commodity prices reduces real consumption of households over time, and this conclusion holds for total, non-durable, and own-categoryconsumption. We also utilize Figure 2 to demonstrate the omitted variable bias problem in the OLS estimatesoftheimpulseresponses(inyellow).TheOLSestimatescapturebothglobaldemandand commodity-specificsupplyshocks. Sinceglobaldemandshocksinevitablyanddirectlyimpact Indianhouseholdconsumption,thisleadstoanomittedvariablebiasintheOLSestimation,as weexplainedearlier.Moreover,sincepositiveglobaldemandshocksarelikelytohaveapositive impactonbothIndianhouseholdconsumptionandglobalcommodityprices,thedirectionof thebiasispositive.IntheIVestimation,onceweeliminatetheimpactofglobaldemandshocks oncommodityprices, weexpecttheIVestimatestobemorenegativethanthecorresponding OLSestimates.23 ThisdirectionofbiasisevidentforbothoilandfoodshocksinFigure2,though thedifferencebetweenOLSandIVismorestarkinthecaseofoil. Globaloilpricesareknown tobeextremelysensitivetoglobaldemandshocks,whileglobalfoodpricesarearguablymore influenced by idiosyncratic supply shocks. Thus, in the OLS estimates, when global oil prices riseduetoademandshockdrivenboominglobaloutput, Indianhouseholdsalsoexperience consumptiongrowthdirectlythroughthisbusinesscycleeffectandthis,inturn,leadstoanerroneousconclusionofpositiveeffectsonhouseholdconsumptionofariseinglobaloilprices. 23Also,IVestimateswillcapturevariationthatisindependentoflocaleconomicconditions. 15

Figure2: ResponseofConsumptiontoExternalFoodandOilPriceShocks(IVandOLS) Notes: CumulativeIRFsonthebasisofEquation(3.1),withouttheinteractioneffectsbyincomegroups,wheretheexternalshockare logchangesintheglobalfoodandoilprice,whichareinstrumentedbyaglobalfoodsupplyandoilsupplyshockrespectively,andthe dependentvariableislogchangesinhouseholdconsumption.Thelightblueregionisthe90%confidenceintervalandthedarkblueregion isthe68%confidenceinterval. 3.4 HeterogeneousConsumptionEffects: IVResults Afterestablishingtheaveragenegativeeffectsofglobalcommoditypricemovementsonhousehold consumption and the importance of accounting for the omitted variable bias in OLS estimates using an IV strategy, we return to the local projection household panel exercise based on the IV estimation of Equation (3.1), where the effects on consumption are allowed to vary alongtheincomedistribution. Thisisourbaselineempiricalexerciseforestablishingfactson heterogeneouseffectsofglobalfoodandfuelpricechanges. 3.4.1 Mainresultsonheterogeneouseffects OurkeyIVresultsareinFigures3and4forfoodpriceshocksandoilpriceshocks,respectively.24 We present results for total consumption, non-durable consumption, and own-category consumption. Theresultsshowthatthereareadverseeffectsonallmeasuresofconsumptionfor 24Thefirst-stageF-statisticsfortheseIVregressionsarereportedinAppendixDinTableA5. 16

boththeshocksandthattheseadverseeffectsareheterogeneousalongtheincomedistribution. Figure3: ResponseofConsumptiontoExternalFoodPriceShocksbyIncomeQuintiles(IV) Notes:CumulativeIRFsonthebasisofEquation(3.1)wheretheexternalshockislogchangesintheglobalfoodprice,whichisinstrumented byaglobalfoodsupplyshock,andthedependentvariableislogchangesinhouseholdconsumption. Thelightblueregionisthe90% confidenceintervalandthedarkblueregionisthe68%confidenceinterval. Intriguingly,intermsofheterogeneouseffectsalongtheincomedistribution,thetwoshocks show different patterns. For the food price shock, the lower income groups are hit harder and the negative effects become progressively less pronounced as we move to higher income groups. Fortheoilpriceshocks,theeffectsaremorenuancedandmuchmoresymmetricalong theincomedistribution. Forinstance,thepeaknegativeeffectsonnon-durableconsumption aresimilarinmagnitudeforallincomegroups,exceptforthelow-incomegroupwhichsuffers theleast. Thedropinconsumptionisslightlyhigherforthelowestincomegroup,butthenegativeeffectsaremorepersistentforthetwohighestincomegroups. Sooverall,thetwotailsof thedistributionsuffermorefortheoilpriceshocks. 17

Figure4: ResponseofConsumptiontoExternalOilPriceShocksbyIncomeQuintiles(IV) Notes:CumulativeIRFsonthebasisofEquation(3.1)wheretheexternalshockislogchangesintheglobaloilprice,whichisinstrumented byaglobaloilsupplyshock,andthedependentvariableislogchangesinhouseholdconsumption. Thelightblueregionisthe90% confidenceintervalandthedarkblueregionisthe68%confidenceinterval. Veryimportantly,thedynamicpatternofheterogeneityinconsumptionresponsesforboth oil and food shocks is quite similar across various consumption aggregates and categories. Thus,ariseinglobalfoodpriceshasregressiveeffectsontotal,non-durable,andown-category consumption. Moreover,ariseinglobaloilpriceshaslargereffectsontotal,non-durable,and own-categoryconsumptionatthetwoextremesoftheincomedistribution.Moreover,notethat as non-durable consumption is a sum of food and fuel consumption, these results imply that afoodpriceshockleadstoadropinfuelconsumptionwhileanoilpriceshockleadstoadrop infoodconsumption, andthepatternofheterogeneityinthecross-categoryresponsesisalso remarkably similar.25 If these shocks were simply relative price shocks, these across-category consumption drops would not occur as expenditure-switching would lead to across-category consumption increases. We note this inference now and will revisit it in more detail when we 25InFigureA5intheAppendixweshowtheseacross-categoryconsumptionresponsesexplicitly. 18

assesstransmissionmechanisms. Wenowsummarizethekeyfactsregardinghowexogenousglobalfoodandoilpriceshocks impactIndianhouseholdconsumption: • Fact 1: Increases in global food and oil prices lead to reduction in real household consumptionfortotal,non-durable,andown-categoryconsumption(see,Figure2). • Fact 2: An exogenous rise in global food prices leads to larger negative consumption effectsonpoorerhouseholds,whereasanexogenousriseinglobaloilpriceshaslargernegativeeffectsonthetwotailsoftheincomedistribution(see,Figures3and4,respectively.) Poorer income groups suffer a substantially larger consumption loss across all horizons followinganexogenousriseinglobalfoodprices,whereasthepoorest,theupper-middle, and the high-income groups are equally vulnerable to an exogenous rise in oil prices. Moreover,thelow-incomegroupisshieldedmostfromoilpriceincreasesbutsuffersmost fromfoodpriceincreases. • Fact3: Thepatternofheterogeneityacrossincomegroupsintermsofhowconsumption responds to global price shocks is similar across total, non-durable, and own-category consumption,andthiscommondynamicsofvariousconsumptionaggregatesacrossincomegroupsisaqualitativelyimportantpatternweanalyzefurtherinSection4.2.1. Next,wepresentstatisticalsignificanceofthepatternofheterogeneity,discusstheirquantitativemagnitudeandeconomicsignificance,andhighlighttheimportanceofaddressingendogeneityconcernsforestablishingthesedistributionaleffects. 3.4.2 Statisticalsignificanceoftheheterogeneouseffects IsthepatternofheterogeneousconsumptionresponsesinFigures3and4statisticallysignificant? We have documented in Fact 2 above that the low-income group suffers the largest real consumptionlossinresponsetoincreasesinglobalfoodpricesandthesmallestrealconsumptionlossinresponsetoincreaseinglobaloilprices.Inordertoassessthestatisticalsignificance oftheheterogeneityinconsumptioneffects,wenowtreatthelowincomegroupasthebaseline whileestimatingthepanellocalprojectionframeworkofEquation(3.1). Dynamicresponsesof real non-durable consumption to global food (bottom row) and oil (top row) price shocks are plottedinFigure5. Thedynamicresponsesforthelowincomegrouparestillthetotaleffect,as inFigures3and4,whileimpulseresponsefortherestofthegroupsshowthedifferentialeffects onthecorrespondinggrouprelativetothelowincomegroup. 19

Figure 5: Relative (to Low Income Group) Response of Non-durable Consumption to External FoodandOilPriceShocksbyIncomeQuintiles(IV) Notes: CumulativeIRFsonthebasisofEquation(3.1)wheretheexternalshockislogchangesintheglobalfoodoroilprice,whichis instrumentedbythecorrespondingsupplyshockandthedependentvariableislogchangesinhouseholdnon-durableconsumption. Column2,forthelowincomegroup,showsthetotaleffectsforthisbaselinegroup,whiletherestofthecolumnsshowtherelativeeffect comparedtothelowincomegroup. Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68%confidence interval. Thestatisticalsignificance(at90%)ofthenegativedifferentialeffectsforallincomegroups relativetothelowincomegroup,inthetoprowofFigure5,confirmthatinresponsetoanincreaseinglobaloilprices,allincomegroupssuffer(statistically)significantlylargerconsumptionlossesrelativetothelowincomegroup. Thebottomrowdepictsanoppositepicture: the differentialeffectisnotsignificantlydifferentfromzeroforthelowestincomegroup,butallthe higher income groups show a significant (again, at 90%) positive differential effect, implying thatwithincreasesinglobalfoodprices,higherincomegroupssuffer(statistically)significantly lowerrealconsumptionlosses.26 26We show in Figure A6 in the Appendix that the conclusions regarding statistically significant differences in consumptionresponsesacrossincomegroupsholdevenifweestimatethepanellocalprojectionmodelofEquation(3.1)separatelyforglobaloilandfoodpriceshocks.Theonlynoticeabledifferenceisthelargertotalnegative effectofglobaloilpriceincreaseonthelowincomegroupinFigureA6(whentheestimationisdoneseparately forthetwoshocks)vis-a-visFigure5(whentheestimationisdonejointly).Thislargerbaselineeffectofglobaloil priceswhentheestimationisdoneseparatelylikelyreflectsapositiveeffectofariseinglobaloilpricesonglobal foodprices,whichiscontrolledforinthejointestimation. 20

3.4.3 Economicsignificanceoftheheterogeneouseffects Are these distributional implications of global price shocks economically meaningful? To answerthis,wecomputethemagnitudeofconsumptionlossduetotheexternalshocksthatdiffers along the income distribution, in Table 2. Here we translate the elasticity estimates presentedinFigures3and4toconsumptionlossfortotal(panelA)andnon-durableconsumption (panelB).ThefirsttworowsofeachpanelinTable2capturethemaximumnegativeimpactofa 1standarddeviationshockinglobalfoodandoilprices(a2.4%riseinthefoodpriceindexand an8.7%riseinBrentcrudeoilprices,respectively,aspresentedearlierinFigure1). Thisagain showsthepatternofheterogeneitywehaveemphasized: foranexogenousfoodpriceincrease, thepooresttwogroupsclearlysufferthemostinconsumptionlossandthereisaclearpattern of monotonicity along the income distribution, while for an exogenous oil price increase, the lowest, upper-middle, and high income groups suffer similarly. In addition, the low-income groupisprotectedmostfromoilpriceincreasesbutsuffersmostfromfoodpriceincreases. Toappreciatethemagnitudeofthisconsumptionlossandtheheterogeneityineffects, we presentinTable2theunconditionalvolatility(standarddeviation)oflogchangesinrealnondurableconsumptionandtotalconsumptionforthevariousincomegroups.Asapercentageof theunconditionalvolatilityinnon-durableconsumption,themaximumeffectofa1standard deviationfoodpriceshockexplains8%forthepoorestincomegroup,10%forthelow-income group,and5%forthehighestincomegroup. Incontrast,asapercentageoftheunconditional volatilityinnon-durableconsumption,themaximumeffectofa1standarddeviationoilprice shockexplains5.5%forthepoorestincomegroup,3.2%forthelow-incomegroup,and5%for thehighestincomegroup.27 27Unconditionally, consumptionchangeismorevolatileatthetwoendsofthedistributionandleastvolatile forthelow-incomegroup. Assumingalogutilityfunctionintotalconsumption,themagnitudeofrealtotalconsumptionlossreportedinpanelAofTable2canbegivenawelfareinterpretationundertheassumptionthatthese estimatedeffectsareaccuratenon-linearly. 21

Table2: MagnitudeofRealConsumptionLossfromGlobalPriceShocks Lowest Low Low-middle Upper-middle High PanelA:TotalConsumption 1SDFoodShock -0.039 -0.039 -0.032 -0.028 -0.024 (-.034,-.043) (-.035,-.043) (-.028,-.036) (-.024,-.031) (-.02,-.027) 1SDOilShock -0.033 -0.023 -0.033 -0.038 -0.037 (-.025,-.042) (-.017,-.029) (-.026,-.04) (-.031,-.044) (-.029,-.045) SDoflogchanges 0.427 0.373 0.387 0.402 0.423 PanelB:Non-durableConsumption 1SDFoodShock -0.032 -0.034 -0.028 -0.023 -0.02 (-.028,-.036) (-.029,-.039) (-.024,-.031) (-.019,-.027) (-.016,-.024) 1SDOilShock -0.022 -0.011 -0.017 -0.021 -0.02 (-.015,-.029) (-.009,-.014) (-.013,-.022) (-.017,-.026) (-.014,-.026) SDoflogchanges 0.394 0.345 0.347 0.353 0.364 Notes:Thistableshowsthemaximumlossinrealtotalandnon-durableconsumptioninresponseto1standarddeviationshocktofoodprices (2.4%)andoilprices(8.7%)forthefiveincomegroupsbasedontheestimatesofelasticitiespresentedinFigures3and4. Standarderrors arereportedintheparenthesis. Italsoreportstheunconditionalvolatility(standarddeviationoflogchangesinrealtotalandnon-durable consumption)ineachpanel. 3.4.4 ImportanceofIVestimationofheterogeneousnegativeeffects As we discussed in detail earlier, our IV estimates avoid omitted variable bias problems that ariseinOLSestimatesduetothepresenceofglobaldemandshocks. Wenowshowtheimportance of the IV estimation strategy for assessing heterogeneous effects by presenting in detail theOLSresultsforoilpriceshocksinFigure6. Forcomparison, wealsoplottheIVresultswe presentedearlierinFigure4. IntheOLSresultsofFigure6,aspredicted,theconsumptioneffectsarenotconsistentlyand persistentlynegativeforanyincomegroup. Thus,asexpected,ifhigheroilpricesarecausedby a positive global demand shock, Indian households are likely to benefit because of their various exposures to global demand. Moreover, the extent of this positive bias can be differential along the income distribution and needs to be assessed rigorously statistically. It is therefore imperativetoremovethevariationcomingfromglobaldemandshockswhilestudyingthedistributionalconsequencesofglobalpriceshocks. Similardifferencesareobservedinthecaseof foodpricechangesinFigureA7intheAppendix,whichshowsthatIVestimatesareconsistently 22

