Changing Jobs to Fight Inflation: Labor Market Reactions to Inflationary Shocks

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Changing Jobs to Fight Inflation: Labor Market Reactions to Inflationary Shocks Gorkem Bostanci, Omer Koru, Sergio Villalvazo 2025-042 Please cite this paper as: Bostanci. Gorkem, Omer Koru, and Sergio Villalvazo (2025). “Changing Jobs to Fight Inflation: Labor Market Reactions to Inflationary Shocks,” Finance and Economics Discussion Series 2025-042. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2025.042. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Changing Jobs to Fight Inflation: Labor Market Reactions to Inflationary Shocks* Gorkem Bostanci† Omer Koru‡ Sergio Villalvazo § June 2, 2025 Abstract: We argue that inflationary shocks affect allocative efficiency by changing the rate and the characteristics of workers’ job-to-job transitions. First, using monetary policy shocks and survey data on search effort, we empirically show that a one percentage point rise in inflation increases job-to-job transitions by up to 4.5%, and workers with higher inflation expectations are more likely to search and do so more effectively. Second, we build a general equilibrium model of directed on-the-job search to quantify the aggregateimplicationsoflabormarketreactions. Higher-than-expectedinflationreduces real wages, prompting workers to search more actively and aim lower. This increases job-to-job transitions but lowers the efficiency gains per transition. Therefore, the effect on output is ambiguous. Last, we calibrate the model to the U.S. economy. Inflationary shocks increase reallocation rates, yet allocative efficiency and output decline. Small deflationaryshocks(e.g.,2%)increaseoutputintheshortrun,whileothersdecreaseit. KeyWords: Inflation,Job-to-jobFlows,WorkerReallocation JELcodes: E24,E31,J31 *First draft: February 2019. We thank Paul Beaudry, Serdar Birinci, Harold Cole, Domenico Ferraro, David Green, Joachim Hubmer, Dirk Krueger, Iourii Manovskii, Guido Menzio, Andreas Mueller, GuillermoOrdonez,GustavoVentura,andseminarparticipantsinASU,FRBSt. Louis,UBC,UPenn,Bank of Mexico, and various conferences for helpful comments and discussions. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of theBoardofGovernorsoftheFederalReserveSystemorofanyotherpersonassociatedwiththeFederal ReserveSystem. †UniversityofBritishColumbia,Email: gorkem.bostanci@ubc.ca ‡PennStateUniversity §FederalReserveBoard

1 Introduction Reallocating workers across firms is crucial for raising aggregate productivity. Theoretically,reallocationcanraiseefficiencyasfirmsenter,exit,andexperienceshiftsinproductivity. Empirically, job-to-job transitions, on average, come with wage increases, which suggests improvements in match productivity.1 In this paper, we identify a novel channel that affects the nature of job-to-job transitions: inflation. If wages are not indexed to inflation, higher-than-expected inflation decreases real wages, increases gains from a fresh contract, and a new offer through job search becomes more valuable.2 Workers could respond by increasing their search effort, thus making a new job offer more likely, and by being less selective, i.e., looking for offers with smaller wage increases. Both responseswouldincreasetherateofjob-to-jobtransitions(quantitychannel),whilethesecond response decreases the associated productivity boost for each switch (quality channel). Hence, the impact of inflationary shocks on output is ambiguous and potentially dependsonthesizeoftheshock. In the first part of the paper, we provide three main pieces of evidence that suggest a causal link from inflationary shocks to J2J rates. First, we run simple vector autoregressionsontheaggregateU.S.data. WhileinflationhelpspredictfutureJ2Jrates,J2Jratesdo not help predict future inflation movements. Second, we use various estimates of structural monetary policy shocks as instruments for inflation. Our results suggest that a 1 p.p. shocktoinflationcausesanincreaseintheJ2Jratesby2.9to4.2%. Third,weprovide indirect evidence of the mechanism using individual-level survey data on inflation expectationsandon-the-jobsearchbehavior. Wefindthataonestandarddeviationincrease in yearly inflation expectations is associated with a 4.3% higher probability of searching. Furthermore, it is associated with 11.6% more hours spent searching and 24.1% more of- 1See,e.g.,FallickandFleischman(2004).Undervariousmodels,jobchangescomewithincreasesinboth wageandproductivity,e.g.,Postel-VinayandRobin(2002)andMenzioandShi(2011). 2Jobswitchers’wagegainrelativetojobstayersishigherwheninflationishigherthanexpectedinthe U.S.SeeFigure9inAppendixF. 2

fersreceivedwithinthenextmonthamongsearchers. In the second part, to account for how the firms and workers react to an inflationary shock, we build a dynamic game between a worker (she) who searches for a new job and a firm that can unilaterally increase her wage to influence her search behavior. The firm commits to continue paying the current wage forever, but cannot commit to future wage increases. We characterize the Markov-Perfect equilibria of the game. Under some restrictions on the parameter space, after a sudden decline in real wages, the firm does not adjust the wage back to its original level, and the worker responds by searching for lessvaluableoutsideoptions(qualitychannel)thatareattainedwithahigherprobability (quantitychannel). Inotherwords,thedownwardwagerigidityendogenouslygenerates upwardwagerigidity. For our quantitative analysis, we integrate this dynamic game into a general equilibrium model of directed on-the-job search with aggregate shocks as in Menzio and Shi (2011). Wefurtheraugmentthemodelbyintroducingex-antefirmheterogeneityandendogenous search effort. Firms optimally increase wages after an unanticipated inflationary shock but fall short of offsetting the full decline. The workers respond by increasing theirsearcheffortsandsearchinginmarketswithlowerpostedwagesastheircurrentsituation deteriorates.3 Hence, they trade a higher wage for a higher probability of finding anewjob. BothresponsesleadtomorefrequentJ2Jtransitions(quantitychannel),which, ceteris paribus, would increase aggregate productivity and output. However, the reduced askingwagemakesthesetransitionslessproductivity-enhancing(qualitychannel),creatingaforcethatdecreasesaverageproductivity. Inshort,inflationaryshocksleadtomore J2Jtransitions,whiletheireffectonproductivityisambiguous. Weprovideanovelsolutionalgorithmthatgreatlysimplifiesthesolutionofadirected 3SeeFabermanetal.(2022)forevidenceonsearcheffortdecreasingwithincomeandChristensenetal. (2005) and Mueller (2010) for evidence on job search effort decreasing as workers move up the job ladder. See Pilossoph and Ryngaert (2024) for workers with higher inflation expectations reporting smaller reservationwages. 3

on-the-job search model with aggregate shocks under inefficient contracting. It relies on a backward-induction solution that iterates over a wage grid. We further introduce a novel estimation algorithm that endogenously selects a vacancy cost distribution consistent with a given wage distribution. The algorithm simplifies the estimation of directed searchmodelswithex-antefirmheterogeneity. Wecalibratethemodelbytargetingtheaggregatejobflows,averagewagegaininaJ2J transition,andthelaborshareofoutput,amongotheraggregatemoments. Furthermore, wetargettheJ2Jrateresponsetoaninflationaryshockthatweestimatedusingthemonetarypolicyshocks. Hence,thecalibrationensuresarealisticincreaseintheJ2Jratesanda realistic change in the average productivity gains from such transitions. Without explicitly targeting it, the model generates an empirically plausible productivity distribution andbroadlycapturesthecyclicalco-movementofaggregates. We subject the calibrated model to unanticipated inflationary shocks of various magnitudes. Theincumbentfirmsarebroadlyunresponsivetothedecreaseinrealwages. The search effort increases while the workers target smaller wages in their on-the-job search. J2J rate increases, yet the average productivity gain decrease dominates: output declines intheshortrun,andthedeclineislargerforlargershocks. Incontrast,deflationaryshocks lead to fewer transitions with an increase in the average productivity gain. The quality channel dominates for small deflationary shocks (e.g., -2%), and the output increases in the short run, despite fewer transitions. When the size of the deflationary shock is larger (e.g., -5%), the quantity channel starts to dominate, and the output decreases in the short run. Although the size of the J2J rate and productivity gain responses are monotone in thesizeoftheshock,theoutputresponseisnotmonotone. Inflationaryshocksalsonarrowthewagedistribution,consistentwiththepost-COVID patterns documented by Autor et al. (2023). Furthermore, they reduce the predictive powerofjobtenureforwages,matchproductivity,andsearchefforts. 4

Lastly,wesimulatecounterfactualrecessionswithandwithoutinflationaryanddeflationary shocks. The recession with an inflationary shock significantly increases J2J rates, yet leads to a slow output recovery. On the other hand, the recession with a deflationary shock generates large declines in J2J rates but a fast output recovery post-recession. These results demonstrate a caveat in equating fast reallocation with increased allocative efficiency. Inflation can grease the wheels by encouraging J2J transitions, yet may lead to short-run declines in productivity. Therefore, our model helps explain why deflationary episodesdo notcorrelate withslower growth(Atkeson andKehoe, 2004)as predictedby Keynesiantheory.4 Our primary contribution is to the literature on the efficiency of job reallocation. Followingvaryingpathsofallocativeefficiencydocumentedacrossrecessions(seeMukoyama (2014)andFosteretal.(2016)),theliteratureaskswhenreallocationisproductivity-enhancing and when it is not. Caballero and Hammour (1994), Barlevy (2003), and Ouyang (2009) discuss adjustment costs, increased credit market frictions, and early exits, respectively, asreasonsforthe‘sullying’effectoftherecessions. Likeours,Barlevy(2002)analyzesthe role of J2J transitions during recessions. He shows that decreasing J2J transitions during recessionscangenerateaneffectlargeenoughtooffsetthe‘cleansing’effectofrecessions. Our model encompasses this channel yet shows that decreased reallocation rates do not guaranteeaworseningallocation. Theproductivitygainsassociatedwithreallocationdepend on the characteristics of transitions, hence, whether the recession is inflationary or deflationary. Martellini and Menzio (2020) and Birinci et al. (2024) also suggest a similar quality-quantitydistinction: followingimprovementsinmatchingtechnology,thematchingratescanremainconstantwhilematchqualityimproves. AcontemporaneouspaperbyAfrouzietal.(2024)proposesamodellinkinginflationary shocks and labor market responses. It argues that inflation leads to welfare losses 4Theideathatinflationhelpsreducelabormarketfrictionsandincreaseproductivitywasproposedby Tobin(1972)andempiricallytestedbyCardandHyslop(1997). Accordingtothisidea,apositiveinflation ratepreventsnominaldownwardwagerigidityfromtranslatingtorealrigidity. Inourbaselinemodel,we shutthischanneldowntofleshoutournovelchannel. 5

by triggering inefficient search activity. While their outcome of interest is the dynamics of aggregate labor market variables, ours is allocative efficiency and output response.5 Fabermanetal.(2022)similarlyinvestigateshowendogenoussearcheffortplaysarolein arandomsearchmodelwithaggregateshocks. Ourmodelendogenizessomedifferences in the search behavior of the unemployed and the employed via directed search. Our empiricalanalysisoftherelationshipbetweeninflationexpectationsandsearchbehavior helps explain the search heterogeneity across survey respondents that they document. Another contemporaneous paper by Pilossoph and Ryngaert (2024) also documents a positivecorrelationbetweeninflationexpectationsandjobsearchactivities. Weindependentlyreachsimilarresults.6 Some recent work focuses on the reverse causality: how the labor markets influence thepathofinflation. MoscariniandPostel-Vinay(2023)incorporatesarandomon-the-job searchframeworkintoaNewKeynesianDSGEmodel. Intheirmodel,whentheworkers are concentrated at the top of the job ladder, many of the offers they receive are matched by their employers. Matched offers are essentially cost shocks to the incumbent firm, followedbyincreasedprices. Hence,on-the-jobsearchcancreateinflationarypressure,and its magnitude depends on the allocation of workers across firms. Birinci et al. (2022) extends Moscarini and Postel-Vinay (2023) into a heterogeneous-agent incomplete-markets environment and characterizes the changes in MPC to discipline aggregate demand response. FacciniandMelosi(2023)allowsshockstoon-the-jobsearchintensityinarandom search environment. We endogenize the search effort and the effectiveness of J2J transi- 5Beyond the differences in our key outcome variables, there are three key differences in our model structure. First, whiletheymodelworkerheterogeneity, wefocusonthefirmheterogeneitytogeneratea realisticproductivitydistribution. Second,wemodelthelackofcommitmentinthefirm-workerrelationship through a firm that can unilaterally increase wages to discourage search. In contrast, they model it throughaworkerwhocanunilaterallytriggerabargaininggame. Hence,weprioritizeaJ2Jtransitionas a threat point for the worker, rather than a quit to unemployment. Third, our model is in discrete time andposesdistinctcomputationalchallenges. Theirmodelisbettersuitedforunderstandingvacancyand unemploymentdynamics,whileoursisbetterforunderstandingmisallocationandoutputdynamics. 6WefindsimilarresultsusingtheSurveyofConsumerExpectationsonthelikelihoodofsearch. While welookatabroadersetofsearcheffortandoutcomevariables,theylookatreservationwagesandutilize additionaldatafromtheReal-TimePopulationSurvey. 6