morenegativethantheOLSestimates.28 Figure 6: Response of Consumption to External Oil Price Shocks by Income Quintiles (IV and OLS) Notes:CumulativeIRFsonthebasisofEquation(3.1)wheretheexternalshockislogchangesintheglobaloilprice.IntheIVversion,the logchangesinglobaloilpriceisinstrumentedbyaglobalsupplyshock.Thedependentvariableislogchangesinhouseholdconsumption, non-durableconsumption,andfuelconsumption.Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68% confidenceinterval. 4 Channels for Heterogeneous Consumption Effects Havingestablishedthebaselinefactsabouthowglobalfoodandfuelpriceshocksleadtoheterogeneouseffectsonhouseholdconsumption,wedelveintointerpretationandtransmission mechanisms. Tothisend, webuildadynamicconsumption-savingmodelforhouseholdsbelongingtodifferentincomegroups. Conceptually,ourframeworkallowsforavarietyofmech- 28Figure A7 shows, on average, narrower gaps between OLS and IV estimates compared to Figure 6. This is consistentwiththemoreprominentroleglobaldemanddynamicsplayindeterminingoilprices,whilefoodprices areoftendrivenbycrop-specificsupplyshocks. 23

anismsthroughwhichglobalfoodandfuelpricechangescanleadtoheterogeneousconsumption effects. In view of the empirical facts we establish in Section 3, we focus on the channels oftransmissionthatworkviarealincome,throughrelativepriceeffects,andthosethatreflect non-homotheticityinpreferences. Wethenturntoexaminingempiricalveracityofthesechannelsbycomparingmodelpredictionswiththeempiricalfacts. 4.1 TransmissionMechanisms: DynamicConsumption-SavingModel AsinAuclert(2019),weconsideraninfinite-horizonconsumption-savingsprobleminaperfect foresightenvironmentwithunexpectedshocks,wherehouseholdi belongingtoincomegroup g cantradenominalandrealassetsofdifferentmaturities.29 (cid:189) (cid:190) Thehouseholdchooses C , Bi,t, Bi,2,t,L tomaximizelifetimeutility i,t g g i,t P P t t ∞  C1−σg L 1+φg  (cid:88) (βg) t  i,t − i,t  1−σg 1+φg t=0 subjecttoasequenceofflowbudgetconstraints 1 1 C i,t +Q t b i,t +Q 2,t b 2,i,t +S t E i,t =b i,t−1 Πg +Q t b 2,i,t−1 Πg +(S t +D t )E i,t−1 +w i g ,t L i,t , (4.1) i,t i,t where C is total household consumption index, L is labor, B is holdings of one-period i,t i,t i,t risk-free nominal bonds, B is holdings of two-period risk-free nominal bonds, and E is 2,i,t i,t holdingsofstocks.30 Q ,Q , andS arepricesoftheone-periodbond, thetwo-periodbond, t 2,t t andthestockrespectively. ThestockyieldsdividendsD . t g HereP g isthenominalpricelevel,Πg = P i,t isgrossinflation,andw g isrealwages. P g i,t i,t P g i,t i,t i,t−1 differacrossincomegroupsbecausedifferenthouseholdsi resideindifferentregionsandmay experiencedifferentunderlyingprices,andalsobecausedifferentincomegroupshavedifferent consumptionsharesforvariouscommodities.31 Here,b = Bi,t istherealholdingsoftheonei,t g P i,t periodnominalbondsofhouseholdi ∈g andb = B2,i,t istherealholdingsofthetwo-period 2,i,t g P i,t nominal bonds. Finally, βg ∈(0,1) is the discount factor, 1 is the intertemporal elasticity of σg substitution,and 1 istheFrischelasticityoflaborsupply. Allparametersoftheutilityfunction φg 29In our empirical results, we assigned households to various income groups according to the initial income distribution,whileallowingswitchingovertime. 30Thehouseholdalsofacesanappropriateno-Ponzigameconstraint. 31Ingeneral,pricesmaydifferacrosshouseholdsforavarietyofreasonssuchasthevarietyorqualitytheyconsume.Inourempiricalapplication,pricesofdisaggregatedcommoditiessuchasfoodorfueldifferbyhouseholds onlytotheextentthatthesehouseholdsresideindifferentlocations. 24

potentiallydifferbyincomegroup. ThetotalconsumptionindexC ismodeledasastandardhomotheticconstantelasticityof i,t substitution(CES)aggregateofnon-durableconsumption(C )andtherestofgoods(C ), N,i,t S,i,t withtheelasticityofsubstitutionparameterηg andtheshareofnon-durableconsumption(1− αg)allowedtodifferacrossincomegroups,asgivenby ηg C = (cid:34) (cid:161) 1−αg(cid:162) η 1 g C ηg ηg −1 +(cid:161)αg(cid:162) η 1 g C ηg ηg −1 (cid:35) ηg−1 (4.2) i,t N,i,t S,i,t g whichleadstodifferencesintheidealpriceindexP ,asgivenby i,t (cid:104) (cid:105) 1 P g = (cid:161) 1−αg(cid:162) P g 1−ηg +αgP g 1−ηg 1−ηg . (4.3) i,t N,i,t S,i,t Notethattheoverallpriceindexandinflationisgoingtodifferbyincomegroupg,evenif all householdsfacethesameindividualcategory-specificprices,duetothemodelallowingforthe possibility of different income groups consuming different baskets of consumption. We allow the real wage to also potentially differ across income groups to allow for the possibility that different income groups may work in different occupations and both earn different nominal wagesandalsofaceadifferentdeflator. Theflowbudgetconstraint,Equation(4.1),makesclearhowshocksinperiod t affectcong sumption and savings decisions through their effects not only on labor earnings w L , but i,t i,t alsothroughrevaluationsoffinancialpositionsbyaffectinginflationandassetpricesΠg ,Q , i,t t and S . In this perfect foresight environment, the asset pricing conditions imply equal intert est rates across the various assets. Using these no-arbitrage conditions and the Transversality conditiontogetherwiththeflowbudgetconstraintsyieldstheintertemporalbudgetconstraint (cid:34) (cid:35) ∞ ∞ (cid:88) ρ i g ,t,t+s C i,t+s = Π 1 g (cid:161) b i,t−1 +Q t b 2,i,t−1 (cid:162)+(S t +D t )E i,t−1 + (cid:88) ρ i g ,t,t+s (cid:179) w i g ,t+s L i,t+s (cid:180) (4.4) s=0 i,t s=0 where ρg =1;ρg = (cid:89) s R g −1;R g = 1 . i,t,t i,t,t+s+1 j=0 i,t+j+1 i,t+j+1 Q t+j Π i g ,t+j+1 The intertemporal budget constraint, Equation (4.4), states that the present discounted valueofconsumption,usingtime-varyinginterestratesfordiscountinganddifferentdeflators allowing for consumption basket heterogeneity, equals the present discounted value of labor income as well as the real value of payoffs from ex-ante financial positions. It also shows that unexpected shocks can affect consumption through (a) wage earnings by affecting current or 25

future wages or labor supply; (b) discount factors by affecting current or future real interest rates; and (c) real value of payoffs on ex-ante financial holdings by affecting current inflation, short-termnominalinterestrate,orstockprices.Heterogeneityinhowsuchunexpectedshocks affectwageearningsorheterogeneityinex-antefinancialpositionsintermsofnominalportfolioandstocksinturncanthengenerateheterogeneityinconsumptioneffects. Goingfurther,ifweimposeaunitintertemporalelasticityofsubstitution(σg=1),since ρg = (cid:89) s βgC i,t+j , i,t,t+s+1 j=0 C i,t+j+1 bymanipulatingEquation(4.4),wegetthesolutionforconsumptionas (cid:34) (cid:35) ∞ C i,t =(cid:161) 1−βg(cid:162) Π 1 g (cid:161) b i,t−1 +Q t b 2,i,t−1 (cid:162)+(S t +D t )E i,t−1 + (cid:88) ρ i g ,t,t+s (cid:179) w i g ,t+s L i,t+s (cid:180) . (4.5) i,t s=0 Equation(4.5)makesclearhowthevarioustransmissionmechanismsdiscussedabove,(a)-(c), govern the effect of unexpected shocks on current consumption. Perhaps even more importantly, it shows clearly that heterogeneity in the response of wage income as well as heterogeneityinex-antepositionsinnominalbonds,maturityofnominalbonds,andstockswilllead toheterogeneityinconsumption. Inflationinequality,suchthatdifferentincomegroupsexperience different inflation rates based on their consumption basket, can also lead to heterogeneousconsumptionaffectsbothbydevaluinginitialnominalportfolioatadifferentrateandby havingheterogeneousimpactontherealdiscountfactorandrealwageincome. Letusdefine presenteddiscountedvalueoflaborincomeandmarketvalueofinitialfinancialpositionsas (cid:34) (cid:35) ∞ Y i g ,t ≡ Π 1 g (cid:161) b i,t−1 +Q t b 2,i,t−1 (cid:162)+(S t +D t )E i,t−1 + (cid:88) ρ i g ,t,t+s (cid:179) w i g ,t+s L i,t+s (cid:180) , i,t s=0 whichmeanswecanwritethesolutionforconsumption32as C =(cid:161) 1−βg(cid:162) Y g . (4.6) i,t i,t Ourdataisextremelyrichintermsofdetailedconsumptionandearningsinformation,aswell as additional labor market indicators such as occupation. Heterogeneous response of wage incometoexternalpriceshocksisthekeytransmissionchannelweanalyzelater. Note that in the empirical evidence presented in Section 3, we have clearly documented thatthepatternofheterogeneousresponsetoglobalfoodandfuelpriceshocksissimilaracross 32Inthelogutilityframework,1−βg istheconstantmarginalpropensityofconsume(MPC)whichcannotexplain dynamicsofconsumption.Inamoregeneralutilityfunction,MPCcanbetime-varying. 26

aggregateconsumptionandvarioussubcategoriesofconsumption(seeFigures3and4). How doesheterogeneityinwageincomeresponseshelpusunderstandheterogeneityinnotjustthe aggregateconsumptionresponse,butalsoinnon-durableandcategory-specificconsumption? To answer this question, we need to model the household’s expenditure allocation problem acrossvariousconsumptioncategories. GiventhattotalconsumptionC isastandardconstantelasticityofsubstitution(CES)agi,t gregatorofnon-durableconsumptiongoodsandtherest,thestandardexpenditureminimizationproblemimpliesthattheoptimalrelativeexpendituresharebetweennon-durableandtotal consumptionarecompletelygovernedbyrelativeprices.However,thelevelofrealnon-durable consumption is a function of aggregate consumptionC and hence, is affected by heterogei,t neouswageincomeresponses,giventheintertemporalbudgetconstraint,Equation(4.5): (cid:195) g (cid:33)−ηg (cid:195) g (cid:33)−ηg P P C =(cid:161) 1−αg(cid:162) N,i,t C =(cid:161) 1−αg(cid:162) N,i,t (cid:161) 1−βg(cid:162) Y g (4.7) N,i,t g i,t g i,t P P i,t i,t g g where P and P are prices of the non-durable and total consumption goods respectively. N,i,t i,t Log-differencingEquation(4.7)weobtainanexpressionforthedynamicsofnon-durableconsumptionforallh≥0: g g P P ∆log(C N,i,t+h )=−ηg∆log( P N g ,i,t+h )+∆log(C i,t+h )=−ηg∆log( P N g ,i,t+h )+∆log(Y i g ,t+h ). (4.8) i,t+h i,t+h Dynamicsofrealnon-durableconsumptionresponseisgovernedbychangesinrelativeprice, g P P N g ,i,t andchangesintotalconsumption,whichinturnreflectschangesinwageincome,w i g ,t+s L i,t+s . i,t Wemodelnon-durableconsumptionasanon-homotheticisoelasticCESaggregatoroffood andfuel,wherecategoryspecificdemand(f ∈(food,fuel))isgivenby: (cid:195) (cid:33) (cid:195) (cid:33) P E log(C g f,i,t )=log(γg f )−σ ϵ g log P g f,i,t +εg f log P N g ,i,t (4.9) N,i,t N,i,t whereE ≡P C isthetotalexpenditureonnon-durableconsumption,εg istheslopeofEn- N N N f gel curve, γg is the share of f in nondurable, σ ϵ g is the (price) elasticity of substitution, and f P g istheidealpriceindexfornonhomotheticCES.33Combiningthecategory-specificdemand N 33Forthisclassofutilityfunction,foraconsumptionbundlex,U(x)isgivenimplicitlyas: [ (cid:88) n γσ 1 U(x) ε f σ − ϵ σϵ x 1− σ 1 ϵ]σ σ ϵ− ϵ 1 ≡1, f f f=1 whereσ ϵ >0ensuresglobalquasi-concavityand ε 1 f − − σ σ ϵ ϵ >0ensuresglobalmonotonicity. Giventotalexpenditure 27

Equation(4.9),demandfunctionfornon-durableEquation(4.7),andtheintertemporalbudget constraintEquation(4.5), weobtaindemandfunctionsfordifferentcategoriesofnondurable, expressedinlog-differencetermforallh≥0as: (cid:195) (cid:33) (cid:195) g (cid:33) ∆log(C g f,i,t+h )=−σ ϵ g∆log P P g f,i,t+h −εg f (ηg −1)∆log P P N g ,i,t+h +εg f ∆logY i g ,t+h (4.10) N,i,t+h i,t+h The common driver of the dynamic response of total consumption Equation (4.5), nondurableconsumptionEquation(4.8),andcategory-specificconsumptionEquation(4.10)isthe dynamic response in wage income. This is the key channel of transmission on which we focus. Relative prices, that is the non-durable price relative to the overall price index, and the foodorfuelpricerelativetothenon-durableprice, alsomatterforthedynamicsofconsumption response. Pass-through of global price shocks on local prices is an important channel of transmissionwhichwealsoexamineempirically. Slope of the Engel curve, denoted by εg , influences the response of category-specific conf sumption as shown in Equation (4.10). In the case of homothetic demand, εg equals one, f whichimpliesrelativeexpenditureisonlyinfluencedbyrelativeprices. Inthepresenceofnonhomotheticity,relativeexpendituresalsorespondtochangesintotalexpenditure (cid:181)E (cid:182)  γg  (cid:181)P (cid:182) (cid:195) E (cid:33) log E f f o u o e d l, , i i , , t t =log γ f g ood  −(σ ϵ g −1)log P f f o u o e d l, , i i , , t t +(εg food −εg fuel )log P N g ,i,t fuel N,i,t (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) Relativenominalexpenditure Relativepriceeffect Totalexpenditureeffect (4.11) where E ≡P C . In Equation (4.11) above, a good f is a necessity if and only if ε <ε¯ and a f f f f luxuryifandonlyε >ε¯,whereε¯isthebudget-shareweightedaverageofε .34 f k Aslongasfoodisasubstitutewithfuel(implyinganelasticityofsubstitution, σ ϵ ≥1, with theequalityholdingforaCobb-Douglascasewherethegoodsareneithersubstitutesnorcomplements), an increase in relative prices weakly reduces relative expenditure via the standard expenditure switching effect. If real non-durable expenditure ( ENt) falls, the only way relative PNt expenditure then may increase with rising relative prices under σ ϵ ≥1 is if ϵ food < ϵ fuel . This condition,ϵ <ϵ ,inatwo-goodframeworkimpliesthatgood f isanecessarygood.Weusethe f k onthisbundleofconsumption,E ≡P C ,thecostoflivingindex(P g )isimplicitlygivenby: N N N N [ (cid:88)γg ( E N ) ϵg f −1 ( P f )1−σ ϵ g ]1− 1 σϵ g ≡1. f P g P g f N N SeeMatsuyama(2022)forfurtherdetailsandreferences. 34Thismeansthatiso-elasticnon-homotheticCEScanallowthesamegoodtobealuxuryoranecessitydependingonthelevelofrealexpenditure. 28

responseofrelativenominalexpendituretorelativepricestorigorouslytesttheassumptionof anecessaryconsumptiongoodandtoestimatethedifferencesintheslopesoftheEngelcurves. Wearenowreadytostatethetwokeytestablepredictionsofthemodel,wherewefocuson howtheyhelpusunderstandtheheterogeneousconsumptioneffectsfromSection3: • TestablePrediction1:FromconsumptionEquation(4.6),non-durableconsumptionEquation(4.8),andcategory-specificconsumptionEquation(4.10),theheterogeneousresponse ofwageincometotheexternalpriceshocksleadstoacommonheterogeneousresponse ofconsumption,non-durableconsumption,andown-categoryconsumption. • TestablePrediction2: Whenσ ϵ ≥1,fromEquation(4.11),asufficient conditionforagood to be necessary is that relative expenditure in the good rises following a rise in relative prices and a fall in total real expenditure. Moreover, Equation (4.11) presents a framework for estimation of ϵ −ϵ , given the impulse responses of a) relative nominal food fuel expenditureoffoodtofuel;b)relativepricetofoodtofuel;andc)realnon-durableconsumptionexpenditure. 4.2 EmpiricalEvidenceonTransmissionMechanisms The theoretical model presented in Section 4.1 and the consumption, labor earnings, and regional price data presented in Section 2.1 allow us to empirically examine three questions, as listedinthetestablepredictionsabove. Dohouseholdearningsrespondtoglobalfoodandfuel priceshocksheterogeneouslyanddoesthepatternofheterogeneityparallelthecommonpatternofheterogeneousconsumptionresponseswedocumentinSection3? Doglobalfoodand fuel prices pass-through to local consumer prices in India and impact relative prices? Finally, canwedecipherthepresenceofnon-homotheticdemandandestimatetheslopeofEngelcurve by studying how relative expenditures across consumption categories respond to global price shocks? ThesearethequestionsweexamineinSections4.2.1,4.2.2,and4.2.3,respectively. 4.2.1 Heterogeneousresponseofwageincome We now assess the heterogeneous real labor earnings effects of these shocks in the household panel IV local projection framework. That is, we estimate Equation (3.1), but with real laborearningsasthedependentvariable. Inourtheoreticalframework,theintertemporalbudget constraint, Equation (4.4), and the solution for consumption, Equation (4.6), have shown howheterogeneouslaborincomeresponsescanleadtoheterogeneoustotalconsumptionresponses. Critically,thesamemechanismofheterogeneousearningsresponsesarereflectedin non-durableconsumption,Equation(4.8),andowncategoryconsumption,Equation(4.10). 29

Figure7showstheresponseofearningstooilpriceshocks(toppanel)andfoodpriceshocks (bottompanel). Itisclearthatfoodpriceshockshaveasignificantnegativeeffectonreallabor earningsthroughouttheincomedistribution. Moreover,thesenegativeearningseffectsoffood priceshocksaremonotonicallydecreasingalongtheincomedistribution,analogouslytotheir negative consumption effects in Figure 3. This suggests that heterogeneity in labor income effects is parallel to the heterogeneity in total, non-durable, and own-category consumption effectsinFigure3. Foroilpriceshocks,thenegativeeffectsaremorelimitedandaresignificant forthepoorestgroupinitiallyandfortherichovertime.Qualitatively,thispatternisstillconsistentwiththenegativeconsumptioneffectsofoilpriceshocksforthesetwotailsoftheincome distribution in Figure 4. In Figure 7 we also present the mean OLS estimates for comparison. WeobservethepatternofupwardbiasinOLSestimatesforwageincomeeffectsduetoomitted variablebias arisingfromglobal demandshocks. These resultsareconsistentwithourearlier resultscomparingOLSandIVestimatesforconsumptioninFigure6foroilshocks. Figure7: ResponseofEarningstoExternalFoodandOilPriceShocksbyIncomeQuintiles(IV andOLS) Notes:CumulativeIRFsonthebasisofEquation(3.1)wheretheexternalshockislogchangesintheglobalfoodprice,whichisinstrumented byaglobalfoodsupplyshock,andlogchangesinglobaloilprice,whichisinstrumentsbyaglobaloilsupplyshock. Thedependent variableislogchangesinhouseholdlaborearnings.Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68% confidenceinterval. 30

4.2.2 Pass-throughofglobalcommoditypriceshockstolocalconsumerprices An important channel via which external commodity price shocks can affect household consumption is through its impact on local consumer prices. In the theoretical framework described in Section 4.1, local prices affect aggregate and category-specific consumption via aggregate CPI, price of non-durable relative to overall CPI, and price of food or fuel relative to non-durableCPI.35Weempiricallyestimatepass-throughofexternalpriceshocksonthesedomesticpricesthatIndianconsumersface. Weuse,forvariouscomponentsofCPI,state-region level monthly data from MoSPI as measures of domestic prices. This rich regional price data wasdescribedinmoredetailinSection2.1. Thespecificationforthestate-regionlevelpanellocalprojectionregressiontoestimatedynamiceffectsonregionalpricesoftheexternalcommoditypriceshocksis: D p s,r,t+h −p s,r,t−1 =βh 0, , r food ext t food×1 r=urban +βh 0, , r oil ext t oil×1 r=urban +γ h X t + (cid:88) δhD t−d d=0 J K K (cid:88) (cid:88) (cid:88) + αh j (p s,r,t−j −p s,r,t−j−1 )+ ext t fo − o k d+ ext t o − il k +θ s +ζ r +ϵ s,r,t+h (4.12) j=1 k=1 k=1 wherep denotes(log)pricesorrelativepricesinperiodt forstates andregionr,h denotes s,r,t theprojectionhorizon,ext denotesdifferentmeasuresoftheexternalcommoditypriceshock, andJ =1,K =1arerespectivelytheARandMAcoefficients.Here,DisthedummyfortheIndian government’sdemonetizationpolicywhile X denotescontrolsforaggregateworldconditions: world industrial production as a proxy for global demand (Baumeister and Hamilton (2019)); US federal funds rate; and global financial volatility as captured by the VIX index. We include stateandcalendar-monthandcalendar-yearfixedeffectsandcomputerobuststandarderrors. InourIVresults,weinstrumentthechangesinglobalfoodandoilpricesbythecorresponding supplyshocks. Wereportcumulativeimpulseresponses. TableA6inOnlineAppendixD.4lists ourcontrolandinstrumentalvariables. We present the results based on the IV specification.36 Figure 8 shows that there is passthrough to consumer prices, both to the direct category prices (second column) as well as to overall prices (first column). Dynamic effects of global food price change on overall CPI very closely follow its effects on the food component of CPI. Global oil price shock passes through 35Theintertemporalbudgetconstraint,Equation(4.4),andthesolutionforconsumption,Equation(4.5),show howaggregateinflationcanaffectconsumptionbyaffectingtherealvalueofpay-offsofnominalassetsandhow heterogeneityinex-anteassetpositionscanleadtoheterogeneouseffectsonconsumption. Moreover,assessing theeffectsoftheseexternalshocksonrelativepricesiscriticaltounderstandingrelativeconsumptionresponses acrossvariouscategories,asgiveninEquation(4.7)andEquation(4.10). 36TheOLSresultsforcomparisonareinAppendixDinFigureA8.Thefirst-stageF-statisticsfortheseIVregressionsareinAppendixDinTableA7. 31

stronglytodomesticenergyprices(comprisingoffuel,electricity,andtransportationandcommunication costs) as well as to headline prices, and the global oil price pass-through on local fuelpricesisparticularlyprominentintheurbanareas.Finally,asthethirdandfourthcolumns ofFigure8show,globalfoodandfuelpricesincreaserelativepriceoffoodandfuelrespectively (whereweplottworelativeprices,withthefirstonerelativetonon-durableCPI).37 Figure8: ResponseofStateLevelPricestoExternalOilandFoodPriceShocks(IV) Notes: CumulativeIRFsonthebasisofEquation(4.12)wheretheexternalshockislogchangesintheglobaloilpriceinthetoppanel andlogchangesinglobalfoodpriceinthebottompanel. Theseexternalpricechangesareinstrumentedbyglobalsupplyshocks. The dependentvariableislogchangesinstatelevelprices.Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe 68%confidenceinterval. ThemaximumimpactofglobalpricechangesonthecorrespondingcomponentofCPIand ontheoverallCPIissummarizedinTable3.Bothglobalfoodandoilpriceshavealargerimpact onCPI(food)andCPI(fuel)inurbanareas. TheimpactofglobalfoodpricesontheoverallCPI is in line with the share of food in the CPI basket, while the impact of global oil prices on the overall CPI is larger than its share, implying broader price effects of a rise in global oil prices. Thisisintuitivegiventheroleofoilasanintermediateinputinproductionofmanygoods.38 37Wealsolookatrelativepriceeffectsusingmoredis-aggregatedfoodcategoriestoinvestigateinmoredetailthe pass-throughtolocalIndianpricesaswellastounderstandlatertheresultsonexpenditureshareeffects.InFigure A9intheAppendix,wepresentresultsforrelativepriceresponsesofvariousfoodcomponents. 38The elasticity of CPI (fuel) to global oil price changes we report here is comparable to the estimates in the 32

Table3: ResponsetoGlobalPriceShocks(IV)(in%) PanelA:ResponsetoGlobalOilPriceShocks All Fuel ShareofFuelinCPI Rural 0.023 0.073 15.5 (0.010,0.035) (0.045,0.101) Urban 0.042 0.175 15.3 (0.024,0.06) (0.013,0.22) PanelB:ResponsetoGlobalFoodPriceShocks All Food ShareofFoodinCPI Rural 0.134 0.241 54.2 (0.085,0.182) (0.162,0.32) Urban 0.118 0.361 36.3 (0.04,0.195) (0.228,0.493) Notes:ThisTablereportsthemaximumeffectonlevelsofCPIofglobalpriceshocks,obtainedbyestimatingEquation(4.12)andwhichwerereportedinFigure8.Standarderrors areinparenthesis.CPIweights(Baseyear2012)arefromMOSPI. Overall, these results confirm that external commodity price shocks have a strong impact ondifferentcomponentsofregionalinflationinIndia,changingboththegeneralcostofliving (ascapturedbyoverallCPI)aswellasrelativeprices(ascapturedbyfoodtofuelpriceratiosand relativepriceswithrespecttonon-durableCPI). 4.2.3 Non-Homotheticityofnon-durablesandnecessaryconsumptiongood While movement in relative prices and earnings affect the level of real consumption for variouscategories,earnings/totalexpenditureaffectsrelative expenditureonlyinthepresenceof non-homotheticity, as is clear from Equation (4.11). If different components of non-durable consumption are substitutable, an increase in relative price leads to a reduction in the correspondingrelativeexpenditureviastandardexpenditureswitchingchannel. Effects on nominal food expenditure share With this theoretical framework, we investigate the effects of global price changes on nominal consumption expenditure ratios within nonliterature.See,forexample,Alp,Klepacz,andSaxena(2023)forcross-countryevidence. 33

durables.39 Inthisexercise,weestimatetheeffectsofglobalfoodandfuelpriceshocksonnominal expenditure ratios of food and fuel. Thus here, the dependent variables in Equation (3.1) E E arethenominalexpenditureratios: food,i,t and food,i,t. EN,i,t E fuel,i,t Figure9: ResponseofFoodExpenditureSharestoExternalFoodPriceShocksbyIncomeQuintiles(IV) Notes:CumulativeIRFsonthebasisofEquation(3.1)wheretheexternalshockislogchangesintheglobalfoodprice,whichisinstrumented byaglobalfoodsupplyshock.Inthetoppanel,thedependentvariableistheratioofhouseholdnominalfoodtonon-durableconsumption expendituresandinthebottompanel,thedependentvariableistheratioofhouseholdnominalfoodtofuelconsumptionexpenditures. Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68%confidenceinterval. Figure9presentsresultsforfood-to-non-durableandfood-to-fuelexpenditureratioswith respect to the global food price shock. In response to the global food price shock, relative local price of food increases (with respect to non-durables and fuel), as we showed previously in Figure 8. Figure 9 shows that this shock leads the low income groups to increase their relative expenditure on food, while the relative expenditure on food falls clearly only for the high incomegroup. Sincetheexpenditureswitchingchannelalwaysdecreasesrelativeexpenditure on the good that is relatively more expensive, these relative expenditure responses of the low incomegroupsindicateanimpactoftotalexpenditureontheexpendituresharesduetononhomotheticity. Given the decline in real non-durable consumption in Figure 3 in response to 39Expenditureswitchingresultsfornon-durablerelativetototalconsumptionispresentedintheAppendixD.5. Wefindthatrelativeexpenditureonnon-durableismainlygovernedbyrelativeprices. 34