tions to respond endogenously to the economic environment. We provide a theory and quantitativeevidencethattheoutputresponsetoaninflationaryshockisnon-monotonic inthemagnitudeoftheshock. Lastly, our mechanism suggests an important role for labor markets in determining the output response to monetary policy shocks. Olivei and Tenreyro (2007) shows that the effects of monetary policy shocks depend on their timing during the year, which is consistent with many firms renegotiating wage contracts at the end of the year. Bjo¨rklund et al. (2019), using data on collective wage agreements in Sweden, find that the output response to monetary policy is bigger when a larger fraction of wage contracts are nominally fixed. We provide a theory of job search that links labor markets and outputresponsestoinflationaryshocks. Theestimatedmodelquantifiesoutputresponsesto inflationaryshocksofvariousmagnitudes. We proceed with the description of the data used. Section 2 provides the reducedformanalysis. Section3laysdownthedynamicgamebetweenafirmandaworker,while Section 4 presents the quantitative general equilibrium model. Our calibration strategy and the quantitative results are presented in Sections 5 and 6, respectively. Section 7 concludes. 2 Empirical Analysis Figure 1 shows the recent movements in the job-to-job transition rate (J2J rate) and CPI inflation for the U.S. Interestingly, the J2J rate took a big hit in all three recessions in our sample. While it took several years for the rate to recover after the 2001 and 2008 recessions,itimmediatelyrecoveredinthe2020recession. The2020recessionwasalsotheonly inflationary recession: while the inflation rate decreased after the previous recessions, it went up to historical levels after the 2020 recession. These patterns raise questions about 7

0.09 0.030 0.06 0.027 0.03 0.024 0.00 0.021 0.018 2000 2010 2020 Year noitalfnI IPC J2J Rate (Dashed) Figure 1: CPI Inflation and Monthly Job-to-job Transition Rates 10/1995 to 06/2022 The dashedlinerepresentsthethree-monthmovingaverageoftheseasonallyadjustedmonthlyJ2Jrate(Fujita etal.,2024). ThesolidlinerepresentstheCPIinflationfromtheU.S.BureauofLaborStatistics. Theshaded regionsrepresentNBERrecessions. the role played by inflation in determining the J2J rate.7 Acknowledging that both J2J ratesandinflationareequilibriumoutcomes,wemoveontounpacktheirco-movement. This section presents two main pieces of evidence to argue that inflationary shocks influence workers’ search behavior. First, Section 2.1 uses estimates of monetary policy and global oil shocks as instruments to get a causal estimate of the effect of inflation on job-to-job transitions. We later use the estimates from this subsection to discipline the structural model. Second, Section 2.2 uses survey data to argue a link between inflation andjobsearchbehaviorbycomparingworkerswithdifferentinflationexpectations.8 7UnexpectedinflationmovementsintheU.S.haveledtolargedropsinrealwagesastheyaccumulated. Figure10inAppendixFpresentstherealwagelossesofaworkerwhosignedacontractaccordingtoSPF inflation forecasts. The losses during the post-Covid inflation period reach 9% while they approach 2% several times after 1981. See Figure 11 for the same plot with the Michigan Survey of Consumers (MSC) inflationforecasts. 8In Appendix C.1, we use time-series data from the U.S. in a simple Vector-Auto-Regression to show thatunexpectedlyhighinflationtodaypredictsahigherJ2Jrateinthefuture. SeeAppendixC.2andC.3for analysesutilizingstate-levelandcountry-levelvariationinJ2Jrates. Althoughbothstateandcountry-level analysesaresuggestiveoftheroleofourchannel,wedon’thavestate-leveldataoninflationexpectations, andthecountry-leveldataistooinfrequent(yearly)totrackchangesinjobtransitions. 8

2.1 Instrumental Variable Analysis with Monetary Policy Shocks We use various monetary policy shock estimates from the literature. The first measure is computedfromnarrativerecordsofFOMCmeetingsandinternalforecastsoftheFederal Reserve by Romer and Romer (2004) and updated further by Wieland and Yang (2020). ThesecondmeasureisbySimsandZha(2006),whousestructuralVARestimatestoidentifyshockstomonetarypolicy. Thethird,fourth,fifth,sixth,andseventhmeasuresareby BarakchianandCrowe(2013),GertlerandKaradi(2015),NakamuraandSteinsson(2018), Bauer et al. (2021), and Bauer and Swanson (2023) who use high-frequency movements infinancialseriesduringpolicyeventstoidentifymonetarypolicyshocks.9 In our main specification, we estimate the following equations in the first and the secondstages: 24 (cid:88) Infl = γ + γ MPS +ϵ (1) t 0 i t−i t i=1 J2J = β +β Infl +β Infl +ϵ . (2) t 0 1 t−1 2 t−12 t wheretdenotesamonth,J2J aremonthlyJ2Jrates,Infl isthepercentagegrowthof t CPIfromt−12tot,andMPS isoneofthemonetarypolicyshockmeasureswehave. Table1showsthatinflationhasasignificantandpositiveimpactonJ2Jtransitions. Inflation in the previous month has a positive coefficient in all specifications and is always significantatthe1%level. Furthermore,themagnitudeoftheeffectissimilaracrossspecifications. Inparticular,aonepercentagepointincreaseininflationleadstoanincreasein J2Jtransitionsby5.5to10.9basispoints,whichtranslatestoa2.2%-4.5%increaseonaverage. Theseresultsfurtheraddtotheevidenceinsupportofourtheory,thatis,inflationary 9See Appendix B for a more detailed explanation of each series and Table 16 in Appendix F for the summarystatistics. 9

Table1: IVEstimates BC GK BLM NS NSFFR RR SZ BS (1) (2) (3) (4) (5) (6) (7) (8) Infl 0.109∗∗∗ 0.055∗∗∗ 0.072∗∗∗ 0.095∗∗∗ 0.058∗∗∗ 0.093∗∗∗ 0.081∗∗∗ 0.061∗∗∗ t−1 (0.034) (0.015) (0.015) (0.020) (0.020) (0.029) (0.027) (0.014) Infl 0.076∗∗ 0.035 0.043∗∗∗ 0.030 0.018 0.046∗ 0.034 0.025∗ t−12 (0.031) (0.023) (0.015) (0.021) (0.023) (0.027) (0.035) (0.014) Range ’95-’08 ’95-’12 ’95-’20 ’95-’14 ’95-’14 ’95-’08 ’95-’03 ’95-’23 Obs 131 179 278 200 200 125 68 308 AdjR2 −0.000 0.102 0.030 −0.077 0.094 0.095 0.105 0.055 Notes: Eachcolumnrepresentsamonetarypolicyshocksource. Theinstrumentsare1to24-month lagsoftheshocks. AllvariablesareseasonallyadjustedandHP-filtered. ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Source: Fujitaetal.(2024);U.S.BureauofLaborStatistics,CPI;authors’calculations. shocksleadtohigherjob-to-jobtransitionrates.10 2.2 Survey Evidence on Search Effort This section supplements the previous analyses by providing evidence at the individual levelusingsurveydata. Sincethereisnovariationininflationsurpriseacrossindividuals, weuseinflationexpectationsasaproxy. We use the publicly available micro-data from the Federal Reserve Bank of New York Survey of Consumer Expectations (SCE) between 2013 and 2022. The core survey in the SCE is a 12-month panel and asks individuals about their inflation expectations each month.11 The Labour Survey supplement is administered in April, July, and November and asks respondents about their work status and basic questions on their job search activity. Lastly, the Job Search supplement is administered in October and asks more detailed questions on job search activities. We combine these surveys to measure how 10TheresultsarequalitativelyandquantitativelyrobusttocontrollingforUEratesandaddingoilprice shocksestimatedbyKa¨nzig(2021)asadditionalinstruments. SeeTable17andTable18inAppendixF. 11Thewordinginthesurveyis: “Whatdoyouexpecttherateof... inflation/deflation... tobeoverthe next12months?” 10

inflationexpectationsarerelatedtojobsearchactivitiesandoutcomes. In our main specification, we regress measures of job search activities and outcomes oninflationexpectationsofrespondents. Werunregressionsoftheform: y = αˆi +γ +β ⃗ X ⃗ +ϵ (3) jt jt t jt jt where j indexes respondents, t indexes survey dates, y and ˆi represent job search jt jt activities (or outcomes) and inflation expectations, respectively, for respondent j measuredatsurveyt. Lastly,thevectorX representsadditionalcontrolsandalwaysincludes survey fixed effects. In our main specification, we also control for demographic and jobrelated variables (natural logarithms of age, tenure, and annual earnings, dummies for sex and marital status, five dummies for race, four dummies for education, and fixed effectsforstate,andtwo-digitindustries)thatcancorrelatewithbothinflationexpectations andjobsearchbehavior.12 Weexcluderespondentswhoare,atthetimeofthesurvey,not betweentheages18and64,non-employedorself-employed. Table 2a shows the results on various measures of job search effort. In particular, respondents with higher inflation expectations are more likely to have searched in the past month. A one standard deviation increase in inflation expectations is associated with 1 p.p. (4.3%) higher likelihood of search. Furthermore, conditional on having searched, theyspent0.4(11.6%)morehourssearchinginthepastweek,tried0.2(5.8%)moremethods, and applied to 0.3 (11%) more employers in the past month. Table 2b shows the results on various measures of job search outcomes conditional on having searched. Respondents with higher inflation expectations have received 0.04 (12.9%) more interviews and0.07(24.1%)moreoffersinthepastmonth. Wefindnosignificantimpactonthenumber of employers respondents heard from. Adding several available controls reduces the 12SeeAppendixB.4fordetailsonhowweestimatetenureforeachindividual. SeeTable19inAppendix Fforsummarystatisticsonsearch-relatedvariables. 11

magnitudeofthecoefficients,yetthequalitativeresultsarebroadlyrobust. Even though there is a robust relationship between inflation expectations and job search behavior, the former might be capturing the agent’s expectations on the broader state of the economy and be unrelated to the real wage erosion mechanism we propose. We re-estimate (3), replacing the inflation expectations with three alternative expectation measures regarding stock markets, interest rates, and unemployment rates.13 The results are summarized in Figure 13 in Appendix F. In short, none of these alternate measures consistentlypredictjobsearchbehaviorasinflationexpectationsdo. The evidence in this section supports a causal link between inflationary shocks and job-to-job transitions. In the next sections, we build and estimate a structural model that allowsustoquantifytheaggregateimpactofthischannel. 3 A Simple Model of Wage Adjustment This section presents a dynamic game between a worker (she) who searches for a new job and a firm that can unilaterally increase her wage to influence her search behavior. We characterize the Markov-perfect equilibria of the game and show how the worker andthefirmwouldreacttounexpectedinflation: asuddendeclineintherealwage. This simplemodelshowsthatboththequantityandqualitychannelsareoperationalwhenthe workers can direct their search. Later, in Section 4, we present a model that endogenizes thejobopportunitiesoftheworkerthroughthefreeentryofprofit-maximizingfirmsand allowsworkerstochoosetheirsearcheffort. 13These variables represent the answers to the following questions: “What do you think is the percent chancethat12monthsfromnow,onaverage,Xwillbehigherthantheyarenow?”whereXvariesbetween “stockpricesintheU.S.stockmarket”,“averageinterestrateonsavingaccounts”,and“theunemployment rateintheU.S.”. SeeTable20inAppendixFforsummarystatisticsontherelevantexpectationmeasures. 12

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3.1 Environment Preferences and Technology Time is discrete with an infinitely lived firm and a worker. They both maximize the present value of their income with joint discount factor β. The firm and the worker produce a random amount of y ∈ {y0,...,yN}, which follows a Markov chain with transition matrix Π. The worker can also apply for a continuum of outside jobs with value V ∈ V = [V,V]. Each application succeeds with probability p(V) > 0wherepistwicecontinuouslydifferentiablewithp′ andp′′ representingfirstand second derivatives. We assume applications for higher-value jobs are less likely to succeed p′ < 0. The worker can only apply for one job each period. We assume the outside jobsarestrictlypreferredtothehighestwagethefirmcouldoffer,thatis,V > maxi{yi} . 1−β Contract Space The firm commits to paying any current wage w− as long as the worker stays. The firm can increase the wage but cannot commit to future increases. Lastly, the firm needs to pay a cost for adjusting wages from w− to w that equals ξ(w −w−)τ where τ ξ > 0,τ > 1.14 Timing Each period starts with the realization of y. First, the firm chooses the continuation wage w ≥ w−, and then, the worker chooses which V to apply for after observing w. Theworkerleavesfortheoutsidejobifsuccessful;ifnot,theproductionhappens,and thefirmpaysw totheworker. 3.2 Markov Perfect Equilibrium WelimitourattentiontoMarkovPerfectEquilibria(MPE),inwhichthefirm’sandworkers’strategiesdependonlyonthepayoff-relevantstates: currentproductivityy andwage ratew−. WedenoteaMarkovstrategyforthefirmwithw∗(y,w−)andfortheworkerwith V∗(y,w−). 14Weintroducetheadjustmentcostheretoensurethedifferentiabilityofthefirm’sobjectivefunctionfor analyticalresults. Weshutitdowninthegeneralequilibriummodel. 14

The firm’s problem can be represented by the following Bellman Equation evaluated rightbeforeproduction: (cid:20) (cid:21) (cid:88) ξ F(y,w−) = y −w− +β Π max (1−p(V∗(y′,w)))F(y′,w)− (w−w−)τ , (4) y,y′ w≥w− τ y′ with the associated policy function w∗(y′,w−). Here, (1−p(V∗(y′,w))) represents the probability that the worker’s application does not succeed and the firm continues to operate. Theworker’sproblemcanberepresentedas: (cid:20) (cid:21) (cid:88) (cid:0) (cid:1) A(y,w−) = w− +β Π maxp(V) V −A(y′,w∗(y′,w−)) +A(y′,w∗(y′,w−)) , (5) y,y′ V∈V y′ withtheassociatedpolicyfunctionV∗(y′,w−). Importantly,boththeworkerandthefirm takeeachother’sstrategiesintoaccount(w∗ andV∗,respectively). Definition1. F(y,w−),A(y,w−),w∗(y′,w−),andV∗(y′,w−)constituteaMarkovPerfectEquilibriumwhere 1. F(y,w−)andw∗(y′,w−)solvethefirm’sproblemin(4)givenV∗(y′,w−),and 2. A(y,w−)andV∗(y′,w−)solvetheworker’sproblemin(5)givenw∗(y′,w−). 3.3 Comparative Statics Now, we characterize the policy functions of the firm and the worker. In particular, we provide sufficient conditions for the policy functions to increase with the current wage w−. Proposition 1. Let τ < 2, ξ be sufficiently large, and p′′ be sufficiently small. Then, w∗(y,w−) andV∗(y,w−)arestrictlyincreasinginw−. Proof. SeeAppendixA. 15

Proposition 1 provides insights into how an individual worker and firm would respond to an inflationary shock, i.e., an unexpected drop in the real wage w−. The firm would not respond to an inflationary shock by bringing the wage to its original level: a strictly increasing w∗ implies w∗(y,(1−π )w) > w∗(y,(1−π )w) for π > π . Hence, 1 2 2 1 the inflationary shock can have a lasting impact on the worker’s real wage. The worker would respond by targeting outside jobs that provide less value. In other words, she would be less selective and more likely to leave for an outside job. Our main insight is present in this simple firm-worker structure: following an inflationary shock, the worker wouldtargetlessdesirablejobsandbemorelikelytoswitch. Thenextsectionintroduces this game to a general equilibrium model to quantify the aggregate implications of our insight. 4 The General Equilibrium Model This section presents a directed search model that maps inflationary shocks, worker allocation, and aggregate output while encapsulating the dynamic game in Section 3. We use the model to quantify the short-run output response to an unexpected inflationary shock: a sudden permanent decline in existing real wages. The model exhibits monetary neutralityinthelongrun: theeconomygoesbacktoitsoriginalstochasticsteadystateas firmsincreaseincumbentworkers’wagesandworkersswitchjobs. However,depending on the size of the inflationary shock, aggregate productivity and output can increase or decreaseintheshortrun. 4.1 Environment PreferencesTheeconomyconsistsofacontinuumofworkerswithmeasureoneandacontinuumoffirmswithpositivemeasure. Workers’utilityislinearintheirincome,andthey 16

dislike searching for jobs. Firms are risk-neutral and want to maximize their discounted profits. Timeisdiscrete,andbothpartiesusethesamediscountfactor,β ∈ (0,1). Production Technology There is a single consumption good in the economy. Unemployedworkersproducebunitsofoutput. Whenaworkerandafirmmatch,theyproduce y + z units of output. The first component, y, is the aggregate productivity. It follows a Markov process, and it is identical across firms. Let Y ⊂ R denote the set of possible + aggregate states. The second component, z, is the firm productivity. It is chosen by firms before they enter the market. The cost of choosing productivity z is given by κ(z), which is strictly increasing and strictly convex, i.e., κ′ > 0 and κ′′ > 0. Once chosen, z remains constantthroughouttheworker’stenureatthefirm. Let Z ⊂ R denotethesetofpossible + firmproductivitylevels. Lastly,ineachperiod,firmspayanoperatingcostthatdependsontheaggregatestate ψ andfirmproductivityz: ϕ(ψ,z). Weusetheoperatingcostasareduced-formrepresentation of capital expenditures. We assume that this payment, along with firm profits, is distributed across workers equally. Since workers’ utility is quasilinear, their non-labor incomedoesnotimpacttheirdecisionsandisignoredgoingforward. MeetingTechnologyWorkersandfirmsmustfindeachothertoproduceoutput. Search is directed, meaning workers and firms target specific submarkets indexed by a wage promise and market tightness. The wage is considered a promise because firms can raise it later based on the state of the economy, but they cannot reduce it. Let w ∈ R denote + therealwagerateofferedbythefirmandtheassociatedsubmarket. Both unemployed and employed workers can search for a job. After selecting a submarket, workers choose their search effort, e. The utility cost of exerting effort is given by c(e), and it is a strictly increasing and convex function with the following properties: c(0) = 0,c′(0) = 0. Ontheotherside,eachfirmselectsasubmarkettopostavacancyand paysthecostκ(z)associatedwithitschosenproductivitylevel. 17

Thematcheshappenthroughaconstant-returns-to-scalematchingfunction. Themarket tightness θ is defined as the vacancy-to-total search effort ratio and is a sufficient statisticforthematchingprobabilities. Aworkerwhoexertseunitsofeffortinasubmarket with tightness θ finds a job with probability ep(θ), where p : R → [0,1] is a strictly increasing and concave function with the following properties: p(0) = 0, p(x) → 1 as x → ∞. Meanwhile, a vacancy posted in a submarket with tightness θ matches a worker with probability q(θ), where q : R → [0,1] is a strictly decreasing function that satisfies thefollowingcondition: θq(θ) = p(θ). Timeline Each period is divided into four sub-periods. In the first sub-period, aggregate productivity y is realized. In the second sub-period, exogenous separations occur with probability δ ∈ (0,1). For surviving matches, the firms adjust their wages upward if they find it optimal. In the third sub-period, entrants choose their productivity level z, pay the cost, and choose where to post their vacancy. In the meantime, workers choose where to search and how much effort to exert. In the last sub-period, production takes place,andwagesarepaid. DiscussionoftheModelElementsWhilesettingtheenvironment,wemakesomesimplifications. First,weexpressallvariablesinrealtermsasalimitingcaseofaNewKeynesian model where pricing frictions are reduced to zero and conceptualize inflation as an unexpected reduction in real wages. This approach isolates the effects of inflation on the labor market. Second, firms cannot make counteroffers to employees who are poached byotherfirms. Whilethiscouldtheoreticallyresultinworkersmovingtolessproductive jobs, such behavior does not occur with the calibrated parameters. Including an explicit pricingdecisionorallowingcounterofferswouldruleoutblock-recursiveequilibria,makingthemodelintractable. Third,wedonotmodelthedeterministicpartoftheinflationprocess,yetthisiswithout loss of generality. When the inflation process is deterministic, firms and workers coulddesignwagecontractstoadjustnominalwagesovertime,keepingrealwagescon- 18

stantintheabsenceofshocks. Themodelhasmonetarynon-neutralityduetotwokeyfrictions: non-state-contingent contractsandsearchfrictions. Becausecontractsarenotstate-contingent,15 aninflationary shock lowers the real wages of workers. To restore their real wages, workers must find a new firm and sign a new contract. However, search frictions prevent them from doing so immediately, delaying the adjustment. As a result, inflation affects labor reallocation through workers’ search behavior and, in turn, impacts the real economy. Our model wouldexhibitmonetaryneutralityifalllaborcontractswereinflation-adjustedoriflabor marketswerecompetitive. 4.2 Problem of a Firm Let us start by describing the problem of a firm that already has a worker. Let K(w,z,ψ) be the value function of a filled vacancy with match productivity z, current wage w, and aggregatestateψ. Oncethematchisformed,theonlydecisionthefirmmakesiswhethertoincreasethe wage. Specifically,theproblemofafilledvacancyis: (cid:20) (cid:21) K(w,z,ψ) = y +z −w−ϕ(ψ,z)+β(1−δ)E max(1−p¯(w′,z,ψ′))K(w′,z,ψ′) . (6) w′≥w The first component is the flow profit, y + z − w − ϕ(ψ,z). The second component is the discounted value of the firm. With probability δ, the worker separates exogenously, leaving the vacancy with zero value. With probability 1 − δ, exogenous separation does not occur and the firm chooses a new wage that is weakly larger than the current one. After the wage adjustment, the worker can search for a new job and leave the firm with probability p¯(w′,z,ψ′). This probability is determined in equilibrium. With the remain- 15SeeAppendixDforabroadoverviewoftheevidenceregardingthe(lackof)wageindexation. 19

ing probability 1 − p¯(w′,z,ψ′), the worker remains at the firm, and the value of the firm becomesK(w′,z,ψ′). Without on-the-job search, the current wage would always bind for the firm. When workers search on-the-job, however, the firm might be willing to pay more to distort the worker’sjobsearchbehavior. Letw⋆(w,z,ψ)betheoptimalwagepolicy. Let us now describe the problem of an entrant. Due to free entry, in equilibrium, the expected profit of posting a vacancy with productivity z and wage w must be nonpositive: κ(z) ≥ q(θ(w,z,ψ))K(w,z,ψ). (7) The left-hand side is the cost, and the right-hand side is the expected value of the vacancy, which is the product of the probability of finding a worker and the value of a filled vacancy. For this condition to hold with equality, there must be a positive mass of workerssearchingforajobinsubmarketw. ¯ Let θ(w,z,ψ) be the solution to equation (7). Among those offering the same wage, ¯ only the market with the highest θ(w,z,ψ) can attract workers by providing the highest job finding probability. Therefore, the relevant market tightness for each wage is determined by the upper envelope of θ ¯ (w,z,ψ) values.16 Then, define θ(w,ψ) and z⋆(w,ψ) as θ(w,ψ) = maxθ ¯ (w,z,ψ), z⋆(w,ψ) = argmaxθ ¯ (w,z,ψ). (8) z∈Z z∈Z 16Note that the above reasoning breaks down if vacancy costs vary sufficiently across z levels. In that scenario,aworkermayprefertosearchinalesstightmarketiftheassociatedzlevelislarger,withpossibly higherfuturewages. Thisscenariosubstantiallycomplicatestheexpositionandthesolutionalgorithm. We restrictouranalysistotheparameterspacewherethisdoesnothappenandlaterconfirmthatourcalibrated parametersareinthisspace. 20