rise in global food prices, these expenditure share responses in fact imply that food is unambiguouslyanecessityforthelowerincomegroups,asweexplainedinTestableprediction2. We showsimilarresultsforsub-categoriesoffoodexpenditureratiosinAppendixD.6.40 Estimationofincomeelasticityofdemandparameters Whiletheresponseofrelativeexpendituretoglobalpriceshockscaninformusqualitativelyaboutthepresenceofnon-homothetic demandandinsomecasesevenprovideunambiguousevidence,ourempiricalexercisenextallowsustodirectlyestimatethekeyincomeelasticityofdemandparametersinEquation(4.11). The estimation of differences in the slope of the Engel curve between food and fuel will rely on the structure of non-homothetic demand described in Section 4.2.3. In particular, we fix σ ϵ, allowing for some expenditure switching when relative prices change, and then estimate εg −εg by matching the dynamic impulse responses on relative expenditures and total food fuel realnon-durableconsumptionexpenditurestoglobalpriceshocksacrossdifferenthorizons. GivenEquation(4.11),dynamicsofrelativeexpenditureshareoffoodandfuelis41: ∆log (cid:181)E food,i,t+h (cid:182) =−(σ ϵ −1)∆log (cid:181)P food,t+h (cid:182) +(ε food −ε fuel )∆log (cid:181) E i,N,t+h (cid:182) E fuel,i,t+h P fuel,t+h P i,N,t+h Dynamicresponsesofrelative(nominal)expenditureonfood, E food,t+h,arepresentedinFigure E fuel,t+h 9andthatofrealnon-durableexpenditure, E N,t+h,areinFigure3.Dynamicresponsesofrelative P N,t+h prices, P food,t+h, are demonstrated in Figure 8. Exploiting dynamic variation in the responses P fuel,t+h andcalibratingtheparameterσ ϵ,weminimizethedistancebetween ∆log (cid:179) E food,t+h (cid:180) ∆log (cid:179) P food,t+h (cid:180) ∆log (cid:179) E Nt+h (cid:180) E fuel,t+h +(σ ϵ −1) P fuel,t+h and P Nt+h ∆ext ∆ext ∆ext t t t Itisimportantforestimationthattheresponsesofvariablesdescribedaboveisdifferentacross horizonsh.Giventhatweestimateheterogeneousconsumptionresponsesacrossincomegroups, thesecondstepofestimationiscarriedseparatelyforeachincomegroup. ThisallowsustoestimatethedifferenceintheslopeoftheEngelcurveforeachincomegroupg: εg −εg . food fuel The results are in Table 4, where we fix σ ϵ =2.42 In the first row, we present the estimates 40Forthericherhouseholds,theresponsewefindcouldbeconsistentwithstandardexpenditureswitchingas relative expenditure on food falls. We can however, still not rule out that food is necessary even for the richer householdsasrelativeexpenditurerisingisonlyasufficientconditionnotanecessaryone,asstatedinTestable Prediction2.WewilladdressthisissuebelowwithastructuralestimationofEngelcurveslopes. 41Notethatinourempiricalapplicationfoodorfuelpricesdifferacrosshouseholdsi onlytotheextentthey resideindifferentregions 42Notethatforthepurposeofestimation, weutilizetheIRFsinresponsetobothglobalfoodandoilshocks, thoughusingonlyglobalfoodshocksleadstoqualitativelysimilarresults. Wealsogetqualitativelysimilar,but statisticallydifferent,resultsfixingσ ϵ =.8,whichimpliesthatfoodandfuelaregrosscomplements. 35

based on the total food to fuel expenditure ratio. Estimates of εg −εg is negative for all food fuel incomegroups,showingthatfoodisanecessarygoodforeveryone,irrespectiveofincome. In theotherrows,weshowrobustnessofourmainresultifweconsidervariousfoodcomponents, usingtheappropriatefoodcomponentstofuelrelativepricesandrelativeexpenditureshares. Itshowsthatvariousfoodcomponentsarenecessarygoodsforallincomegroups. Table4: EstimatesofDemandFunctionParameters(ϵ −ϵ ) i j Lowest Low Low-middle Upper-middle High Food(All) -0.359*** -0.407*** -0.394** -0.414** -0.657** (0.095) (0.091) (0.106) (0.117) (0.179) Sugar -1.412*** -1.523*** -1.432*** -1.425*** -2.338*** (0.128) (0.106) (0.139) (0.171) (0.317) OilsandFats -0.343** -0.404*** -0.239 -0.134 -0.217 (0.103) (0.098) (0.125) (0.190) (0.227) Vegetables -0.507* -0.755*** -0.675** -0.811** -1.335* (0.215) (0.188) (0.230) (0.266) (0.540) Pulses -0.968*** -1.337*** -1.057*** -1.103** -1.165* (0.241) (0.233) (0.258) (0.296) (0.433) Spices -0.402* -0.708*** -0.593** -0.737** -1.009** (0.145) (0.162) (0.162) (0.223) (0.279) Notes:ThisTablereportstheestimatesofϵ i −ϵ j obtainedbyestimatingEquation(4.11)inaregressionframework afterfixingσϵ=2andusingasdatatheimpulseresponsesofrelativeprices,relativeexpenditures,andrealnondurableconsumptionexpenditure.Eachrowrepresentsestimatesfromaseparateregression,with26observations (correspondingtoIRFsforthetwoshocksfor13horizons)usedinestimation. Thecolumnsrepresentthevarious incomegroups.ϵ i −ϵ j<0indicatesthatgoodi(foodhere)isanecessaryconsumptiongood. 4.3 MappingModelMechanismstoEmpiricalFacts InthisSubsection,weformallyassessthedegreetowhichthetransmissionmechanismshighlightedinthemodelinSection4.1andempiricallyestablishedinSections4.2.1,4.2.2,and4.2.3 help us understand the key facts regarding the distributional effects of global price shocks on householdconsumptionestablishedinSection3.4. How well does the theoretical model capture the estimated dynamics of non-durable and category-specific consumption, given the estimated impulse responses of total consumption and relative prices? We address this first in Figure 10 focusing on the food price shock. In particular, in the first row of Figure 10, the estimated line plots the impulse responses of real non-durableconsumptionfromFigure3whilethepredictedlineplotsthemodel-consistentre- 36

sponsesofrealnon-durableconsumptiononthebasisofEquation(4.8)whentherelativeprice estimatesareobtainedfromFigure8,therealconsumptionresponsesareobtainedfromFigure 3, andthepriceelasticityofdemand, ηg, isfixedat2∀g. Thegoodfitbetweentheestimated and predicted impulse responses in the first row of Figure 10 is remarkable. For example, the predictedimpulseresponsesexplainbetween82%to92%ofvariationinrealnon-durableconsumptiondynamicsforfoodshock. Relativepricesplayarelativelyminorroleasdemonstrated bythedashedlineinthefirstrowofFigure10,wherethedashedplotisconstructedusingonly therelativepricetermofEquation(4.8)andtherelativepriceestimatesareobtainedfromFigure8. Thus, theincreaseinrelativepriceleadstosomedeclineinnon-durableconsumption, butthemajoritycomesfromafallinwageincome,asweshownext. That is, having established the general good fit of our theoretical model to the empirical estimatesandtheimportanceoftotalconsumptionresponsesinexplainingnon-durableconsumption, we next turn to ask: How far can wage income dynamics explain the dynamics of total consumption responses? In particular, we rely on the intertemporal budget constraint, Equation(4.5). Weconstructproxiesofpresentdiscountedfutureearnings(threemonthaverage) using the estimated future wage earnings responses from Figure 7 and compute the predictionsfornon-durableconsumption(again,onthebasisofEquation(4.8))usingourproxyof presentdiscountedearningsinplaceoftotalconsumption. Theresultsareinthedashedlines inthesecondrowofFigure10anddepictagoodfit. Goodnessoffitfornon-durableconsumptionusingthismeasureofpresentdiscountedearningsvarybetween69%to80%(asopposed to82%to92%ifweusetotalconsumptiondynamicsasinthefirstrow). WeusethethirdrowofFigure10todemonstratetheroleofnon-homotheticityinexplaining the(level)responseofrealfoodconsumptioninresponsetoanincreaseinglobalfoodprices. In the third row of Figure 10, the estimated line plots the impulse responses of real food consumptionfromFigure3whilethepredictedlinesplotsthemodel-consistentresponsesofreal food consumption on the basis of Equation (4.10) when the relative price estimates are obtainedfromFigure8andtherealconsumptionresponsesareobtainedfromFigures3. Inthis case, boththepriceelasticitiesofdemand, σ ϵ g andηg arefixedat2∀gandtheslopeofEngel curveforfood(εg )isobtainedfromTable4(aftertheslopeofEngelcurveforfuel(εg )is food fuel normalized to unity). In the predicted (homothetic) version, i.e., the dashed line, the slope of Engel curve for food is normalized to unity instead of using the estimated Engel curve slopes fromTable4. Thedashedlineshowslargernegativeresponsesinfoodconsumptionforallincomegroups,demonstratinghowhouseholdsprotectnecessaryfoodconsumptionintheface ofadverseincomeshockswhendemandisnon-homothetic. 37

Figure10:ResponseofRealNon-durableandFoodConsumptiontoExternalFoodPriceShocks byIncomeQuintiles(DatavsTheory) Notes: Thefirstrow: EstimatedreferstomeanestimatesoftheCumulativeIRFsofrealnon-durableconsumptiontoglobalfoodprice shocksfromFigures3. Predictedrefersthemodel-consistentresponsesofrealnon-durableconsumptiononthebasisofEquation(4.8) whentherelativepriceestimatesareobtainedfromFigure8andtherealconsumptionresponsesareobtainedfromFigure3(fixingηg at2∀g.). Thesecondrow: EstimatedreferstomeanestimatesoftheCumulativeIRFsofrealnon-durableconsumptiontoglobalfood priceshocksfromFigures3.ThePredicted(withrealearnings)line,indash,referstothemodelpredictionwherethedynamicsofthetotal consumptiontermofEquation(4.8)isreplacedbyasmoothed(3monthaverage)proxyofpresentdiscountedlaborearningsfromFigure7 whiletherelativepriceestimatesarestillobtainedfromFigure8.Predictedline,insolid,issameasthefirstrow.Thethirdrow:Estimated referstomeanestimatesoftheCumulativeIRFsofrealfoodconsumptiontoglobalfoodpriceshocksfromFigure3.Predictedrefersthe model-consistentresponsesofrealnon-durableconsumptiononthebasisofEquation(4.10)whentherelativepriceestimatesareobtained fromFigure8andtherealconsumptionresponsesareobtainedfromFigures3.Boththepriceelasticitiesofdemand,σ ϵ g andηg arefixed at2∀g,slopeofEngelcurveforfood(εg )isobtainedfromTable4,aftertheslopeofEngelcurveforfuel(εg )isnormalizedtounity. food fuel Forcomparison,inthePredicted(Homothetic)version,thedashedline,Engelcurveslopeforfoodisfixedatunity. 5 Further Evidence, Discussion, and Sensitivity Analysis InthisSection,wepresentsomecomplementaryevidence,discussfurtherourresults,andestablishrobustnessofdistributionaleffectsofglobalpriceshocksonconsumption. 38

5.1 FurtherEvidence Firstwepresentthreesetsofcomplementaryevidencethatcorroborateourmainfindings. ResponseofconsumptioninequalityatstatelevelWehavedocumentedfrommicrodata (Fact2inSection3.4)thatanincreaseinglobalfoodpriceshasalargeradverseeffectonpoorer incomegroups, whileanincreaseinglobaloilpriceshitsbothtailsoftheincomedistribution similarly. Consistent with this, we show in Figures A12 and A13 in Appendix E.1 that various measures of state level inequality (constructed from the same underlying micro data used in our baseline empirical exercise) clearly rise with a rise in global food prices. The response of statelevelinequalitytoanincreaseinglobaloilpricesishowevermixed.43 Occupation-specific earnings responses Figure 7 showed that an increase in global food priceshasalargeradverseeffectonwageincomeofpoorerincomegroups,whileanincreasein globaloilpriceshitswageincomeofbothtailsoftheincomedistributionsimilarly. Itisuseful to explore further what causes this differential pattern of heterogeneous effects on household earningsinresponsetoglobalcommoditypriceshocks.44 One explanation could be that there are composition effects due to differential shares of various occupations across income groups and that different occupations are exposed differentially to the commodity price shocks.45 To investigate further, we use individual level (as opposedtohouseholdlevelusedinSection4.2.1)earningsandoccupationdatafromtheConsumerPyramidHouseholdSurvey. AsshowninTableA2,poorerincomegroupsaremorelikely tobeemployedininformaloccupations,whilehigherincomehouseholdsaremorelikelytobe in formal or self-employed/business occupations. To further corroborate our heterogeneous earnings response, we then examine how earnings of different occupation groups respond to global commodity price shocks using a panel local projection estimation strategy. Figure 11 presents our results. As the bottom panel confirms, informal occupation groups suffer larger realearningslosseswithariseinglobalfoodprices,confirmingtheregressivenatureofglobal food price shock. The rise in global oil prices continues to have an inverse U-shaped impact, withbothinformalandself-employed/businessgroupssufferinglargerrealearningslosses. 43SeeAppendixE.1fordetails.OurmeasuresofinequalityaresimilartoCoibionetal.(2017)whofindsignificant impactofcontractionarymonetarypolicyshocksonconsumptionandincomeinequalityintheUS. 44Theempiricalliteratureonmonetarypolicyfindsdifferentpatternsofheterogeneityinlaborincomeresponses tothesametypeofshock. Thus,forcontractionarymonetarypolicyshocks,Andersenetal.(2023)findaclearly monotonicpatternwhileAmbergetal.(2022)findaninverseU-shapedpattern. Inourcase,theunderlyingexternalshocksaredifferent,buttheybothleadtoacontractionarypolicyresponsetotheexternalshocks,andour impulseresponsescaptureboththedirectrelativepriceeffectsandtheindirectGEeffects. 45Thedifferentialexposuresbyoccupationmightbeduetoinstitutionalfeaturesofwagecontractsthatgovern rigidityorindexationtoinflationorduetodifferencesacrossoccupationsintermsofcomplementarityoflabor withcommodityuseinproduction. 39