4.3 Problem of a Worker Let H(w,z,ψ) be the lifetime value of a worker employed at a firm with productivity z with wage w when the aggregate state is ψ. Similarly, let U(ψ) be the lifetime value of an unemployedworkerwhentheaggregatestateisψ. Consider a worker with a current lifetime utility of V. The worker chooses where to search for a job and how much effort to exert. With probability e · p(θ(w,ψ)) the worker finds a job at a firm with productivity z⋆(w,ψ), and her lifetime utility becomes H(w,z⋆(w,ψ),ψ). Withtheremainingprobability,shedoesnotfindajob,andherlifetime utilitystaysatV. Theworkerincursasearcheffortcostc(e)independentoftheoutcome. Thus,herjobsearchproblemcanbeexpressedas: maxep(θ(w,ψ))H(w,z⋆(w,ψ),ψ)+(1−ep(θ(w,ψ)))V −c(e). w,e Thisproblemcanbedecomposedintotwoparts: R(ψ,V) = maxp(θ(w,ψ))(H(w,z⋆(w,ψ),ψ)−V), (9) w maxeR(ψ,V)−c(e). (10) e The first part involves choosing the optimal wage w to search for, considering the difference between the lifetime value of a new job and the current lifetime value. The second part involves selecting the optimal search effort e to maximize the expected gain fromthesearch,netofthesearchcostc(e). Weusem(V,ψ)todenotethesolutionto(9). An unemployed worker consumes b in the current period. In the next period, the worker decides where to search for a job and how much effort to exert. Thus, the value functionofanunemployedworkeris: (cid:104) (cid:105) U(ψ) = b+βE maxeR(ψ′,U(ψ′))−c(e)+U(ψ′) . (11) e 21

An employed worker consumes w in the current period. In the next period, with probabilityδ,theworkerbecomesunemployed. Ifsheremainsemployed,thefirmadjusts the wage after the aggregate state is realized. At that point, the worker’s lifetime utility becomes H(w⋆(w,z,ψ′),z,ψ′), and she decides where to search and how much effort to exert. Thus,thevaluefunctionofanemployedworkerisgivenby: (cid:104) H(w,z,ψ) = w+βE δU(ψ′)+(1−δ)max{eR(ψ′,H(w⋆(w,z,ψ′),z,ψ′))−c(e) (12) e (cid:105) +H(w⋆(w,z,ψ′),z,ψ′)} . 4.4 Market Equilibrium Following Menzio and Shi (2011), we consider block-recursive equilibria where policy functions do not depend on the distribution of workers, thus, ψ ≡ y. Matched workers andfirmsplayaMarkovPerfectEquilibriumsimilartotheoneinDefinition1. Definition 2. A block-recursive equilibrium consists of a market tightness θ : R × Y → R , + the associated firm productivity z⋆ : R × Y → Z , endogenous job separation probability p¯ : + R × Z × Y → [0,1], workers’ value functions U : Y → R and H : R × Z × Y → R , the + + firm’s value function K : R ×Z×Y → R , the worker’s policy functions m : R×Y → R and + e∗ : R×Y → [0,1],andthefirm’spolicyfunctionw⋆ : R ×Z×Y → R suchthat + + 1. H(w,z,ψ)satisfies(12),U(ψ)satisfies(11),K(w,z,ψ)satisfies(6) 2. p¯(w,z,ψ)satisfiesp¯(w,z,ψ) = e∗(H(w,z,ψ),ψ)p(θ(m(H(w,z,ψ),ψ),ψ)), 3. e∗(V,ψ)andm(V,ψ)solveworker’sproblemin(9)and(10), 4. w⋆(w,z,ψ)solvesfirm’sproblemin(6), 5. θ(w,ψ)andz⋆(w,ψ)aregivenby(8). 22

4.5 Impact of an Inflationary Shock As we defined our model in real terms, an inflationary shock can be represented by a decline inwages without achange in matchproductivity. In other words, aninflationary shockalterstheshareofsurplusthatgoestofirmsandworkers. A decline in wages generates three responses: firms adjust wages upwards, workers searchforlowerwages,andexertmoresearcheffort. Thefirsttworesponsesfollowfrom thefirm-workergamepresentedinSection3. Firmscanincreasewagestodistortworkers’ search,butthiswouldonlypartiallyoffsettheimpactoftheinitialshock. Workerssearch for jobs in submarkets with lower wages than they did before: as the workers’ current situation deteriorates, the return to finding a job increases. Hence, the workers search in submarkets with a higher probability of finding a job. The third response is through the searcheffort. Sincethereturntosearchincreases,workersexerthighereffort. Theseresponsestogetherimplymorejob-to-jobtransitionsafteraninflationaryshock, consistentwiththefactswedocumentedinSection2. Becauseworkersmovetomoreproductivejobsonaverage,anincreaseinthenumberoftransitions,ceterisparibus,increases aggregate output. However, because workers direct their search to lower wages than they did before, the productivity gain associated with each job-to-job transition will be lower compared to transitions before the shock. In other words, while the ‘quantity’ of job-to-job transitions increases, their ‘quality’ decreases. Therefore, the aggregate output can increase or decrease based on the magnitudes of these responses. In the next section, wecalibrateourmodeltoquantifytheimpactofinflationaryshocksonaggregateoutput throughlabormarketadjustment. 23

5 Quantitative Analysis This section calibrates the model to the U.S. economy around 2005. The calibration ensuresthatthemodelaccuratelyreplicateskeyfeaturesofthelabormarket,includingflow rates and the surplus sharing between firms and workers under typical business cycle conditions. Wethenassesstheaggregateimpactofanunanticipatedinflationaryshock. For the model predictions on output response to be accurate, two implied elasticities must be plausible: (1) the response of job-to-job transitions to an inflationary shock and (2) the response of aggregate output to job-to-job transitions. We measure the former elasticity from an instrumental variable analysis with inflationary shocks in Section 2. The latter can be inferred from wage increases following job switches and a measure of howsurplusissharedbetweenfirmsandworkers. 5.1 Functional Forms and Externally Calibrated Parameters We assume y follows an AR(1) process of the form ln(y ) = ρ ln(y ) + ε where ε ∼ t y t−1 t t N(0,σ2). We adopt a CES matching function as in Menzio and Shi (2011) which leads to y job finding probability p(θ) = θ(1+θγ)−1/γ . We define the search cost for employed as c(e) = ((1−e)−η−ηe−1)andforunemployedasνc(e). Thisfunctionalformensuresthat c(0) = 0, lim c(x) = ∞, and ∂c(x)/∂x is invertible; hence, the effort choice problem is x→1 well-behaved. We choose the operating cost function, ϕ(ψ,z), based on the labor shares across firm productivity distribution, estimated by Gouin-Bonenfant (2022). Specifically, ˜ ˜ ˜ wesetϕ(y,z) = ϕ(z)·(z +y),andset1−ϕ(z)tothelaborshare. ϕ(z)isgivenbyTable3. Wealsointroduceaone-timejobtransitioncostforworkers,λ(w−w−)2,whichispaid iftheworkersuccessfullylandsanewjob. Thiscostisnotnecessaryforthemodeltogenerate the discussed mechanisms, but it helps smooth the worker’s job search problem. It can be interpreted as the adjustment a worker needs to make to settle in an unfamiliar 24

environment. We assume the transition cost of moving to a smaller real wage is prohibitively large. This greatly simplifies the model computation by allowing the use of backwardinduction(seeAppendixE). Table3: OperatingCost z Percentile 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ˜ ϕ 0 0 0.064 0.089 0.142 0.198 0.239 0.258 0.333 0.561 Note: Thevaluesforϕ˜(z)areextractedfromTableD.IIoftheOnlineAppendixofGouin-Bonenfant(2022) withthelaborsharecappedat1. We discretize the aggregate productivity process using Rouwenhorst (1995) with levels {y ,y }. We also discretize the firm productivity levels as z ∈ {z ,...,z } and accord- L H 1 Z ingly,κ ∈ {κ ,...,κ }whereZ = 40. 1 Z Thefullsetofparametersnecessarytocomputethemodelisthevector: Ω = {b,γ,β,δ,η,ν,λ,{z ,κ }Z ,ρ ,σ } (13) i i i=1 y y We set the model period to one month and normalize unemployment benefits to the averagelevelofaggregateproductivity. Theexogenousseparationrateispinneddownby theunemploymentratein2004asδ = 0.015giventhetargetedUErate. Wesetβ = 0.951/12 and ρ = 0.7881/3, which equals the implied monthly persistence of the logged and HPy filtered GDP series from the U.S. data. We set γ = 0.4 as in Eeckhout and Sepahsalari (2024).17 Lastly, following the evidence presented in Appendix D, we assume 20% of the workersaresubjecttoautomaticinflation. Theremainingparametersarecalibratedinternallytoensurethemodelreplicateskey labor market features. The internal calibration is performed in the presence of aggregate 17A common practice in the literature is to set γ to the elasticity of job finding rate to market tightness. Thepresenceofeffortinourmodelcreatesawedgebetweenthetwovalues. 25

shocks,astheseshocksinfluencebothjobtransitionsandwagedynamics. 5.2 Calibration of the Productivity Parameters For our quantitative analysis, it is important for our model to generate a realistic productivity distribution. Ideally, we would choose {z ,κ }Z to generate the desired proi i i=1 ductivity distribution. However, with directed search, the productivity levels that firms haveaccesstoandthosethatemergeinequilibriumdiffer: (1)aproductivitylevelisonly observed if it can generate the highest expected profits (net of vacancy costs) for some observed wage and (2) a wage is only observed if it is the ideal wage to target for some workers. As a result, estimating the model can take a long time if we do a naive search forthe{z ,κ }Z values. i i i=1 Our strategy is based on the efficient search of productivity and vacancy cost levels to avoid these challenges. In particular, we use a heuristic that transforms the problem of picking {z ,κ }Z and comparing the resulting wage distribution to data to picking a i i i=1 data-consistentwagegridandchoosing{z ,κ }Z todividethewagegridbetweenfirms i i i=1 ofdifferentproductivities. Wesetthemiddleofthewagegridtobe2.5timestheunemploymentbenefit,b,which is the average replacement rate reported by the U.S. Department of Labor in 2005. The width of the wage grid (w ) is internally calibrated. For each guess of w , we divide wid wid thewagespaceintoZ equalpiecesandassociateeachpiecewithaparticularproductivity level. Let w ,w ,...,w be denote the edges of these grid pieces, where w and w are the 0 1 Z 0 Z lowerandtheupperboundsofthegrid,respectively. Wesetz suchthattheperiodpayoff i withhighybecomeszeroatw ,guaranteeingapositiveperiodpayoffforwagesinpiece i+2 i. Then,theproblemboilsdowntoappropriatelychoosingκlevels. Weset{κ }Z intwosteps. First,wesetκ = K(w ,Z,y ),i.e.,κ makesthevalue i i=1 Z max H Z of posting a vacancy at w zero when the probability of meeting a worker is 1. Second, max 26

foreachguessofκ ,otherκ aredeterminedaccordingto: 1 i (cid:18) z −z (cid:19)2 i 1 κ = κ +(κ −κ ) . i 1 Z 1 z −z Z 1 Hence, the problem of choosing {z ,κ }Z boils down to choosing two parameters: the i i i=1 width of the wage grid (w ) and the vacancy cost for the least productive firm (κ ). Yet, wid 1 ourheuristiccreatesawell-balancedproductivitydistributionforany{w ,κ }guess. wid 1 5.3 Calibration of the Remaining Parameters Weusethemethodofmomentstocalibratethesixremainingparameters{η,ν,κ ,w ,λ,σ } 1 wid y tomatchsixmoments. Thecalibrationusesallmomentstodisciplineallparameterssince general equilibrium effects through market tightness prevent isolating individual channels. Here, we provide intuition on how the used moments are helpful for particular parameters. Two parameters, ν and κ , jointly determine the firm productivity and the tightness 1 associated with each wage level. A larger κ (which increases all κ ) reduces the average 1 i tightness across markets, making both the J2J and UE transitions more difficult. A larger unemployed effort cost (ν) similarly makes UE transitions more difficult, but it has no directeffectontheJ2Jrates. Therefore,foragivenJ2Jrate,asmallerν impliesalargerUE rate. Hence,theJ2JandUErateshelpdistinguishν andκ . 1 Two parameters, w and λ, both impact the labor share in the same direction. As wid w grows, the wage distribution and the productivity distribution become more diswid persed, while as λ grows, job switches become more costly. Hence, for a given J2J rate, bothalargerw andalargerλmakeitmoredifficultforworkerstoreachfirmswithtop wid productivity levels where the labor share is significantly lower. The average wage gain fromjob-to-jobtransitionshelpsseparatelypindowntheseparameters. Ahigherλ,holding the J2J rate constant, induces the workers to climb the job ladder with smaller steps, 27

reducing the average wage gain. In contrast, w does not have a direct impact on the wid averagewagegainbeyondthegeneralequilibriumresponsethroughchangingtightness. Hence,thelaborshareandaveragewagegainhelppindown{w ,λ}. wid We use the J2J rate response to an unanticipated inflationary shock to pin down the search cost elasticity η. A larger η makes it difficult for a worker to increase her search effort when her existing situation deteriorates. We target the IV results we have from Section2tohelpdisciplinethesearchcostelasticity. Lastly, we use the variance of the HP-filtered log output to discipline the variance of theaggregateproductivityshockσ . y 5.4 Calibration Results and Validation The exogenously and endogenously calibrated parameters, together with the matched moments,aregiveninTables4and5. Table4: Exogenouslysetparameters Parameter Role Value Source b UnemployedEndowment 1.0 Normalized β DiscountFactor 0.951/12 Common δ SeparationRate 0.013 UnemploymentRate ρ AggShockPersistence 0.7881/3 USGDPPersistence y ϕ˜(z) OperatingCost Table3 Gouin-Bonenfant(2022) γ MatchingFunctionElasticity 0.4 EeckhoutandSepahsalari(2024) 28

Table5: InternallyCalibratedparameters Parameter Value Moment Data Model Source κ VacancyCost 0.1 UERate 27.7% 25.3% Fujitaetal.(2024) 1 ν EffortCostMultiplier 0.02 J2JRate 2.4% 2.3% Fujitaetal.(2024) λTransitionCost 90 J2JResponse 4.5% 5% Section2.1 ηEffortCostElasticity 4.5 LaborShare 0.6 0.59 Common w WageWidth 0.18 AvgWageGain 9% 9.7% Birincietal.(2022) wid y Var(AggShock) 0.035 Var(Output) 10−4 10−4 Authors’Calculation var Note: Allparametersinthetablearejointlycalibratedinthestochasticsteadystatetomatchall themoments. J2JResponsecorrespondstothepercentagechangeinJ2Jratesfollowinga1p.p. unanticipatedinflationaryshock. The calibrated parameters imply an expected cost of hiring a worker that ranges up to 10% of the average yearly wage in our simulated economy. The average job transition cost implied by our calibration is roughly equal to 15% of the average yearly wage. The average monthly effort cost is 2.8% of the average monthly wage for the employed and 11% for the unemployed. The calibrated wage grid leads to a wage dispersion where the topwageis40%largerthanthebottomwage. Themodeldoesagoodjobofmatchingtheempiricalproductivitydistribution,which is important for quantifying output responses. In particular, we validate the model using the moments of producer-level productivity distribution in the U.S. manufacturing sector reported by Syverson (2004). In our calibration, we don’t target any moments related to productivity, and we only indirectly target the wage distribution through the average wage gain in transitions. However, the calibrated model does a remarkable job of generating an empirically plausible productivity distribution. Table 6 summarizes the results. The simulated percentile ratios fall within the bounds of the estimates for plant- 29

andindustry-specificinputelasticities.18 Table6: ProductivityDistribution,Modelvs. Data Model Plant-Specific IndustrySpecific InputElasticities InputElasticities 90/10ratio 1.73 1.86 1.44 95/15ratio 1.86 2.41 1.71 50/10ratio 1.20 1.30 1.18 75/25ratio 1.21 1.32 1.18 Note: The ratios in the first column are calculated from the simulatedmodel. Theratiosinthesecondandthirdcolumns arecalculatedfromtheestimatesinTable1inSyverson(2004), assumingasymmetricdistribution. We also look at the implied persistence, variances, and cross-correlations between model aggregates at the business cycle frequency. In particular, we construct series for aggregate consumption, J2J and UE rates, unemployment rate, and number of vacancies. We take a 3-month moving average of these series before taking logs and applying the HPfiltertoisolatethecyclicalpart. Wecomparethemodel-impliedstatisticswithempirical statistics as documented in Moscarini and Postel-Vinay (2023). Table 7 presents the results. The model generates empirically plausible time series persistence for all aggregates. However, the model generates a lower variance for the labor market aggregates. The lack of variation in J2J, UE, and unemployment rates is due to the high elasticity of searchcosts,whichisnecessarytomatchtheempiricalresponseofJ2Jratestoinflationary shocks. Asaresult,theunemployeddonotrespondaggressivelytodecliningjobcreation byfirms. Anticipatingthis,thefirmsdonotrespondaggressivelytoaggregateshocks. Our model matches the signs of all cross-correlations and is broadly consistent with theempiricalmagnitudes. Onaverage,ourmodelgeneratesstrongercorrelationsamong 18AnindirectmethodtoverifytheproductivitydistributionisemployedbyMenzioandShi(2011),which reliesoncomparingthesimulatedandempiricdistributionsofjobtenures. Figure12inAppendixFshows thatourmodelbroadlydoesagoodjobbutunderstatestheaveragetenure. Intheabsenceofworker-level heterogeneity,ourmodelcannotaccountforasmallnumberofworkersbeingresponsibleforthemajority ofjob-to-jobtransitions. 30

Table7: BusinessCycleStatistics PanelA:VarianceandAuto-Correlation PanelB:Cross-Correlations Variance AC Data Model Data Model Data Model u UE v EE u UE v EE u 0.049 0.0001 0.99 0.98 UE 0.018 0.0001 0.97 0.96 -0.94 -0.93 v 0.032 0.0033 0.96 0.96 -0.85 0.8 -0.89 0.99 EE 0.003 0.002 0.89 0.97 -0.71 0.7 0.79 -0.86 0.97 0.99 C 0.0001 0.0003 0.89 0.96 -0.72 0.76 0.68 0.64 -0.82 0.96 0.98 0.99 Note:PanelAsummarizesvarianceandauto-correlationstatistics,whilePanelBshowscross-correlations betweenvariablesinthedataandthemodel. DatafromMoscariniandPostel-Vinay(2023). aggregates. Additional shocks would help reduce the correlation by creating wedges, at the cost of added complexity. The only force in our model that prevents perfect correlationsistheslowmovementoftheallocationofworkersacrossfirms. 6 Counterfactual Analyses In this section, we investigate the impact of unanticipated inflationary and deflationary shocks using our calibrated economy. For demonstrative purposes, we hit the economy with positive and negative inflation shocks of 2% and 4% and present the responses in Figures2and3. Let’sstartwithanalyzingtheresponseofoureconomytoa2%inflationshock(dotted line) in Figure 2. The first panel shows the average real wage declines by 1.6% (with the 20% automatic indexation) as firms’ endogenous response to offset the real wage decline is minimal. The low response is because the elasticity of quit probability to wages is not large enough to dissuade firms from enjoying lower wages.19 While the initial posted wage by the firm needs to be high enough to attract the worker to a market, the firm enjoys monopoly power over the worker after hiring. Hence, firm’s ideal wage becomes 19Ourestimatesindicatea20%increaseinquitratewitha10%declineinrealwages,whichisinlinewith the20-30%rangereportedusingalabexperimentbyNaiduandCarr(2022). 31

Wage Effort 1.04 1.1 -4% 2% -2% 4% 1.02 1.05 1 1 0.98 0.95 0.96 0.9 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Wage Searched z Searched 1.03 1.1 1.02 1.05 1.01 1 1 0.99 0.95 0.98 0.97 0.9 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Figure2: Agents’ResponsestoUnanticipatedInflationaryShocks Responsestounanticipatedpositiveandnegative2and4p.p. inflationaryshocks. Foreachplot,they-axis valuesindicatetheindexrelativetothebaselinevalue. smallerafterthematch. The workers respond by increasing their search effort by 5%. The average wage they search for declines by roughly 1%, yet the productivity of the firms in the markets they search decreases by about 3%. In other words, the inflationary shock triggers the quality channel. Figure3showshowtheaggregatesrespondtothechangingpolicies. TheJ2Jrate goesupby10%whiletheaverageproductivitygaininatransitiondecreasesbyabout18% on impact. We observe a decrease in output despite increasing job-to-job transition rates. The decrease in output reaches as high as 0.2% while the decrease in welfare (output net ofvacancy,effort,andtransitioncosts)reachesashighas0.9%. When the inflationary shock increases to 4% (dashed-dotted line), the effort response becomes gradually stronger, as well as the decline in the wages searched. The J2J rate increases around 20% with the 4% shock, yet the average productivity gain in transitions declinesbyalmost40%. Thedeclineingrossoutputreaches1%,andthedeclineinwelfare 32

J2J Rate z Gain 1.2 1.2 -4% 2% 1.1 -2% 4% 1.1 1 1 0.9 0.8 0.9 0.7 0.8 0.6 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Output Welfare 1.002 1.02 1 1.01 0.998 1 0.996 0.99 0.994 0.992 0.98 0.99 0.97 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Figure3: ResponsesforAggregateOutcomestoUnanticipatedInflationaryShocks Responsestounanticipatedpositiveandnegative2and4p.p. inflationaryshocks. Foreachplot,they-axis valuesindicatetheindexrelativetothebaselinevalue. exceeds2%. The impact of a deflationary -2% shock (solid line) is almost symmetric to the inflationary2%shock,withadeclineinthesearcheffortandanincreaseinthewagesearched. J2J rates go down by about 8%, yet the average productivity gain in each transition goes up byas muchas 10%. The quality channel dominates thequantity channel: outputgoes upby0.2%,andthewelfaregoesupby0.5%. Asthedeflationaryshockincreasesinmagnitude,however,theoutputresponsestarts to exhibit non-monotonicity. A -4% shock leads to a bigger decline in J2J rates and a bigger increase in productivity gains than a -2% shock. Yet the additional productivity gain it brings is not sufficient to make up for the additional decline it causes in J2J rates. As a result, the output roughly stays the same. The welfare increase is larger in the short run thanks to reduced vacancy creation and effort. Yet, the reduced allocative efficiency leadstosmallerwelfareinthemediumandlongrun. 33

J2J Rate z Gain Output 1.6 1.5 1.02 1.4 1 1 1.2 0.98 0.5 1 0.96 1m 0 0.8 0.94 1yr 3yrs 0.6 -0.5 0.92 -0.1 0 0.1 -0.1 0 0.1 -0.1 0 0.1 NPV of Output Gain NPV of Welfare Gain 1 1 0 0 -1 -1 -2 -3 -2 -4 -3 -5 -4 -6 -0.1 0 0.1 -0.1 0 0.1 Figure4: InflationaryShockMagnitudevsAggregateResponsesatFixedHorizons For each plot, the x-axis values indicate the shock magnitude, and the y-axis values indicate the index relative to the baseline value. The figures in the top row depict responses to unanticipated positive and negativeinflationaryshocksat1-month,1-year,and3-yearhorizons. Thefiguresinthebottomrowdepict thenetpresentvalueofoutputandwelfaregainsinunitsofthemonthlyaveragevaluesofeach. We investigate a broader set of shocks at fixed horizons in Figure 4. As expected, the J2J rate and the productivity gain from each transition are monotonic in the size of the inflationary shock. However, the output response is non-monotonic. The bottom two figures calculate the Net Present Value (NPV) of output and welfare gains in units of their monthly averages. The magnitude of the inflationary shock that maximizes the net present value of output and welfare is around -2% and leads to around a quarter of a month of output increase (2% of the annual output) in net present value terms. As we moveawayineitherdirection,weseesmallershort-runoutputincreasesand,eventually, short-runoutput(andwelfare)losses. 34