Figure 11: Response of Earnings to External Food and Fuel Price Shocks by Occupation Groups(IV) Notes:CumulativeIRFsonthebasisofequation(3.1),butwithinteractioneffectsbyoccupationgroupsinsteadofincomegroups,where theexternalshockislogchangesintheglobalfoodprice,whichisinstrumentedbyaglobalfoodsupplyshock,andlogchangesinglobal oilprice,whichisinstrumentsbyaglobaloilsupplyshock.Thedependentvariableislogchangesinhouseholdlaborearnings.Thelight blueregionisthe90%confidenceintervalandthedarkblueregionisthe68%confidenceinterval. ImpactofglobalfoodpriceshocksontheagriculturesectorIndiaisanetexporterofagriculturalgoods,althoughagricultureconstitutesarelativelymodest,lessthan10%,shareinthe total export basket of India for our time period.46 In this context, conditional on our IV strategyhavingisolatedvariationinfoodpricesthatisexogenoustoIndianlocalsupplyshocks,one mightask: DoesapositivefoodpriceshockleadtoanincreaseinIndia’sagriculturalexports? This might be expected as higher global food prices, that happen due to exogenous reasons, provideincentivesforexportersinIndiatosellabroad.Toanswerthisquestion,weusemonthly IndianexportpriceindexfromtheIMFandmonthlyproductlevelexportvolumedata(seasonally adjusted) from COMTRADE. Our empirical framework is a Bayesian VAR where our food IVisusedasanexogenousshock. EstimatedimpulseresponsesarepresentedinFigureA14in theAppendix,andtheyshowaclearincreasebothinIndianagriculturalexportsandtheexport priceindexfollowingapositivefoodpriceshock. While agriculture exports increase, the main focus of our paper is on the distributional effectsofglobalpriceshocks. Toassesshowagriculturalproducersmightbeaffectingourresults, weundertakethefollowingexercise. Wefirstnotethatagriculturalhouseholdsinourdataare distributedacrossincomegroups.Thus,itisnotthecasethatagriculturalhouseholdsareexclu- 46See,ChatterjeeandSubramanian(2020)forrecentdataonsectoralcompositionofIndia’sexports. 40

sivelyinthelowestincomegroup. Next,were-estimateourbaselinespecificationforwageincomeeffectsexcludingagriculturalhouseholdsfromthesample.47 FigureA15intheAppendix showsthatthedistributionaleffectsofaglobalfoodpriceshockonrealearningsarerobust. 5.2 FurtherDiscussionofMainResults InthisSection,wediscussthreeaspectsofourempiricalresults:first,arelativelylargereffectof globaloilshockontotalconsumptionrelativetonon-durable; second, comparingthemagnitudeofdistributionaleffectsontotalconsumptionversusearnings,andthird,arathernuanced roleofshare-heterogeneityinunderstandingourkeyresultsregardingdistributionaleffectsof globalpriceshocksonhouseholdconsumption. Comparisonoftotalconsumptionandnon-durableconsumptionresponsesFromtheresultsinTable2,wenotethatwhileglobalfoodpriceshocksexplainasimilarshareofvariation fornon-durableortotalconsumption,globaloilpriceshocksexplainahighershareofvariation oftotalconsumption.48 Forexample, forthehighestincomegroup, a1standarddeviationoil shockexplains5%ofthevariationinnon-durableconsumption,butnearly9%ofvariationin totalconsumption. Thissuggeststhattheremightanadditionaltransmissionmechanismthat affectsdurablespendingbythehighincomehouseholdsinresponsetoglobaloilshocks. Comparisonofeffectsontotalconsumptionversusearnings Comparing Figures 3 and 4 with Figure 7, we note that for all income groups other than the poorest, effects on total consumptionarelargerinmagnitudethanthoseonlaborearnings. Theoretically,thesolutionfor consumption in Equation (4.5) shows that a relatively larger response of total consumption (compared to the present discounted value of labor earnings using a constant discount factor)mayariseeitherduetotime-varyinginterestratesandwealtheffectsorduetoassetprice changesthataltertherealvalueofpayoffsfromex-anteassetpositions.Giventhatalargershare of household income is from earnings and transfers for the poorer income groups, we expect thewealtheffectstobemoresalientforhigherincomegroups. Infact,wedofindevidenceof sucheffectsonthestockpriceandtheinterestrate,aspresentedinFigureA3. Ourresultsshowingastrongresponseofconsumptiontotheseshocks, comparedtowage income, isalsoreminiscentofthepositiveeffectofunanticipatedinflationonhouseholdsavingobservedinDeaton(1977).Asanexplanation,Deaton(1977)offersthefundamentalinsight thatindividualconsumershavenopossiblemeansofdistinguishingrelativepricechangesfrom absolutepricechangesandthismechanismislikelytobeatworkforusaswell. Finally,ourre- 47Agriculturalhouseholdsareidentifiedasagriculturallaborers,smallfarmers,andorganizedfarmers. 48Thisisconsistentwithalargereffectofglobaloilpriceriseondurable&service(asopposedtonon-durable) consumption and larger price effects of global oil price increase on durable and service components of CPI in FigureA10. PriyaandSharma(2024)alsofindthatthe(average)effectsofanincreaseinCPI(fuel)arelargeron durableconsumptionusingCPHSdata. 41

sult on this front also connects to the unconditional stylized facts from the emerging market business cycle literature. For instance, Uribe and Schmitt-Grohe (2017) document that consumptiongrowthisclearlymorevolatilethanincomegrowthforemergingmarketeconomies.49 Role of expenditure share heterogeneity Here we discuss the literature on consumption basketheterogeneityandresultinginflationinequality,surveyedinJaravel(2021),toassessits role in understanding our results. We have documented a common pattern of dynamic heterogeneousresponsesacrossvariousconsumptioncategoriestobothglobalfoodandoilprice shocks. On average, as shown in Table A1, food shares vary across income groups while fuel sharesdonot. Butvariationinthesesteady-statesharesbythemselvescannotexplainthedynamicsofconsumptionresponses,thoughtheimpliedheterogeneityinincome-groupspecific priceindicescanplayaroleinaffectingoverallpurchasingpowerofgivennominalwages. To understand in detail the role of share heterogeneity, we refer to Equation (4.10) and makethreeobservations. First,changesinrelativeprices(foodrelativetonon-durable,ornondurable relative to overall CPI) can lead to heterogeneous consumption effects due to heterogeneityinsharesoffoodornon-durableconsumptionacrossincomegroups. However,relying onsuchheterogeneityalonewillimplydifferentpatternsofheterogeneousresponsesforcrosscategory consumption, contradicting our evidence in Figure A5. Since we observe the same dynamicpatternofheterogeneousresponsesacrossdifferentconsumptioncategories,heterogeneityinearningsresponseisamoreplausiblemechanismforexplainingourresults. Second,income-groupspecificpriceindicescanimplydifferentialfallinrealearningseven ifnominalearningsdonotchange. Thisistheoftendiscussedchannelthroughwhichpurchasing power of a given nominal wage income can be affected differentially, for the same underlyingshock, acrossincomegroups. Itisstraightforwardto show thatahigher share offoodin theconsumptionbasketcanleadtoalargerfallintotalconsumptionforpoorerincomegroups withincreaseinfoodprice,astheyhaveahighershareoffoodintheirbasket,butthatitgoestogetherwithasmallerfallinfoodconsumption. Thus,thischannelcannotexplainthecommon estimateddynamicsofheterogeneousresponsesacrossvariousconsumptioncategories. Finally, theliteratureoninflationinequalitydocumentsthatpoorerincomegroupsgenerallyexperienceahigherrateofinflation,particularlyifoverallinflationisdrivenbyriseinfood prices. Poorerincomegroupsarehowever,morelikelytohaveanetnominaldebtposition,as in our data in Table A1. The combination of higher rate of inflation and a net nominal debt position would imply a less negative impact on the poor due to a rise in food prices, which is theoftendiscussedchannelthroughwhichdebtorsbenefitfromunanticipatedinflation. This 49Using Indian annual data (1965-2010), Uribe and Schmitt-Grohe (2017) finds that relative volatility of con- σ sumptionishigherthanincome(relativevolatility c: 1.07)inIndia,whilewereachthesameconclusionusing σ y first-differencedorHPfilteredquarterlynationalincomeaccountsdata(1996:Q2to2019:Q4). 42

iscontrarytotheheterogeneousconsumptioneffectsofariseinfoodprices. In sum, in the absence of any income response, share heterogeneity and resulting differencesinpriceindicesandinflationratesexperiencedbydifferentincomegroupscannotqualitativelyexplainthepatternofcommonheterogeneityforallconsumptioncategoriesforagiven external price shock. However, differences in consumption basket across income groups amplifythepatternofheterogeneityintotalconsumptionresponsesacrossincomegroups.50 5.3 SensitivityAnalysis Howrobustarethekeyresultsondistributionalimplicationsofglobalpriceshocks? Wediscuss foursensitivityexercisesbelow. First, wehavedemonstratedthataddressingomittedvariable biasproblemduetotheinfluenceofglobaldemandshocksiscrucialforthepatternofheterogeneousconsumptionresponses.AnotherendogeneityconcerncouldarisespecificallywithregardtoglobalfoodpricesduetoIndiabeingamajorexporterofricesuchthatlocalshocksthat affect rice production in India, for example, can influence both global food prices and Indian consumption.Moreover,India’spublicdistributionsystemensuresthatpoorerhouseholdscan purchasecereals(mainlyriceandwheat)atsubsidizedprices. Inordertoaddressboththeendogeneityproblemandtheroleofthepublicdistributionsystem, were-estimatethepanelIV local projectionEquation(3.1)forrealfood consumptionexcluding cereals, suitably adjusting the corresponding price deflator. The results are presented in the Appendix in Figure A16. It showsthatthepatternofheterogeneityinresponsetoglobalfoodpriceshocksisunchanged. Second, we use alternate IVs for global food price changes. With the objective of removing the impact of global demand shocks from global food prices, we consider two alternates: residualizing changes in the food price index by only our estimated common factor, or by the economicactivityshockofBaumeisterandHamilton(2019).TheresultsarepresentedinFigure A17. BoththealternateIVstrategiesconfirmtheregressivenatureofglobalfoodpriceincrease. Third, our baseline results presented in Figures 3 and 4 do not include household specific fixedeffects. Thepanellocalprojectionsareestimatedonlogchangesinhouseholdlevelconsumption, which absorbs the household specific intercept term, but different demographic groups may experience different trend growth in consumption. In order to allow for differential trend growth rates of consumption across different demographics, we re-estimate the householdpanellocalprojectionofEquation(3.1)includingfixedeffectsforhousehold’scaste, religion, education, residence in a big city, and age. The results are presented in Figures A18 andA19,andthepatternofheterogeneityisunchanged. Thisisalsore-assuringfromtheperspectiveofourIVstrategyhavingsuccessfullyisolatedexogenousvariation. 50Ifhouseholdsresidingindifferentregionsexperiencedifferentratesofinflationandthatincomegroupsdiffer intheregiontheyreside(see,TableA2),roleofinflationinequalityisalreadyincorporatedinourempiricalexercise. 43

Finally, we explore sensitivity to alternative definitions of income groups, as presented in AppendixE.3.2. FigureA20presentsbothourbaselineresultsandthesealternativecases. This comprehensivesetofexercisesleadustoconcludethatthefactsaboutthedistributionaleffects ofglobalcommoditypriceshocksonIndianhouseholdconsumptionarerobust. 6 Conclusion Inthispaper,westudythedistributionalimplicationsofincreasesinglobalfoodandoilprices by utilizing panel data on Indian consumption and income. We show that while both sectorspecificshocksleadtostagflationarymacroeconomicdynamics,theydifferintermsofdistributionalconsequences. Consumptionoflowerincomedecilesisaffectedmorebyanexogenous increase in food prices, while consumption of both tails of the income distribution is affected similarly by an exogenous increase in fuel prices. We also find that these heterogeneous consumption responses mirror the pattern of heterogeneity in earnings response to these global priceshocks. Examiningrelativeexpenditureresponses,inlightofrelativepriceeffects,allows ustouncoverpatternsofnon-homotheticityinnon-durableconsumption. Wefindthatfood, comparedtofuel,isanecessaryconsumptiongoodforallincomegroupsinIndia. Weprovide a novel way to identify necessary consumption components by relying on a non-homothetic isoelasticCESdemandstructureandimpulseresponsematchingusingexternalinstruments. Ourfindingshaveimplicationsformonetarypolicy. Forariseinglobalfoodprices,wedocument a strong stagflationary impact, a monetary policy contraction, and regressive distributionalimplications. ThedistributionaleffectsonconsumptionthatwehavedocumentedsuggestthatinEMEs,monetarypolicymayneedtoreacttoglobalshocksinfoodprices,despitethe flexibilityofpricesinthissector,echoingtheinsightsofOlivietal.(2023). Iffiscalpolicyplaysa roleinaddressingthedistributionalconcerns,cantheoptimalmonetarypolicyprescriptionsof canonicalopeneconomystickypricemodels(suchasClarida,Galı,andGertler(2002)),which suggestslooking-throughexternalshocksfromflexiblepricesectors,berestored? Infutureresearch,weplantoaddresssuchquestionsinheterogeneousagenteconomiesexplicitlyallowingforroleofmonetary-fiscalpolicymix(similartoSchaabandTan(2023))inaddressingboth efficiencyanddistributionalconcernsinthepresenceofanecessaryconsumptiongood. References Afrouzi, H., S. Bhattarai, and E. Wu (2024). Relative-price changes as aggregate supply shocks revisited: Theoryandevidence. JournalofMonetaryEconomics148(S). 44

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Food,FuelandFacts:DistributionalEffectsofGlobalPriceShocks Disclaimer: This research presents views of the authors and not that of the Federal Reserve BoardortheFederalReserveSystem. Appendix A Data Description Surveydata WeusedatafromtheConsumerPyramidHouseholdSurvey(CPHS)dataset,asurveyconductedbytheCentreforMonitoringtheIndianEconomy(CMIE).TheCPHShassurveyedover 232,000uniquehouseholdssinceitbeganin2014andisthemostcomprehensivelongitudinal consumptiondataavailableforIndia. TheCPHSisdividedinto4distinctdatasets: Consumption Pyramids, Income Pyramids, People of India Survey, and Aspirational India survey. We use the data from the Consumption and Income Pyramid surveys to construct our monthly consumption and income variables and data from the People of India survey for our control variablesaboutdemographics. WeusedatafromJan2014toDec2019. We construct consumption closely matching the categories constructed by Coibion et al. (2017). Theconsumptionvariableweconstructisthesumofnon-durableconsumption(food, fuel which includes cooking fuel, electricity, transport and communication, and intoxicants), durable consumption (appliances, furniture, jewelry, clothing, electronics, toys, cosmetics), andserviceconsumption(entertainment,highwaytolls,beautyservices,fitnessservices,restaurantsetc). We construct income, earnings, and consumption categories closely following the definitionsgivenbyCoibionetal.(2017). Wefirstconstructincomeasthesumofhouseholdincome fromrent,wages,self-production,privatetransfers,governmenttransfers,businessprofits,sale of assets, lotteries and gambling, pensions, dividends, interest and deposits, provident fund, and insurance. These categories are an exhaustive list of all income sources collected in the CPHS survey. Our (labor) earnings measure is constructed using only the category of income fromwagesandovertimebonuses. Wealsowinsorizeourconstructedvariablesatthe1percentlevel. Wethendeflateourtotal consumption, incomeandearningsmeasuresbytheConsumerPriceIndex(CPI)-Combined series (2012 base) available at a monthly frequency from The Ministry of Statistics and ProgrammeImplementation(MoSPI),GovernmentofIndia. DataonpricesTheMinistryofStatisticsandProgrammeImplementation(MoSPI),Government of India, releases detailed data on prices at a monthly frequency. The base year is 2012 and data is available from January 2011. The data is dis-aggregated by geography as well as by-products. Geographically,thedataareavailableforurbanandruralareaswithineachstate. 1