Wage Level z Gain (%) Markdown 0.112 0.52 0.298 0.1115 0.5 0.296 0.111 0.48 0.294 0.1105 0.46 0.292 0.11 0.44 0 20 40 60 0 20 40 60 0 20 40 60 Figure5: CoefficientofVariationResponsestoa4%InflationaryShock Lastly,sincethewagesofnewhiresareperfectlyflexible,jobswitchesundotheeffects of the one-time inflation shocks. Therefore, the model exhibits money neutrality in the long run, even though the effect of shocks can last for more than 5 years. Overall, the exercise confirms our theoretical analysis of the channels in Section 4. Quantitatively, we findaminimalrolefortheendogenousresponseoffirmstooffsetinflationaryshocks. 6.1 Distributional Implications of the Inflationary Shocks Now,weshiftourattentionfromaggregatevariablestoheterogeneityacrossworkersand matches. Figure5presentstheresponseofameasureofdispersion,thecoefficientofvariation,totheinflationaryshock. Werestrictattentiontoa4%shocktomakedistributional changeseasiertospot. The first panel in Figure 5 shows the response of the wage dispersion. On impact, wagedispersionincreasesas(1)inflationaryshockisiidacrossworkers,and(2)thehighproductivityfirms(whopayhigherwagesonaverage)respondbyincreasingwagesmore aggressively. However, the wage dispersion shrinks as workers change their search behavior: low-wageworkersreactmoreaggressivelytotheirinitialwagedeclineandclimb back to their original wages faster than high-wage workers. Our findings suggest an alternativechannelthatcanexplainthepost-COVID-19wagecompressiondocumentedby 35

Autor et al. (2023). The productivity-gain dispersion increases as the lowest-wage workers reduce the productivity they aim for the most.20 Lastly, the dispersion of the markdownsdecreasesonimpactashigh-wagefirms,onaverage,havehigherproductivityand markdownsanddoamoreaggressiveinflationcorrection. Effort and Tenure Wage and Tenure z and Tenure -0.3 0.4 0.42 0.38 0.41 -0.35 0.36 0.4 0.34 0.39 -0.4 0.32 0.38 0.3 -0.45 0.37 0 20 40 60 0 20 40 60 0 20 40 60 Figure6: CrossSectionalCorrelationResponsestoa4%InflationaryShock Figure6showshow,inthecross-section,tenurebecomesaweakerpredictorofworker and match characteristics after an inflationary shock. The workers with higher tenures tend to work for high-wage and productive jobs and exert less search effort in the steady state. These patterns weaken with an inflationary shock. Workers with high tenure become those stuck at the old wage levels. Workers with low tenure who have signed their contracts after the inflationary shock tend to have higher wages. This leads to hightenureworkersbeinglesssatisfiedwiththeirsituationthantheirlow-tenurecounterparts. Lastly, the inflationary shock initially strengthens the correlation between productivity and tenure as workers at low-productivity matches are the first to find another job and restart their tenure. However, after around 15 months, the productivity-tenure connection weakens as workers of all productivity levels complete their moves and reset their tenureclocks. 20Thisisduetothenatureoftheworkertransitionsinourmodels:whilethewagegainsarelargerforthe low-wageworkers,theproductivitygainsaresmaller. Thedecreasinglaborsharetowardsthetopprevents wagesfromincreasing1-1withproductivity. 36

Wage Effort 1.05 1.1 -5% 5% 0% 1.05 1 1 0.95 0.9 0.85 0.95 0.8 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Wage Searched z Searched 1.04 1.15 1.1 1.02 1.05 1 1 0.98 0.95 0.96 0.9 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Figure7: Agents’ResponsestoVariousRecessions Responsestoanaggregateproductivityshockaccompaniedwithandwithoutunanticipated5p.p. and-5 p.p. inflationaryshocks. Foreachplot,they-axisvaluesindicatetheindexrelativetothebaselinevalue. 6.2 Inflationary and Deflationary Recessions In this section, we simulate three counterfactual recessions. First, we simulate the impulse response to an aggregate productivity shock on its own, which corresponds to low y realizations for one year before the economy goes back to the high y realizations forever. In the second and the third counterfactuals, we couple the productivity shock with a 5% inflationary shock and a 5% deflationary shock, respectively.21 We document how the impact of the productivity shock on the labor market is attenuated or exacerbated by theunanticipatedpricemovements. Figure 7 shows how firms and workers respond to various shock bundles. In the absenceofaninflationaryshock(solidline),theaggregateproductivitydeclineleadstoa declineinsearcheffortsduetoworseningjobopportunities. Thisleadstoasmalldecline 21DuringtheCOVIDcrisis,therealizedinflationexceededthe1-yraheadSPFforecastby6%atitspeak. DuringtheGreatRecession,theSPFforecastexceededtherealizedinflationby4%atitspeak. SeeFigure 10inAppendixF. 37

J2J Rate z Gain 1.3 1.4 -5% 5% 1.2 0% 1.2 1.1 1 1 0.8 0.9 0.8 0.6 0.7 0.4 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Output Welfare 1.02 1.02 1.01 1 1 0.98 0.99 0.98 0.96 0.97 0.94 0.96 0.92 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Figure8: AggregateOutcomeswithVariousRecessions Responsestoanaggregateproductivityshockaccompaniedwithandwithoutunanticipated5p.p. and-5 p.p. inflationaryshocks. Foreachplot,they-axisvaluesindicatetheindexrelativetothebaselinevalue. in real wages as well. The average target wage and productivity go up as lower y forces low z firms out. As a result of the firm and worker responses, the J2J rate goes down, and the average productivity gain from transitions goes up, as shown in Figure 8. Both net output and welfare remain low for the duration of the recession, with a small postrecession bump thanks to the cleansing effects of the recession through the selection of higherproductivityfirms. The dotted line presents the results when the same aggregate productivity shock is accompanied by an unanticipated inflationary shock. The inflation leads to a decline in the targeted wage, which more than offsets the decline in the effort. Furthermore, inflationlargelyoffsetstheincreaseinselectionbroughtaboutbythedeclineinaggregate productivity, leading to a decrease in the average productivity of the firms targeted. As a result, the J2J rate increases instead of decreasing, and the average productivity gain in transitions decreases instead of increasing. The decline in net output and welfare for the durationoftherecessionissharper,andrecoverytakeslonger. 38

Lastly, the dashed line presents the results from a combination of the aggregate productivity shock and an unanticipated deflationary shock. The deflation exacerbates the decline in effort and the increase in the wage and productivity levels that workers target. These lead to a larger J2J rate decline but also a larger average productivity gain in transitions. Theincreaseinproductivitygainisrelativelysmall: boththeinitialdeclinein output is sharper, and the post-recession levels are lower. However, the welfare is higher throughouttherecessionepisodethankstosmallervacancyandeffortcosts. We abstract from some key characteristics of past recessions, yet our analysis sheds light on some puzzling patterns of past recessions. The Great Depression led to theories linking deflation and recession (e.g., Tobin (1972), Tobin (1975)). However, Atkeson and Kehoe (2004) analyzes 17 countries over 100 years and finds no correlation between the changeinpricelevelsandoutputgrowth. Wearguedeflationimprovesworkerallocation, which can offset its other recessionary effects. Furthermore, while the J2J rate declined and remained low after the deflationary Great Recession, it recovered quickly after the inflationaryCOVID-19recession,consistentwithourexercise. 7 Conclusion This paper explores how inflation impacts allocative efficiency by changing the workers’ job search behavior. We start by providing reduced-form evidence supporting a causal link between inflationary shocks and a higher job-to-job transition rate. First, we find that inflation shocks precede shocks to job-to-job transition rates: inflation lags are good predictors of job-to-job transitions, while the opposite is not true. Second, using monetary policy and oil price shocks as instruments, we show a causal link from unexpected inflationtojob-to-jobtransitionrates. Third,usingsurveydata,weshowthatindividuals with higher than average inflation expectations are (1) more likely to search and (2) exert moreeffortandgetbetterresultsconditionalonsearching. 39

We proceed by constructing a model that captures two primary channels through which unexpected inflation impacts worker behavior. Higher-than-expected inflation rates increase the benefit of receiving a new offer in a setting with rigid wages. Hence, workersrespondtoinflationaryshocksbysearchingmoreintensivelyandtargetinglowerwagejobsthatareeasiertoattain. Asaresult,morejob-to-jobtransitionsoccur. However, because workers are less selective than before, each transition leads to a smaller boost in aggregateproductivity. Hence,laborallocationacrossfirmsmightimproveordeteriorate intheshortrun. We estimate the model to quantify the regions of monetary policy shock magnitudes thatleadtoapositiveversusanegativeoutputresponseintheshortrun. Themodelconfirmsthenon-monotonicresponseofoutputtoinflationaryshocksintheshortrun: small recessionary shocks lead to short-run output increases, while others lead to short-run output declines. A recession with a large inflationary shock, similar to the 2020 recession,wouldbringasharperoutputdeclineeventhoughjob-to-jobtransitionrateswould be high. A recession with a large deflationary shock, similar to the 2008 crisis, would recovermuchfaster,eventhoughthereallocationisslow. The proposed mechanism has important implications. Most importantly, it provides a novel channel explaining why some recessions are associated with a more pronounced ‘cleansing’ effect than others: the size of the unexpected price movement affects both the speedandtheeffectivenessofjobreallocationduringrecessions. Second,itexplainshow output response may be non-monotonic in the size of the inflation shock. Thus, it provides a bridge between seemingly disparate estimates of the literature on the real effects of monetary policy shocks.22 Third, it provides a novel mechanism for how monetary policy can affect the real economy in the short run. The monetary authority can improve labor allocation in the short run through monetary policy shocks and influence the experienceofarecession. 22SeeWolf(2020)foranoverviewofthesefindings. 40

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Appendices A Proof of Proposition 1 Proof. Notice that both F(y,w−) and A(y,w−) are bounded and continuous in w− since theirBellmanequationsmapthesetofboundedandcontinuousfunctionsintoitself. This follows from the theorem of the maximum as (1) the choice sets are compact-valued and continuous,23 and (2) the objective functions in the maximization problems are bounded andcontinuousifthevaluefunctionsareboundedandcontinuous. Tosimplifytheproof, we will assume the value functions are also twice differentiable with respect to w−, even thoughthemainideawouldgothroughwithnon-differentiablevaluefunctions. w∗(y,w−) behaves differently based on whether the constraint binds or not. In the regionswheretheconstraintisbinding,w∗ istriviallyincreasinginw− since ∂w∗ = 1 > 0. ∂w− Themoreinterestingcaseiswhentheconstraintisn’tbinding,wherew∗satisfiesthefirm’s first-ordercondition: ∂F(y′,w∗) −ξ(w∗ −w−)τ−1 = 0. ∂w∗ Differentiatingbothsideswithrespecttow− andrearrangingtermswouldgive ∂w∗ ξ(τ −1)(w∗ −w−)τ−2 = ∂w− −∂2F(y′,w∗) +ξ(τ −1)(w∗ −w−)τ−2 ∂(w∗)2 As ξ grows, the term from the menu cost grows without bound for τ < 2 and eventuallydominatesthetermwithpartialderivativeasthelatterwoulddeclineinmagnitude.24 Hence,forasufficientlylargeξ, ∂w∗ becomespositive. ∂w− V∗(y,w−)satisfiestheworker’sfirst-ordercondition: (V∗ −A(w∗(w−)))p′(V∗)+p(V∗) = 0. 23Withoutlossofgenerality,wecanboundthewagechoiceofthefirm: w∗(y,w−)∈[w−,max {yi}]. i 24As an extreme version of this idea, as ξ approaches infinity, ∂w∗ would approach one since the con- ∂w− straintwouldbindeverywhere. 45

Differentiatingbothsideswithrespecttow− andrearrangingtermswouldgive ∂V∗ p′(V∗) ∂A ∂w∗ = ∂w∗∂w− . ∂w− 2p′(V∗)+(V∗ −A(y′,w∗(y′,w−)))p′′(V∗) By assumption, p is strictly decreasing in V. It is straightforward to show A is strictly increasinginitssecondargument. Thefirstpartoftheproofestablishedthatw∗ isstrictly increasing in w−. Hence, the numerator is always negative. Furthermore, for an initial wagew ,V∗ −A(y′,w∗(y′,w−))isboundedabovebyV ¯ −w /(1−β). Then, ∂V∗ > 0iffor 0 0 ∂w− allV ∈ V, d2p/dV2 2 > − . dp/dV V ¯ −w /(1−β) 0 B Data Sources B.1 Monthly Data Job-to-JobTransitions: InsectionsC.1and2.1,weusetheseriesmadeavailablebyFujita etal.(2024). Itcorrectsthemonthlyjob-to-jobtransitionratescomputedfromtheCurrent PopulationSurvey(CPS)forsurveyattrition. Inflation: We use Consumer Price Index (CPI) inflation from the Bureau of Labor Statistics. As an alternative measure of inflation, we also use Personal Consumption Expenditures (PCE) inflation from the Bureau of Economic Analysis (BEA). Both measures describeyear-over-yearinflation,whichisreportedmonthly. Inflation Forecasts: To construct the measures of inflation shocks, we use quarterly data from the Survey of Professional Forecasters (SPF) by the Philadelphia Fed. Professional forecasters are surveyed quarterly and asked to predict various statistics of the 46

economy, including inflation. We use the one-year-ahead inflation forecast (INFCPI1YR) andtakethelinearinterpolationofquarterlyforecaststoconstructmonthlyforecasts. We thentakethedifferencebetweenrealizedinflationandthecorrespondingforecasttoconstruct our shock measure. For robustness, we also use inflation expectations from the Survey of Consumers from the University of Michigan. These are the median expected pricechangesforthenext12months. Monetary Policy Shocks: In our instrumental variable analysis in section 2.1, we use various monetary policy shock estimates as instruments for inflation. The first estimate we use is constructed by Romer and Romer (2004) and extended by Wieland and Yang (2020). They first obtain a series of intended federal funds rate changes from meetings of the Federal Open Market Committee (FOMC) and the Weekly Report of the Manager of Open Market Operations. They then regress these intended changes on the Federal Reserve’s internal forecasts of inflation to account for changes to monetary policy in anticipation of future economic developments. The residuals from this regression should reflect idiosyncratic changes in monetary policy. This series is available from January 1969toDecember2007. The second measure is from Sims and Zha (2006), who use a regime-switching structural VAR model. In particular, they use the residuals for the federal funds rate series to estimate monetary policy shocks. This series is available monthly from January 1959 to March2003. The remaining estimates all utilize high-frequency financial data to measure unexpected changes in monetary policy. The third estimate is from Barakchian and Crowe (2013). TheymeasurethedifferenceinprivatesectorbeliefsabouttheFed’spolicystance before and after FOMC meetings, implied by the federal funds futures contracts, as a measure of monetary policy shocks. This series is available from December 1988 to June 2008. The fourth measure is from Gertler and Karadi (2015) and uses futures rate surprises on FOMC dates. They study one-month and three-month Fed Funds future rates, 47

aswellassix-month,nine-month,andone-yearaheadfuturesonthree-monthEurodollar deposits. It is available monthly from November 1988 through June 2012. The fifth and sixth measures are from Nakamura and Steinsson (2018) and similarly use federal funds andEurodollarfuturestoestimatemonetarypolicyshocksbutwithamoreflexiblefunctional form. The first series is available from January 1995 to March 2014. The second excludes unscheduled meetings and those around the height of the Financial Crisis and is available from February 2000 to September 2019. The seventh measure is from Bauer etal.(2021),whoagainuseEurodollarfuturesaroundFOMCmeetings. Unliketheprevious papers, they isolate the part of the monetary policy surprises that are not correlated witheconomicandfinancialdata. ThisseriesisavailablefromJanuary1994toSeptember 2020. The eighth and final measure is from Bauer and Swanson (2023). They extend the monetary policy events to include the Federal Reserve Chair’s speeches. This series is availablefromJanuary1988toDecember2023. Oil Shocks: We also use oil price shocks from Ka¨nzig (2021) as an instrument in section 2.1. He constructs oil price shocks by observing the difference in oil futures prices surroundingOPECannouncements. TheseshocksareavailablefromJanuary1974toDecember2017. Controls: Weuseunemployment-to-employmenttransitionrates(UE)andtheunemployment rate (U) as controls in the regressions in Appendix F. The UE rates are from Fujitaetal.(2024). TheunemploymentrateseriesisfromtheU.S.BureauofLaborStatistics(LNS14000000). B.2 Quarterly Data Job-to-Job Transitions: In our state-level analysis in Appendix C.2, we use job-to-job transitionmeasuresfromtheLongitudinalEmployerHouseholdDynamics(LEHD)data by the U.S. Census. They provide the number of hires to (J2JHire) and separations from 48

(J2JSep)jobsineachstatethroughjob-to-jobtransitions. Wetransformthesenumbersinto ratesusingthestate’slaborforce. Theseseriesareavailablefrom2000Q2to2022Q1. Inflation: Forourmeasureofstate-levelinflationrates,weusetheestimatesbyHazell et al. (2022). They construct quarterly inflation measures for 34 states from 1978 to 2017. We focus on annual inflation (pi in the dataset), but we also repeat our analysis using annual inflation in the non-tradeable and annual inflation in the tradeable sector (pi.nt andpi.t,respectively). Inflation Expectations: We use the quarterly inflation expectations from SPF. We assume inflation expectations are uniform across states because state-level inflation expectationsareunavailable. Controls: We use the state unemployment to employment transition rate (NEHire) from the LEHD as a control in our state-level regressions. We construct this measure by dividing the number of individuals transitioning to employment from unemployment by the state’s labor force. We also use state-level unemployment rates from Local Area Unemployment Statistics (LAUS) from the BLS as a control variable. These are available monthlyfromJanuary2000toApril2022. Toconvertthedatafrommonthlytoquarterly, we take the value from the first month of each quarter. Statewide labor force data also comefromLAUS. B.3 Annual Data Job-to-Job Transitions: In our country-level analysis in Appendix C.3, we use yearly job-to-job transition measures from Donovan et al. (2023). They construct two variables: wage-to-wage transitions (WW) and employment-to-employment (EE) transitions. The formerconsidersonlytransitionsfromwageemploymenttowageemployment,whereas thelatteralsoconsiderstransitionstoandfromself-employment. Thedataspans41countriesfrom1994to2020. 49

InflationSurprise: Toconstructourmeasureofinflationshocks,weuseinflationforecast data from the IMF (Fall 1-yr ahead forecasts) and the OECD (Total, Annual growth rate(%)). Inflationshocksaredefinedasthedifferencebetweentherealizedinflationand itsforecast. TheIMF forecastsspan 200countriesfrom 1990to 2024. Werestrict attentiontocountries in upper-middle-income and high-income groups and country-year pairs with less than 20% inflation and more than -10% inflation. The former is to minimize informality,andthelatteristominimizeautomaticwageindexation,whichwouldcounteractthe mechanismswefocusoninthispaper. We use the World Bank forecasts for robustness. They are annual and span 45 countries from 1961 to 2023. We supplement it with annual realized CPI inflation from the WorldBanktoconstructtheinflationsurprise. B.4 Job Search Survey Data Inflation Expectations: The respondents are asked what they expect the inflation to be over the next 12 months (question Q8v2part2 in the survey). We use the response to this questionasourmeasureofinflationexpectations. For robustness checks, we use expectations on other macroeconomic aggregates reported by the respondents. In particular, we use binary responses to questions asking whethertherespondentexpectstheunemploymentrate,theaverageinterestrateonsavingaccounts,andtheaveragestockprices(questionsQ4new,Q5new,andQ6new,respectively)tobehigherthanthepreviousyear. Job Search Activities: We use one job search activity question from the Labor Survey Supplement: ”Have you done anything in the last four weeks to look for new work?” (question L6). We code a positive response as a one and a no as a zero. The remainder 50

of our job search variables come from the annual Job Search Supplement. These are the numberofhoursspentsearchingforworkinthelastfourweeks(questionJS7),thenumber of methods used to look for a job in the last four weeks (constructed from question JS6), and the number of applications sent to potential employers in the last four weeks (questionJS14). Job Search Outcomes: All but one job search outcome come from the Job Search SupplementoftheSCE.Thesearethenumberofpotentialemployersthathavecontactedthe individual (question JS15), the number of job interviews attended (question JS18b), and the number of offers received (question JS19) in the last four weeks. Lastly, we get the number of offers received in the last four months (question NL1) from the Labor Survey supplement. TenureCalculations: Therearetwopotentialwaystoidentifyjobswitches: (1)through changesinreportedprimaryjobstartdatesand(2)throughthebinaryresponseofwhether the respondent is still working for the same employer as the previous month. We found the latter to be more reliable: in about half of the cases where the start date changed, yet the worker claimed they worked for the same main employer, the change in start dates was illogical: the worker would claim an earlier start date at a later survey. Using the binaryresponse,weapplyacorrectiontothereportedstartdates. Thiscorrectionmatters for calculating job tenure, which is a control variable. Of the 12570 eligible observations, wecouldestablish449asassociatedwithswitchingjobssincetheprevioussurvey,11888 as no job switches, and 233 as indeterminate. We discard the indeterminate observations inexercisesthatrequiretenureinformation. Control Variables: We use several control variables from the SCE in our analysis. These are the natural logarithms of age (Q32 in the survey), tenure (Q37), and annual earnings (Q47), dummies for sex (Q33) and marital status (Q38), five dummies for race (Q35), four dummies for education (Q36), and fixed effects for the state (D5). Other controls from the Labor Survey supplement are dummies for job start-year (L1), and two- 51

digitindustries(LMtypeandLmind). C Additional Empirical Analyses C.1 Predictive Regressions In this exercise, we ask whether the shocks to the J2J rate precede the shocks to inflation or follow them. For J2J and unemployment-to-employment (UE) transition rates, we use the series by Fujita et al. (2024) that runs from September 1995 to June 2022.25 We utilize three measures of inflation: (1) over-the-year changes in the Consumer Price Index (CPI), (2) inflation expectations from the Survey of Professional Forecasters, and (3) the ‘inflation surprise’, i.e., the discrepancy between the forecasted and the realized inflation for a twelve-month period. At time t, this is the accumulated unexpected price moves sincet−12. Weseasonallyadjust and HPfilterallvariableswithasmoothingparameter 1600×34. In our main specification, we run a VAR(2) with a measure of inflation and J2J transitionrate: y = β y +β x +β y +β x +ϵ (14) t y,1 t−1 x,1 t−1 y,2 t−12 x,2 t−12 t where y : [Infl ,J2J ] and x represents additional controls. Table 8 presents the ret t t sultsfromaVAR(2)exercisewithone-monthandone-yearlags. Theone-monthlagofall three inflation-related measures has a significant positive coefficient for predicting subsequent J2J transition rates. On the other hand, the coefficients for J2J transition rates for predicting inflation-related variables are insignificant. Although the predictive relationship is suggestive, the mechanism might be through the demand side, i.e., the inflation mightbechangingthehiringincentivesoffirmsratherthanthesearchbehaviorofwork- 25SeeAppendixBfordetailsonthedatasourcesusedthroughouttheempiricalanalysis. 52