There is some missing data at the state-geography level, but it is not a major concern (97% of India’sconsumptioniscoveredinthestate-geographydata). On the product side, aggregate CPI is broken down into six broad sub-classifications (national level weights are in parenthesis): i) food and beverages (45.86%); ii) pan, tobacco, and intoxicants (2.38%); iii) clothing and footwear (6.53%); iv) housing (10.07%); v) fuel and light (6.84%);andvi)miscellaneous(28.32%). Thecoverage(intermsofsub-products)variesacross the sub-classifications. The most detailed data is available only for food categories. It comprisesofi)cerealsandproducts;ii)meatandfish;iii)egg;iv)milkandmilkproducts;v)oilsand fats; vi) fruits; vii) vegetables; viii) pulses and products; ix) sugar and confectionery; x) spices; xi)non-alcoholicbeverages;andxii)preparedmeals,snacks,sweets,etc. Weconstructpriceindexesforfuelandnon-durables. AlthoughtheMoSPIprovidesanindexforfuel,itonlyincludesfuelusedforcookingandlightandexcludesthefuelusedintransportation; the index for transportation is available under the “miscellaneous (transportation and communication)” category.51 We use the state-geography level weights of fuel and light (FL) and miscellaneous (transportation and communication, or TC) categories to construct a newcompositeindex: W(FL) CPI(FL) +W(TC) CPI(TC) CPI(FL+TC) = s,r s,r,t s,r s,r,t s,r,t W(FL) +W(TC) s,r s,r wheresubscripts representsstate,r ∈{Urban,Rural}representsgeography,andt represents month. Thisprovidesaclosermeasureoflocalenergyprices. Thenon-durablepriceindexincludesfoodandthecompositefuelprices. Itiscalculatedas CPI(NonDur.) =W(Food)s,rCPI(Food)s,r,t +W(FL)s,rCPI(FL)s,r,t +W(TC)s,rCPI(TC)s,r,t +W(Pan)s,rCPI(Pan)s,r,t s,r,t W(Food)s,r +W(FL)s,r +W(TC)s,r +W(Pan)s,r Macrodata WeuseIMF’sGlobalPriceofFoodIndex(NominalUSD)andBrentcrudeoilprices(USD)at monthlyfrequencyasourdataforglobalfoodandoilprices. Weconstructglobalpricechanges by takingdifferencesofthelogsofbothfoodandoil prices. TheGlobalPriceofFoodIndexis anindexof28differentfoodcommodityprices,wheretheweightsareglobalimportshares. 51Whilethiscategoryhasseveralmissingvaluesatthestate-geographylevel,themissingvaluesareconcentrated amongsmallerstates(suchasAndamanandNicobarislands)thatcontributetounder3%ofIndia’sconsumption. 2

Appendix B Summary Statistics by Income TableA1: SummaryStatisticsbyIncomeDecile Decile No.ofHhs Income Earnings Consumption Non-dur.Share FoodShare FuelShare 1 33,830.51 827.37 504.42 2,520.58 0.78 0.62 0.24 2 5,644.08 3,943.66 3,191.57 3,908.62 0.79 0.65 0.21 3 8,093.39 4,899.28 4,238.48 4,295.64 0.79 0.64 0.22 4 10,576.03 5,899.26 5,218.08 4,716.47 0.78 0.63 0.23 5 12,287.31 6,923.61 6,101.26 5,145.57 0.77 0.61 0.24 6 12,892.10 8,177.10 6,997.05 5,543.09 0.77 0.60 0.25 7 14,493.92 9,834.17 8,274.90 5,944.41 0.76 0.59 0.26 8 16,485.14 12,095.56 9,660.60 6,532.69 0.75 0.58 0.27 9 19,543.08 16,126.54 12,189.33 7,344.10 0.75 0.56 0.29 10 29,928.75 32,483.79 21,010.59 9,434.76 0.73 0.52 0.32 Notes: Thistablepresentssomesummarystatisticsbyincomedeciles. Incomeandconsumptionareinrealtermswheretheyaredeflated bythestate-regionlevelconsumerpriceindex(base2012). Thestatisticsarecalculatedbyadjustingforsamplingweightsandnon-response factorsprovidedbytheCenterforMonitoringIndianEconomy.Non-durableandfoodsharerefertothesharesofnon-durableandfoodintotal consumption. 3

TableA2: SummaryStatisticsbyBaselineIncomeGroups Lowest Low Lowermiddle Uppermiddle High Consumption SD(∆log(C ) 0.242 0.205 0.216 0.233 0.248 i,t SD(∆log(C ) 0.205 0.170 0.172 0.178 0.182 i,N,t Non-durable(%ofC) 91.04 90.78 89.62 88.73 87.09 Food(%ofnon-durable) 69.72 72.53 69.61 66.01 61.32 LaborMarketIndicators SD(∆log(earnings)) 0.576 0.274 0.233 0.268 0.4 Earnings(%ofincome) 34.77 84.21 86.69 78.34 67.05 Informaloccupation(%) 82.51 89 82.8 72.4 52 Formaloccupation(%) 15.99 6.12 9.03 15.75 30.91 Self-employed/business(%) 1.49 4.76 8.25 11.87 13.01 Region Urban 58 53 64 73 81 Rural 42 47 36 27 19 EducationCategory Upto7thStd 48 67 57 46 25 Upto12thStd 35 29 36 39 38 ≥CollegeGraduate 16 4 7 15 38 Religion&Caste Hindu 85 87 85 84 85 SC 17 28 25 20 12 ST 7 9 6 4 3 AgeofHouseholdHead 25-49years 40 55 53 37 24 >49years 60 45 47 63 76 Notes:Thistablepresentssummarystatisticsofkeydependentvariablesandsocio-economicvariablesbybaselineincomegroups. Thestatisticsarecalculatedbyadjustingforsamplingweightsandnon-responsefactorsprovidedbytheCenterforMonitoringIndianEconomy.Wecategorisetheavailableoccupationdata.Informaloccupationsincludeagriculturallaborers,home-basedworker, smallfarmer,smalltrader/hawker/businessmanwithoutfixedpremises,legislator/socialworkers/activistsandwagelaborer.Formaloccupationsincludeindustrialworkers,managers,non-industrialtechnicalemployee,organisedfarmer,qualifiedselfemployed professionals,supportstaff,whitecollarclericalemployeesandWhite-CollarProfessionalEmployeesandOtherEmployees. 4

Appendix C Instrumental Variables for Global Price Changes C.1 EstimationoftheFoodPriceShockIV TableA3: Non-energyPricesusedinestimatingtheDynamicFactorModel Food Food IndustrialMetals Rice Wheat Ironore Bananas Barley Aluminium Beef Cocoa Copper CoffeeArabica CoffeeRobust Cotton Fishmeal Corn Lead Poultry Fish Softlogs Shrimp Sugar Hardlogs Orange Tobaco Nickel Tea OliveOil Rubber PalmOil RapseedOil Tin SoybeanOil SunflowerOil Woolcoarse Groundnutoil Coconutoil Woolfine Zinc Notes:CommoditypricesdataarecollectedfromFREDandBloombergand arequotedinUSDollarperunit.Theunitsdifferbycommodity,butinthe estimationweonlyusethelogdifferenceinpricelevels,i.e.,returns. InordertoestimatethefoodpriceIV,wefirstestimateadynamicfactormodelwithonecommonfactorandafood-specificfactorinapanelof37non-energycommodityprices(see,Table A3),whichcomprises13industrialinputsandmetalsand24foodprices. Weusemonthlydata from1990-2022. Thedynamicfactormodelcanbedescribedas: r c,t =B 0 cF t +B 1 cF t−1 +..+B P cF t−P +ζ C,t wherer isthelogdifferenceinthecommoditypricec,F isavectoroftwofactors,Bc,k=0:P, c,t t k isa1×2vectoroffactorloadingsforcommoditycatlagk,andζ istheidiosyncraticcompoc,t nent. The factor loadings reflect the degree to which variation in commodity returns can be explained by each factor. The first factor (Fcommon) is the common factor affecting all comt food modities in the sample, the second factor is a food factor (F ) affecting only the 24 food t commodityprices. Theunexplainedidiosyncraticerrors,ζ ,areassumedtobenormallydisc,t tributed,butpossiblyseriallycorrelated. TheyfollowQ-orderautoregressions, 5

ζ c,t =φc 1 ζ c,t−1 +φc 2 ζ c,t−2 +..+φ Q c ζ c,t−Q +η c,t whereφc,j =1:Q areautocorrelationcoefficients. Alltheinnovations,η ,andthefactorsare j c,t assumedtobezeromean,contemporaneouslyuncorrelatednormalrandomvariables: η ∼N(0,σ2),F ∼N(0,Σ). c,t c t Here, Σ is a diagonal matrix with variance of the factors, Fcommon and F food , as the diagonal t t entries. However,thefactorsaffectthecommoditypriceswithPlags.52 Also,theidiosyncratic errorsareorthogonaltothefactors. Thetimepathsofthefactors,{F },thefactorloadingsBc, t k the autocorrelation coefficients φc, the error variances σ2, and the factor variances, σ2 j c Fcommon t andσ2 arejointlyestimated. food F t Estimation of the dynamic factor model requires further identification and normalization assumptions. Identificationdenotesexclusionrestrictionswiththeaimofinterpretingthefactorsasrepresentingshocksofdifferentnature.Themainexclusionrestrictionweimposeisthat while the common factor, Fcommon, potentially affects all commodity prices, the food factor, t F food ,onlyaffectsthe24foodcommoditypricesincludedinourestimation. Hence,Bk(1,2)= t c 0, for all c belonging to the industrial metals group and ∀k. To identify the common factor as anaggregatedemandfactor,followingtheinterpretationofAlquistetal.(2020),weimposethe signrestrictionthatthefactorloadingsofthecontemporaneouscommonfactor,B0(1,1)≥0∀c. c This implies that all commodity prices comove with the unobserved common factor–an improvementinglobaldemandleadstoanincreaseinallcommoditypricesandvice-versa. We impose a normalization restriction, in order to overcome the well-known problem of unidentifiedmodelsresultingfromrotationalindeterminaciesoffactorsandloadings. Following Kose et al. (2008), we normalize the contemporaneous factor loading of the iron ore for thecommonfactor, andthecontemporaneousfactorloadingofpoultryforthefoodfactor, to unity. Ourmainfocusisestimatingthecommonfactor. Wehaveconductedrobustnessanalysiswherewenormalizedfactorloadingsforcopperinsteadofironore,giventheroleofcopper pricesinpredictingglobalbusinesscycles.Wealsoestimatedanextendedmodelincorporating crudeoilpricesalongwiththenon-energypricesinTableA3.53 52Analternativeassumptionwouldbethatthefactorsaffectcommoditypricesonlycontemporaneously,butthe factorshaveautoregressiverepresentation.Whilethesetwoassumptionsareequivalenttheoretically,theassumptionmadehere,lagsinfactorloadingsandnoautoregressioninfactors,allowsforasimplerestimationtechnique followingJustiniano(2004). ThealternativeformulationisemployedbyKose,Otrok,andWhiteman(2003)and Kose,Otrok,andWhiteman(2008)forestimatingglobalbusinesscycleandbyDelleChiaie,Ferrara,andGiannone (2022)forestimatingaglobalfactorincommodityprices. 53Wehavealsousedalternativenormalizationsofthefoodfactor, settingfactorloadingsforotherfooditems to unity. The results are remarkably similar. Normalizing poultry is the baseline case since it is an important 6

We cast the dynamic factor model in the state space form and estimate it using Bayesian methodsusingMarkovChainMonteCarlo(MCMC).Thestatespacemodelisdescribedindetail in Justiniano (2004). We follow an extensive literature on Bayesian estimation of dynamic factor models (see, for example, Bernanke, Boivin, and Eliasz (2005), Kim and Nelson (2017), Kose et al. (2003), Kose et al. (2008)) which can easily accommodate restrictions on how the factorsaffectsubsetsofseriesthatlieattheheartofourinterpretationofthefactors. Theestimationprocedureisbasedonthefollowingobservation: ifthefactorswereobservable, under a conjugate prior, the models would be a set of regressions with Gaussian autoregressiveerrors;thatsimplestructurecan,inturn,beusedtodeterminetheconditionalnormal distribution of the factors given the data and the parameters of the model. This conditional distribution can, then, easily be used to generate random samples, which can serve as proxy seriesfortheunobservedfactors. Asthefullsetofconditionaldistributionisknown−parametersgivendataandfactorsandfactorsgivendataandparameters−itispossibletogenerate samplesfromthejointposteriordistributionfortheunknownparametersandtheunobserved factorsusingsequentialsamplingofthefullsetofconditionaldistributionsinaGibbssampling method. The process is iterated for a large number of times. Under the regularity conditions satisfiedhere,theMarkovchainsoproducedconverges,andyieldsasamplefromthejointposteriordistributionoftheparametersandtheunobservedfactors,conditionedonthedata. Inourimplementation,thelaginfactorloadings(P)andthelengthofidiosyncraticautoregressivepolynomial(Q)areboth1.WefollowKoseetal.(2008)tospecifythepriordistributions. TheprioronallthefactorloadingcoefficientsandtheautoregressiveparametersisN(0,1).The priorassumptionsonthefactorloadingsreflecttheexpectationthatonaverage,thefactorsdo not affect commodity returns. We use a diffuse Inverted Gamma prior for the error variances andthefactorvariances. Onceweestimatethecommondemandfactorandthefood-specific factorfromthedynamicfactormodel,weresidualizethelogchangesintheglobalfoodpriceindexwiththesetwofactorstoconstructourfoodcommodityshockthatweuseasaninstrument inthehouseholdpanellocalprojections. Astatisticalfactorbasedapproachallowsustocircumventnon-availabilityofhighfrequency productiondataforfoodcommodities,theproblemofaggregationandalsorelianceonfewmajorcrops(suchasriceandwheat)whichcouldbeproblematicinthecontextofIndia. However, itisimperativetounderstandwhatdrivesourestimatedfactors. Our identification of the common factor relies on comovement of this factor with nonpartofthefoodconsumptionbasketinIndia(themostcommonlyconsumedmeat),andunlikeothercommonly consumeditemssuchasriceandwheat,isnotsubjecttodomesticpricecontrols. Riceandwheataresubjectto variouspricecontrolswithintheIndianeconomyintheformofpublicdistributionsystemforconsumersand minimumsupportpriceforfarmers. ThisisalsowhywedonotusetheharvestshockconstructedinDeWinne andPeersman(2016)becauseitreliesonfourmajorcropsincludingriceandwheat. 7

energycommodityprices,theaimbeingtointerpretitasanindicatorofglobaldemand. Crude oil price is very responsive to global business cycles. Baumeister and Hamilton (2019) use oil price,quantity,inventoryandworldIPdatainaBayesianVARwithsignrestrictionstoidentify oilsupply,oildemand,inventoryandeconomicactivityshocks. Ifcommoditypricestrulycomove with global demand, we expect positive comovement between the estimated common factor (note our baseline estimation doesn’t use any oil price data) and the economic activity shock of Baumeister and Hamilton (2019). In Figure A1, we plot our common factor and the economic activity shock of Baumeister and Hamilton (2019).54 Our common factor co-moves with the economic activity shock capturing major downturns in the global economy (such as theGlobalFinancialcrisis).Thecontemporaneouscorrelationis0.23.55DelleChiaieetal.(2022) find a similar strong positive correlation between world industrial production and the global factorestimatedfromapanelofcommodityprices. How to interpret the food-specific factor? Unlike the sign restrictions to identify the commonfactor, wedonotimposesignrestrictionsonthefactorloadingsofthefoodfactor(apart from the exclusion restriction, which implies that this factor only affects the 24 food prices in our panel). However, in our baseline estimation and in various robustness exercises we performwithrespecttonormalization,thefactorloadingsforthefoodfactorareoverwhelmingly positiveandstatisticallysignificant.56 Thatcanariseduetothefood-specificfactorcapturing global demand for food (for example, due to faster growth in poorer economies in our sample), or global weather shocks leading to correlated negative supply shocks across all 24 food commodities, without affecting industrial metal commodities. Contemporaneous correlation between the first principal component of various dimensions of weather shocks in De Winne andPeersman(2021)andourestimatedfoodfactorisnegativebutverylow(-0.03).57 Thisleads ustoconcludethatthefoodfactormostlycapturesfood-specificdemand.58 54Ourestimatedfactorandtheeconomicactivityshockhavedifferentscales. Werescalecommonfactorestimatesin2007foreaseofvisualization. 55Tocheckthedynamiccorrelationpattern,weestimateabivariateVARwith12lagsandtheeconomicactivity shockasthefirstvariable,toshowthatthecommonfactorrespondsinapositiveandsignificantwaytotheeconomicactivityshockforall12monthsaftertheinitialimpulse. Theforecasterrorvarianceofthecommonfactor explainedbytheeconomicactivityshockvariesbetween4-14%over12months. 56Only4outof24foodcommoditypriceshaveweaklynegativefactorloadingsforthefoodfactor. 57ThevariousdimensionsofglobalweathershockinDeWinneandPeersman(2021)are:temperature,temperaturesquared,precipitation,andprecipitationsquared. Tocheckthedynamiccorrelationpattern,weestimatea bivariateVARwith12lagsandthefirstprincipalcomponentoftheweathershocksasthefirstvariable,toshow thatthefoodfactorrespondsinanegativebutinsignificantwaytotheweathershockfor10outof12monthsafter theimpulse.Theforecasterrorvarianceofthefoodfactorexplainedbytheweathershockisnearlyzeroforfirst5 monthsandrisestoabout6-7%after10-11months. 58WeprovideadditionalsupportforthishypothesisintheSensitivityAnalysissection(FigureA17)whereinstead ofresidualizingtheglobalfoodpriceindexbytheestimatedfoodandcommonfactors,weresidualizeonlywith respecttothecommonfactor,oronlywithrespecttotheeconomicactivityshockofBaumeisterandHamilton (2019).OurIVresultswhenresidualizingwithrespecttobothfactorsleadtomorenegativeeffects,whichstrongly 8

FigureA1: ComparisonofAggregateDemandFactorandEconomicActivityShock Notes:ThisfigureplotsthetimeseriesoftheestimatedeconomicactivityshockfromBaumeisterandHamilton(2019)andthecommon factorestimatedfromthedynamicfactormodelasdescribedinOnlineAppendixC.Bothseriesarenormalizedtohavethesamescalein 2007January. Afterweresidualizethe(changesinlog)globalfoodpriceindexbytheestimatedcommon factorandthefoodfactor,whatremainsislargelyfoodcomponentspecificidiosyncraticsupply shocks and potentially some speculative component (because these are globally traded commodityprices). WeusethisresidualizedchangesinglobalfoodpriceindexasourIVinhouseholdpanellocalprojections. C.2 IVsforGlobalPriceChanges: TimeSeriesandMacroEffects We described above in detail how we construct the IV for global good price change. For the globaloilpricechange,ourIVisthesupplyshockfromBaumeisterandHamilton(2019).Figure A2 presents global food and oil price changes with the respective IVs, which we take to micro dataasourmeasureofsector-specificexternalshocks. suggeststhatitremovesmorevariationcomingfromdemand. 9

FigureA2: OilandFoodPriceShocksandtheRespectiveInstrumentalVariables Notes:Thisfigureplotsthetimeseriesofoil(toppanel)andfood(bottompanel)priceshocksandtherespectiveIVs.Theoilpriceshock seriesisthemonth-on-monthchangeinlogBrentcrudeoilprices;foodpriceshockisthemonth-on-monthchangeinthelogglobalfood priceindexpublishedbytheIMF.ThesupplyinstrumentforoilpriceshocksistakenfromBaumeisterandHamilton(2019). Thefood supplyinstrumentisconstructedusingadynamicfactormodelasdescribedinAppendixC. InFigureA3wedemonstratehowanadversefoodsupplyshock,measuredusingourmethod, leadstoastagflationaryimpactontheIndianmacroeconomywithfallingrealeconomicactivity (proxiedbymonthlyrealGDPinterpolatedusingindustrialproduction),risingconsumerprices (proxied by monthly GDP deflator interpolated using CPI), rising short term interest rate, and fallinglocalstockmarket. OurspecificationisaBayesian4-variableVARwith12lagswherethe food supply shock is the exogenous shock. For comparison, in Figure A4 we present macroeconomiceffectsoftheadverseoilsupplyshockofBaumeisterandHamilton(2019)estimated usingthesamemethod,whichshowsthatthemacroeconomiceffectsaresimilar.59 59BothsetsofVAR-basedIRFsarescaledsuchthatthefoodoroilsupplyshockhasunitimpactontheloglevel ofglobalfoodandoilpricesrespectively. 10

FigureA3: MacroeconomicEffectsofFoodPriceShocks Notes:ThisfigureplotstheimpulseresponseofIndianRealGDP,GDPdeflator,3-mothinterestrate,andlocalstockmarketindextoan adverse(positive)foodsupplyshockthatraiseslogofglobalfoodpriceindexbyoneunitonimpact.Theimpulseresponsesareestimated fromaStructuralVARwithfourendogeneousvariablesandthefoodsupplyshockasanexternalshock,allowingfor12lagsofendogenous variablesandexternalshock.ThefoodsupplyinstrumentisconstructedusingadynamicfactormodelasdescribedinAppendixC.Stock marketandinterestratedataarecollectedfromtheGlobalEconomicMonitoroftheWorldBank,whiletherealGDP,GDPdeflator(andIP andCPIusedininterpolation)arecollectedfromHaverAnalytics.Sampleused:2000-2019.Dummiesincluded:GFC,TaperTantrumand India’sdemonetizationpolicy. 11

FigureA4: MacroeconomicEffectsofOilPriceShocks Notes:ThisfigureplotstheimpulseresponseofIndianRealGDP,GDPdeflator,3-mothinterestrate,andlocalstockmarketindextoan adverse(negative)oilsupplyshockofBaumeisterandHamilton(2019)thatraiseslogofBrentcrudeoilpricebyoneunitonimpact. TheimpulseresponsesareestimatedfromaStructuralVARwithfourendogeneousvariablesandtheoilsupplyshockasanexternalshock, allowingfor12lagsofendogenousvariablesandexternalshock.StockmarketandinterestratedataarecollectedfromtheGlobalEconomic MonitoroftheWorldBank,whiletherealGDP,GDPdeflator(andIPandCPIusedininterpolation)arecollectedfromHaverAnalytics. Sampleused:2000-2019.Dummiesincluded:GFC,TaperTantrumandIndia’sdemonetizationpolicy. 12

Appendix D Details on Specifications and Results TableA4: InstrumentalandControlVariablesinHouseholdPanelLocalProjection PanelA.InstrumentalVariables ◦ OilsupplyshockestimatedinBaumeisterandHamilton(2019) ◦ Foodsupplyshockestimatedusingadynamicfactormodelofnon-energycommodityprices PanelB.ControlVariables ◦ Lagsofoutcomevariables –3lags ◦ Lagsofglobaloilandfoodpricechanges –3lags ◦ State-by-time-fixedeffects –State-by-calendarmonth-fixedeffects –State-by-calendaryear-fixedeffects ◦ Aggregateworldconditioncontrols(interactedwithhouseholdincomegroupdummies) –WorldIndustrialProduction(BaumeisterandHamilton(2019)) –USFederalFundsRate –ChangeinglobalVIX ◦ Demonetizationpolicydummy Notes: Thistableshowsourinstrumentalvariablesandasetofcontrolvariablesinourbaselinepanelhousehold localprojectionregressions.DataonallaggregateworldconditioncontrolsareobtainedfromtheFRED. TableA5: F-statisticsforPanelLocalProjectionIVRegressionsofHouseholdConsumption (1) (2) Consumption Consumption (Total) (Non-durable) PanelA:GlobalFoodPrice Shock&FoodSupplyIV FirststageF-stats 3,761.7 3,759.1 PanelB:GlobalOilPrice Shock&OilSupplyIV FirststageF-stats 856.8 838.6 Notes:ThistableshowsF-statisticsfromfirst-stage regressionsforourpanelIVlocalprojectionestimationofeffectsonhouseholdconsumption(Column(1))andnon-durableconsumption(Column (2)). 13

D.1 AcrossCategoryConsumptionResponses InFigureA5weshowacross-categoryconsumptionresponsestotheexternalpriceshocks. FigureA5:ResponseofCross-CategoryConsumptiontoExternalPriceShocksbyIncomeQuintiles(IV) Notes:CumulativeIRFsonthebasisofEquation(3.1)wheretheexternalshockislogchangesintheglobaloil(food)price,whichisinstrumentedbyaglobaloil(food)supplyshockandthedependentvariableislogchangesinhouseholdfood(fuel)consumption.Thelightblue regionisthe90%confidenceintervalandthedarkblueregionisthe68%confidenceinterval. 14

D.2 Non-jointEstimation In Figure A6, we present results relative to the low-income group for both food and oil price shockswhentheestimationofEquation(3.1)isdoneseparatelyforthetwoshocks. FigureA6: Relative(tolowincomegroup)ResponseofNon-durableConsumptiontoExternal FoodandOilPriceShocksbyIncomeQuintiles(IV) Notes: CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobalfoodoroilprice,whichis instrumentedbythecorrespondingsupplyshockandthedependentvariableislogchangesinhouseholdnon-durableconsumption. Column2,forthelowincomegroup,showsthetotaleffectsforthisbaselinegroup,whiletherestofthecolumnsshowtherelativeeffect comparedtothelowincomegroup. Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68%confidence interval. 15

D.3 OLSandIVComparisonforFoodPriceShocks FigureA7: ResponseofConsumptiontoExternalFoodPriceShocksbyIncomeQuintiles Notes:CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobalfoodprice. IntheIVversion, thelogchangeinglobalfoodpricesisinstrumentedbyaglobalsupplyshock. Thedependentvariableislogchangesinhouseholdconsumption,non-durableconsumption,andfoodconsumption.Thelightblueregionreferstothe90%confidenceintervalandthedarkblue regionisthe68%confidenceinterval. 16

D.4 EffectsonRegionalPrices TableA6: InstrumentalandControlVariablesinRegionalPanelLocalProjection PanelA.InstrumentalVariables ◦ OilsupplyshockestimatedinBaumeisterandHamilton(2019) ◦ Foodsupplyshockestimatedusingadynamicfactormodelofnon-energycommodityprices PanelB.ControlVariables ◦ Lagsofoutcomevariables:1lag ◦ Lagsofglobaloilandfoodpricechanges:1lag ◦ State-fixedeffects ◦ Time-fixedeffects –Calendarmonth –Calendaryear ◦ Aggregateworldconditioncontrols –WorldIndustrialProduction(BaumeisterandHamilton(2019)) –USfederalfundsrate –ChangeinglobalVIX ◦ Demonetizationpolicydummy Notes:Thistableshowsourinstrumentalvariablesandasetofcontrolvariablesinourbaselinepanelregionallocal projectionregressions. TableA7: F-statisticsforPanelLocalProjectionIVRegressionsofState-RegionLevelPrices (1) (2) (3) CPI(All) CPI(Food) CPI(Fuel) PanelA:GlobalFoodPrice Shock&FoodSupplyIV FirststageF-stats 3,635.9 3,614.5 2,384.7 PanelB:GlobalOilPrice Shock&OilSupplyIV FirststageF-stats 1,848.2 1,876.0 1,255.8 Notes:ThistableshowsF-statisticsfromfirst-stageregressionsforourpanelIV localprojectionestimationofeffectsonregionalprices.Columns(1)through(3) showtheF-statisticsforestimationofeffectonCPI(headline),CPI(Food),and CPI(Fuel)respectively. 17

D.4.1 OLSresultsonregionalpriceeffectsofexternalshocks FigureA8: ResponseofStateLevelPricestoExternalOilandFoodPriceShocks(OLS) Notes:CumulativeIRFsonthebasisofequation(4.12)wheretheexternalshockislogchangesintheglobalBrentpriceinthetoppaneland logchangesinglobalfoodpriceinthebottompanel.TheseareOLSestimates.Thedependentvariableislogchangesinstatelevelprices. Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68%confidenceinterval. D.4.2 Detailedfoodcategoryrelativepriceresults Welookatrelativepriceeffectsusingmoredis-aggregatedfoodcategoriestoinvestigateinmore detailhowtheexternalpriceshockspass-throughtolocalIndianpricesaswellastounderstand the results on expenditure share effects. In Figure A9 we present results for relative price responsesofvariousfoodcomponents,asaratiotofuelprices,forthecaseoffoodpriceshocks. Thatis, FigureA9presentsinamoredis-aggregatedformtheresultsthatwepresentedbefore for food to fuel CPI ratio. It shows that in response to an exogenous increase in global food prices, relative prices of many food categories (compared to fuel prices) increase. While the increaseintherelativepriceoffoodcategoriesisbroad-based,quantitatively,theyappearparticularly salient for certain food types, such as pulses, sugar, oil and fats, and vegetables. In addition,theincreaseinrelativepricesoffoodcategoriesoccursinbothruralandurbanIndia. 18

FigureA9: ResponseofStateLevelRelativePricestoExternalFoodPriceShocks(IV) Notes:CumulativeIRFsonthebasisofequation(4.12)wheretheexternalshockislogchangesintheglobalfoodprice.Theexternalfood pricechangesareinstrumentedbyglobalsupplyshocks. Thedependentvariableislogchangesinstatelevelrelativeprices,theratioof variousfoodcategoryCPItofuelCPI.Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68%confidence interval. D.5 ExpenditureSwitchingofNon-durables FigureA10: ResponseofNon-durabletoTotalPriceRatioandNon-durableExpenditureShare toExternalOilandFoodPriceShocks(IV) Notes:CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobalBrentoilprice(toppanel),which isinstrumentedbyaglobaloilsupplyshock,andlogchangesinglobalfoodprice(bottompanel),whichisinstrumentedbyaglobalfood supplyshock.Thedependentvariableisthenon-durableconsumptionshareintotalexpenditures.Theleftcolumnplotstheresponseof thenon-durablepricetotheoverallprice. 19

Weinvestigatetheeffectsonthenominalconsumptionexpenditureratioofnon-durabletototalconsumptiontoshowthatexpenditureswitchingisareasonableassumption. InFigureA10 weshowthatglobalfoodpriceshocksincreasetherelativepriceofnon-durableswhileglobaloil priceshocks,afteradelay,decreasetherelativepriceofnon-durables. Then,inthehousehold panelIVlocalprojectionframeworkweestimateequation(3.1),butwiththenominalexpenditureshareofnon-durableconsumptiontototalconsumptionasthedependentvariable.Figure A10presentsresultsfortheresponseofthenon-durabletototalconsumptionexpenditureratio forbothexternalpriceshocks.Theresultsshowthatconsistentwithexpenditureswitchingthat comesaboutduetorelativepricechanges,thisratioincreasesfortheglobaloilshock,whileit decreasesfortheglobalfoodshock.60 Inaddition,theresponseofthenon-durableexpenditure sharesareverysimilaracrossvariousincomegroups,suggestingthatrelativepricemovements arethemaindeterminant,ascapturedbyahomotheticCESaggregator. D.6 ResponsesofDetailedFoodCategoriestoFuelExpenditureRatios Here we delve into expenditure ratio results for various food components. As food expenditure is a composite of different food categories, the average response might not be indicative ofnon-homotheticityforalltypesoffoodexpenditures. TestablePrediction2hadsummarized that relative expenditure on food components increasing in response to the food price shock would be a sufficient proof for non-homotheticity, as the relative price of these food componentsincreases(FigureA9)andrealnon-durableconsumptionfalls(Figure3). Figure A11 presents results for responses of various food components to fuel expenditure ratios. We also plot the relevant relative price response in the left column (from Figure A9). It shows that the evidence for non-homotheticity in preferences of the poor (including the two lowest income groups) with respect to various food categories is quite clear for sugar, oil and fats,andvegetablesastheexpenditureratiosforthesecategoriesincrease. Inaddition,inthese threefoodcategories,fortherich,theexpenditureratiogoesdown.Moreover,FigureA11shows thattheclearpatternoflackofexpenditureswitching(onnet)bythepoor(againincludingboth thelowincomegroups)isprominentalsoforotherfoodcategories,suchaspulsesandspices.61 Interestingly, for pulses and spices, the results suggest no expenditure switching even by the rich. Thus,pulsesandspicesareclearlyanecessarygoodforallincomegroupsinIndiaasthe resultsforthemsatisfythesufficientconditionlaidoutinTestablePrediction2. 60Theresultsforthefoodpriceshockarecomparativelynoisiertowardstheendofthehorizon. 61Topreservespace,weonlyreportedfourincomegroupsinFigureA11. 20

Figure A11: Response of Various Food Categories Expenditure Shares to External Food Price ShocksbyIncomeQuintiles(IV) Notes: CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobalfoodprice(bottompanel), whichisinstrumentedbyaglobalfoodsupplyshock. Thedependentvariableistheratioofhouseholdnominalfoodcategoriestofuel consumptionexpenditures.Theleftcolumnshowstheresponsesoftherelevantrelativeprices.Thelightblueregionisthe90%confidence intervalandthedarkblueregionisthe68%confidenceinterval. 21

Appendix E Additional Results E.1 EffectsonRegionalInequality Here,weassesstheeffectsonregionalinequalityoftheglobalcommoditypriceshocks,which wemakeoperationalbyconstructingseveralmeasuresofregionalinequalityfromunderlying householdlevelpanel. Thespecificationforthestate-levelpanellocalprojectionregressionto estimatedynamiceffectsonregionalconsumptioninequalityoftheexternalcommodityprice shocksis: J Cineq −Cineq =c+βh,food extfood+βh,oil extoil+ (cid:88) αh(Cineq −Cineq )+ s,t+h s,t−1 0 t 0 t j s,t−j s,t−j−1 j=1 K D (cid:88) (cid:88) βh k ext t−k + δhD t−d +γ h X t +θ s +δ t +ϵ s,t+h (E.1) k=1 d=0 whereCineq denotesvariousmeasuresofstate-regionlevelinequality(inlogs)fortotalcons,t sumption and non-durable consumption in period t, h denotes the projection horizon, ext denotesdifferentmeasuresoftheexternalcommoditypriceshock,and J =1,K =1arerespectively the AR and MA coefficients in the specification. Finally, our specification includes state andtimefixed-effects. Standarderrorsareclusteredatthestatelevel. Thisspecificationissimilar to the state-region level price regression specification in equation (4.12). We present IV resultsregardingtheeffectsofglobalpriceshocksonregionalinequalitywhereweinstrument thechangesinglobalfoodandoilpricesbythecorrespondingsupplyshocks. Howdoesregionalconsumptioninequalityevolvedynamicallyinresponsetoexternalfood and oil price changes? Figure A12 presents the IV results for the food price shock. Broadly speaking, we observe that an increase in global food prices increases consumption inequality within a state over time, with effects on both total and non-durable consumption inequality statisticallysignificantandpersistent. FigureA13presentstheIVresultsfortheoilpriceshock. Itshowsthatanincreaseinglobal oil prices does not have as clear of an effect on consumption inequality as does global food prices, suggesting that traditional inequality measures might not capture the subtle ways in whichhouseholdsaredifferentiallyaffectedalongtheincomedistributionbyoilpriceshocks. The effects of oil shocks on regional inequality hence appear to be more nuanced, consistent withwhatweuncoverfromdetailedhousehold-leveldata.62 62Forexample,consistentwithlargereffectofglobaloilpriceincreaseespeciallyontotalconsumptionofhigher incomegroups(asopposedtonon-durableconsumption), weseeadeclineintotalconsumptioninequalityin FigureA13. 22

FigureA12: ResponseofRegionalInequalitytoExternalFoodPriceShocks(IV) Notes:CumulativeIRFsonthebasisofequation(E.1)wheretheexternalshockislogchangesintheglobalfoodprice,whichisinstrumented byaglobalfoodsupplyshockandthedependentvariableislogchangesininequality.Thelightblueregionreferstothe90%confidence intervalandthedarkblueregionisthe68%confidenceinterval. 23

FigureA13: ResponseofRegionalInequalitytoExternalOilPriceShocks(IV) Notes:CumulativeIRFsonthebasisofequation(E.1)wheretheexternalshockislogchangesintheglobaloilprice,whichisinstrumented byaglobaloilsupplyshockandthedependentvariableislogchangesininequality. Thelightblueregionreferstothe90%confidence intervalandthedarkblueregionisthe68%confidenceinterval. 24

E.2 ImpactofGlobalFoodPriceShocksontheAgricultureSector FigureA14: ResponseofExportPriceIndexandAgriculturalExportstoFoodIV Notes: ThisfigureplotstheimpulseresponseofIndia’sexportpriceindexandagriculturalexportstoanadverse(positive)foodsupply shockthatraiseslogofglobalfoodpriceindexbyoneunitonimpact. TheimpulseresponsesareestimatedfromaStructuralVARwith twoendogeneousvariablesandthefoodsupplyshockasanexternalshock,allowingfor12lagsofendogenousvariablesandexternal shock.ThefoodsupplyinstrumentisconstructedusingadynamicfactormodelasdescribedinAppendixC.Theexportpriceindexdatais collectedfromIMFandtheproductlevelmonthly(availablefrom2011)tradedataiscollectedfromCOMTRADE.Sampleused:2011-2019. Dummiesincluded:TaperTantrumandIndia’sdemonetizationpolicy. Figure A15: Response of Earnings of Non-Agri Households to External Food Price Shocks by IncomeQuintiles Notes:CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobalfoodprice,whichisinstrumented byaglobalfoodsupplyshockandthedependentvariableislogchangesinhousehold(real)earnings.Wepresentourbaselineestimates fromFigure7witherrorbandandthedashedlinereferstomeanresponsesfortherobustnessexercisewherewedropagriculturalhouseholdsfromoursample.Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68%confidenceinterval. 25

E.3 SensitivityofKeyConsumptionHeterogeneityResults Figure A16: Response of Non-Durable Consumption (without cereal) to External Food Price ShocksbyIncomeQuintiles Notes:CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobalfoodprice,whichisinstrumented byaglobalfoodsupplyshockandthedependentvariableislogchangesinhousehold(real)foodconsumption.Wepresentourbaseline estimatesfromFigure3witherrorbandandthedashedlinereferstomeanresponsesfortherobustnessexercisewherewedropcereals fromfoodconsumptionandsuitablyadjustthestate-regionspecificpricestodeflate.Thelightblueregionisthe90%confidenceinterval andthedarkblueregionisthe68%confidenceinterval. Figure A16 shows that the adverse impact of a rise in global food prices on household food consumption is largely similar to Figure 3. The adverse impact is slightly larger in magnitude potentiallyreflectingtheroleofpublicdistributionsysteminprotectingcerealsconsumption. ThetwoalternateinstrumentsusedinFigureA17areglobalfoodpricechangeresidualized by: (a)onlyourestimatedcommonfactorand(b)economicactivityshockofBaumeisterand Hamilton (2019), while in the baseline we residualize with respect to both common and food factor, asdescribedinAppendixC. Note thatbothofthe alternate instrumentsusedinFigure A17implythesameregressivenatureofanincreaseinglobalfoodpriceincrease,butthenegativeimpactissmallerinmagnitudecomparedtoourbaselineinstrument. Thislargernegative impactonconsumptionafterremovingthefoodfactorfromtheglobalpricevariation(ontop of removing the common demand factor) is consistent with interpreting the food factor as a globaldemandfactorspecifictofoodcommodities.63 63Ifthefoodfactormainlycapturedcorrelatedglobalweatherevents,weexpectanoppositesignfromtheomittedvariablebias. Also,notethatthethreeIVsimplyverysimilarmagnitudeofimpactfirstfourmonthsafterthe shockbutdifferdynamically. 26

Figure A17: Response of Non-Durable Consumption to External Food Price Shocks (alternate IVs)byIncomeQuintiles Notes:CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobalfoodprice,whichisinstrumented byaglobalfoodsupplyshockandthedependentvariableislogchangesinhousehold(real)non-durableconsumption. Wepresentour baselineestimatesfromFigure3witherrorbandandthetwodashedlinerefertomeanresponsesfortherobustnessexerciseswherewe usealternateinstrumentsfortheglobalfoodpriceshock.Thelightblueregionisthe90%confidenceintervalandthedarkblueregionis the68%confidenceinterval. E.3.1 Roleofhouseholdfixedeffects We include a set of household characteristic specific fixed effects in our baseline panel local projections described in equation 3.1 and present the results in Figures A18 and A19.64 Our conclusionsregardingdistributionaleffectsofglobalpriceshocksonhouseholdconsumption remainunchangedrelativetoFigures3and4. 64Weincludefixedeffectsforcaste,religion,educationgroups,bigcityandagebins. Wedefineatotalofeleven agegroupsbasedontheageofthehouseholdhead.Theyoungestandtheoldestgroupsconsistofhouseholdsbelowtwentyyearsandabove65yearsrespectively.Householdsbetweenthesetwoages,whichroughlycorresponds toworkingage,areclassifiedintogroupsoffiveyearseach.Wedefineeducationgroupssimilarlybasedontheeducationlevelofthehouseholdhead.Weconsiderthreegroups–belowhighschool,highschooleducatedbutless thancollegeeducated,andcollegeeducatedandabove.Summarystatisticsfordifferenthouseholdcharacteristics arepresentedinAppendixBinTableA2. 27

FigureA18: ResponseofConsumptiontoExternalFoodPriceShocksbyIncomeQuintiles(IV) afterallowingfordemographicspecificfixedeffects Notes:CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobalfoodprice,whichisinstrumented byaglobalfoodsupplyshockandthedependentvariableislogchangesinhouseholdconsumption.Theseregressionsincludearichset ofhouseholdfixedeffects.Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68%confidenceinterval. Figure A19: Response of Consumption to External Oil Price Shocks by Income Quintiles (IV) afterallowingfordemographicspecificfixedeffects Notes:CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobaloilprice,whichisinstrumented byaglobaloilsupplyshockandthedependentvariableislogchangesinhouseholdconsumption.Theseregressionsincludearichsetof householdfixedeffects.Thelightblueregionisthe90%confidenceintervalandthedarkblueregionisthe68%confidenceinterval. 28

E.3.2 Alternatedefinitionsofincomegroups Inourfinalrobustnessexercise,weaddresstheissuethatouranswertothekeyresearchquestionmaybesensitivetohowweassignindividualstodifferentincomegroups. Inourbaseline results,householdsaregroupedaccordingtocut-offsbasedontotalhouseholdrealincomein theinitialperiod. Whilethedefinitionofthegroupsisonthebasisoftheinitialincomedistribution,householdscananddotransitiontoadifferentincomegroupovertimedependingon currentincome.Wenextreporttwoimportantsensitivityanalysesofourbaselineresultswhere wechangethedefinitionofincomegroups. Inthefirstsensitivityanalysis,insteadoftotalhouseholdrealincome,wegrouphouseholds according to per capita household real income in the initial period. Because average householdsizesdifferbyincomegroups,percapitahouseholdincomemaymoreaccuratelycapture theresourcesavailabletohouseholdmembers(Deaton(2019)). Toaccountforthis, wegroup households into five income groups according to the per capita income deciles and estimate theheterogeneousconsumptionresponsesaccordingtoequation(3.1). TableA8: TransitionMatrixofRealIncome Q Q Q Q Q Total 1 2 3 4 5 Q1 81.02 3.02 3.94 6.20 5.82 100 Q2 7.58 73.65 14.86 2.76 1.15 100 Q3 4.13 5.22 79.50 10.11 1.04 100 Q4 4.55 0.69 6.61 83.60 4.56 100 Q5 6.98 0.54 1.30 7.40 83.78 100 Notes:Thistablepresentstheaveragetransitionprobabilities(in% terms)betweendifferentincomegroupsinoursample. Inthesecondsensitivityanalysis,weretainthegroupingaccordingtototalhouseholdreal incomeintheinitialperiod,butwerestrictthetransitionmatrix.Thebaselinetransitionmatrix acrossincomegroupsispresentedinTableA8. Whilemorethan80%ofhouseholdsremainin the same income group over time (as captured by the diagonal entries of Table A8), there are some households who transition from the highest to lowest income groups. Such a transition can potentially reflect measurement error. In order to restrict such unusual movements, we estimatethebaselinepanelIVlocalprojectionframeworkofequation3.1whilerestrictingthe transitionmatrixsuchthatnohouseholdisallowedtomovemorethantwo(absolute)stepsin thetransitionmatrix. 29

FigureA20: ResponseofNon-DurableConsumption(sensitivitytoalternateincomegroups)to ExternalOilandFoodPriceShocksbyIncomeQuintiles Notes:CumulativeIRFsonthebasisofequation(3.1)wheretheexternalshockislogchangesintheglobalfoodoroilprice,whichisinstrumentedbythecorrespondingsupplyshocksandthedependentvariableislogchangesinhousehold(real)non-durableconsumption. WepresentourbaselineestimatesfromFigures3and4witherrorbandsandthedashedlinesrefertomeanresponsesfortherobustness exercisewhereweusealternatedefinitionsofincomegroups.Thelightblueregionisthe90%confidenceintervalandthedarkblueregion isthe68%confidenceinterval. The results for both sensitivity analysis are presented in Figure A20. These results again are similar in nature to the baseline results of Figures 3 and 4. Thus, alternate definitions of income groups leave our key conclusions regarding heterogeneous household consumption response to global price shocks unchanged. While everyone suffers consumption losses due torisingfoodprices,poorerincomegroupsarefarmorevulnerabletosuchfoodpriceshocks. Incontrast,thelowestandhighestincomegroupssufferequallyfromanincreaseinglobaloil prices. 30