ers. We add UE rates as a control for demand side channels. Table 12 in Appendix F showsthattheresultsaresimilar.26 Table8: VAR(2)Estimates J2JRate CPIInfl J2JRate SPFInflSurprise J2JRate SPF1-yrAheadInfl (1) (2) (3) (4) (5) (6) Infl 0.03∗∗∗ 0.92∗∗∗ 0.03∗∗∗ 0.92∗∗∗ 0.20∗∗∗ 0.97∗∗∗ t−1 (0.01) (0.03) (0.01) (0.03) (0.04) (0.02) Infl 0.00 −0.13∗∗∗ 0.01 −0.13∗∗ −0.01 −0.05∗ t−12 (0.01) (0.05) (0.01) (0.05) (0.04) (0.03) J2J 0.22∗∗∗ 0.04 0.22∗∗∗ 0.01 0.18∗∗∗ 0.00 t−1 (0.07) (0.15) (0.07) (0.17) (0.06) (0.03) J2J 0.03 −0.07 0.04 −0.15 −0.01 −0.03 t−12 (0.04) (0.14) (0.04) (0.15) (0.05) (0.03) Obs 319 319 319 319 319 319 Adj. R2 0.13 0.88 0.13 0.88 0.16 0.93 Notes: InflisCPIyear-to-yearinflationincolumns(1)and(2),inflationsurprisefromSPFforecasts in columns (3) and (4), and SPF forecasts in columns (5) and (6). Columns (1), (3), and (5) have the J2Jrateattimetwhiletheothershavetheinflationmeasuresasthedependentvariable. Allvariables areseasonallyadjustedandHP-filtered. ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Source: Fujitaetal.(2024);U.S. BureauofLaborStatistics,CPI;authors’calculations. C.2 Quarterly Analysis, State Level Here, we utilize the Longitudinal Employer Household Dynamics (LEHD) data by the US Census Bureau, which provides J2J rates in quarterly frequency at the state level. For inflation, we use the series by Hazell et al. (2022), which constructs quarterly inflation measures for 34 states from 1978 to 2017. State-level inflation forecasts are unavailable; hence, we assume inflation expectations are uniform across states. We seasonally adjust andHPfilterallvariableswithasmoothingparameterof1600. 26The results are also robust to excluding the COVID period, adding a third lag, using Personal Consumption Expenditures (PCE) Deflator or core PCE Deflator (excluding food and energy) for price index insteadofCPI,andusingMichiganSurveyofConsumers(MSC)insteadofSPFforinflationforecasts. See Tables12,13,14and15inAppendixF. 53

Inourmainspecification,werunafixed-effectsregressionwithameasureofinflation andJ2Jtransitionrate: y = β x +β z +γ +η +ϵ (15) it x i,t−1 z i,t−1 i t it where i and t represent state and quarter, y and x are the J2J rate and SPF inflation surprise,γ andη arestateandquarterfixedeffects,andz representsadditionalcontrols. i t The results are in Table 9. Again, a positive inflation surprise predicts higher inflation in the next quarter across various specifications. Unlike the VAR analysis with monthly aggregate data, higher job-to-job transition rates also predict larger inflation surprises in thenextquarter. Table9: State-LevelEstimates J2J Infl t t (1) (2) (3) (4) (5) (6) (7) (8) Infl 0.069∗∗∗ 0.014∗∗ 0.035∗∗∗ 0.014∗∗ t−1 (0.007) (0.006) (0.007) (0.006) NE 0.625∗∗∗ 0.141∗∗∗ 0.637∗∗∗ −0.196∗∗∗ t−1 (0.097) (0.038) (0.177) (0.051) J2J 0.645∗∗∗ 0.411∗ 0.324∗∗∗ 0.549∗∗ t−1 (0.067) (0.225) (0.106) (0.228) State-QuarterFE No Yes No Yes No Yes No Yes Obs 2,162 2,162 2,162 2,162 2,129 2,129 2,129 2,129 Notes: The measure used for Infl is inflation surprise from SPF forecasts. Columns (1)-(4) have the job-to-job transition rate at time t as the dependent variable, while the others have the inflation measures at time t. All variables are seasonally adjusted and HP-filtered. The standard errors are clustered at the state level. ∗p<0.1; ∗∗p<0.05;∗∗∗p<0.01. Source: Hazelletal.(2022);U.S.CensusBureau,LEHD;authors’calculations. C.3 Yearly Analysis, Country Level Here,weutilizetheyearlycross-countryJ2JdatafromDonovanetal.(2023)kindlymade availabletousbytheauthors. Thedataisfromapanelof41countriesfrom1994to2020. 54

We focus on wage employment to wage employment (WW) transitions. We supplement thetransitionrateswithCPIinflationdatafromtheWorldBankandinflationforecastdata from the IMF. In our main specification, we run a fixed-effects regression with a measure ofinflationandWWtransitionrate: y = β x +γ +η +ϵ (16) it x i,t i t it where i and t represent country and year, y is a measure of J2J rate, x is the inflation surprise,andγ andη arecountryandyearfixedeffects. TheresultsareinTable10. There i t isapositivecorrelationbetweeninflationsurpriseandboththeWWrates. Controllingfor thecountryandyearfixedeffectsdoesnotchangethesignofthecorrelation,yetreduces the magnitude. Table 11 shows that using OECD forecasts leads to qualitatively similar conclusions. Table10: Country-LevelEstimates,IMFForecasts WW (1) (2) (3) (4) InflS 0.066∗∗∗ 0.067∗∗∗ 0.039∗∗ 0.039∗∗ t (0.016) (0.016) (0.019) (0.019) CountryFE No Yes No Yes YearFE No No Yes Yes Observations 450 450 450 450 Notes: The measure used for Infl is constructed using the inflation surprise from IMF forecasts. The WW transition rate at time t is the dependentvariable.AllvariablesareHP-filtered.Thestandarderrors areclusteredatthecountrylevel. ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 D Evidence on the Extent of Wage Indexation Explicit measures of what fraction of wage contracts are indexed to inflation are unavailable for the US economy. Measures that are based on the actual contract terms are re- 55

Table11: Country-LevelEstimates,OECDForecasts WW (1) (2) (3) (4) InflS 0.048∗∗∗ 0.049∗∗∗ 0.019 0.019∗ t (0.011) (0.011) (0.012) (0.012) CountryFE No Yes No Yes YearFE No No Yes Yes Obs 361 361 361 361 Notes: The measure used for Infl is constructed using the inflation surprise from OECD forecasts. WW transition rate at time t isthedependentvariable. AllvariablesareHP-filtered. Thestandard errors are clustered at the country level. ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01 stricted to collective agreements, which vary in coverage over the years and do not represent a random sample of workers. Measures based on changes in the nominal wages confound several other factors affecting the wage process. However, even the most conservative estimates imply a very low level of wage indexation (less than 25%) in developedcountries. Here,wediscusstheimplicationsofpriorresearchontheextentofwage indexation. D.1 Evidence Based on Contract Terms Thepapershereinvestigatetheprevalenceof‘cost-of-livingadjustment’(COLA)termsin contracts. Card (1990) looks at the universe of manufacturing union contracts in Canada (withmorethan500employees)signedbetween1968and1983. Hefindsthat26%ofthem havean‘escalationclause’whiletheexplicitindexationisveryrare. Thefractionwith‘escalation clause’ peaks at 65% in a period where the inflation is over 10%. Ragan Jr and Bratsberg (2000) use BLS data on collective bargaining settlements. They document that even though 61% of the settlements had COLA provisions back in 1976, it has fallen all thewaydownto22%in1996,thelastyearthedataisavailable. Eventhoughthesenumbers may seem large, the COLA provisions are known to be much less prevalent among 56

non-unionworkers. Furthermore,withthedeclineinunionization,collectiveagreements coverasmallerfractionofthelaborforceineithercountrytoday. Druantetal.(2012)utilize a firm-level survey conducted in 17 European countries regarding wage adjustment practices. Across 15,000 firms from all industries, they document that only 11.5 % of the firmsemployanyformalindexationclausewhileonly10.9%reportanyinformalinflation considerationsinwagesetting. Thesurveyalsoasksaboutthefrequencyofwageadjustments. This gives us a back-of-the-envelope mapping between the degree of indexation andthefrequencyofwageadjustments. Wageadjustmentshappeneitheryearlyormore frequently for 74.4% of the firms. Thus, even when firms adjust wages frequently, this doesnotimplyanimplicitwageindexation. D.2 Evidence Based on Wage Movements McLaughlin (1994), using PSID data, finds that the effect of unanticipated inflation on nominal wage growth is consistent with 42% indexation between 1970 and 1986. Hofmannetal.(2012),usingaDSGEmodel,inferstheextentofwageindexationintheeconomy from the time variation in U.S. wage dynamics. They estimate a degree of wage indexation to be 0.17 in 2000, compared to 0.91 in 1974, which is consistent with the time pathofCOLAcoverageincollectivebargainingagreements. Morerecently,Grigsbyetal. (2021), using data from a payroll processing company in the U.S., finds that approximately36%ofjobstayersexperiencenonominalwagechangesinaone-yearperiod. Consistentwiththelackofwageindexation,workersdonotexpecttheirwageincome to catch up with price inflation. Using the U.S. and Canadian survey data, respectively, Hajdini et al. (2023) and Jain et al. (2022) report low levels of pass-through (ranging from 0.1to0.2)frompriceinflationexpectationstoexpectationsoftheirownwagegrowth. 57

E Solution Algorithm Wediscretizethedistributionofz with50gridpoints,y withtwogridpoints,andw with 100 grid points. Our algorithm consists of two main stages. The first stage solves for the policy functions of the firms and the employed, while the second stage solves for the policyfunctionsoftheunemployed. WestartthefirststagewithanarbitraryU (y).27 Then,weapplyanalgorithmbasedon 0 backwardinductiontosolvetheemployedandthefirm’sproblems. Weusethefollowing idea: if we know H (w ,.,.),K(w ,.,.) and θ(w ,.,.) ∀j > i for some i, then we can solve 0 j j j forthevalueandthepolicyfunctionsforw sinceworkerswillneversearchforasmaller i wage given the prohibitive transition cost. Let us start with the highest wage on the grid,w¯. H (w¯,.,.)andK(w¯,.,.)aresimplythepresentvalueoftheperiodpayoffwithan 0 exogenousdiscountrate. Thisisbecause,inamatchwherew¯ isagreedupon,theworker will not leave for another firm (i.e., p¯(w¯,.,.) = 0). Using the free entry condition, we can alsopindownθ(w¯,.,.). Then,forwageeachw ,wedothefollowing: i 1. Startwithaguessfortheprobabilitythataworkerwillleaveforanotherjob: p¯g(w ,.,.). i 2. SolveforK(w ,.,.)andw∗(w ,.,.)usingthefirm’sproblem. i i 3. SolveforH (w ,.,.),m(H (w ,.,.),.),e(H (w ,.,.),.)givenw∗(w ,.,.)usingvaluefunc- 0 i 0 i 0 i i tioniterationontheworker’sproblem. 4. Computep¯(w ,.,.)impliedbym(H (w ,.,.),.),e(H (w ,.,.),.)andcomparewithp¯g(w ,.,.). i 0 i 0 i i 5. Iftheimpliedvalueisnotcloseenoughtotheguess,startagainwithanotherguess. If they are close enough, then, set p¯(w ,.,.) = p¯g(w ,.,.) and compute θ(w ,.,.) using i i i K(w ,.,.)inthefreeentrycondition. i 27AlthoughU (y)linearlyscalestheemployedvaluefunctionH(),itisirrelevanttothepolicyfunctions 0 oftheemployedandthefirm. 58

In the second stage, we start with an initial guess Ug(y), and use value function itera- 1 tion. Inparticular,atsteps,wedothefollowing: 1. Solve for H (w ,.,.),m(H (w ,.,.),.), and e(H (w ,.,.),.) given Ug(.) using the ems i s i s i s ployedproblem. 2. Solveform(Ug(.),.),e(Ug(.),.)usingtheunemployedproblem. s s 3. ComputetheU (.)givenm(Ug(.),.),e(Ug(.),.),andH (w ,.,.). s s s s i 4. If U (.) is not close enough to the guess, then set Ug (.) = U (.) and start again. If s s+1 s theyarecloseenough,stop. F Additional Figures and Tables 59

Table12: VARX(2)Estimates J2JRate CPIInfl J2JRate SPFInflSurprise J2JRate SPF1-yrAheadInfl (1) (2) (3) (4) (5) (6) Infl 0.03∗∗∗ 0.91∗∗∗ 0.03∗∗∗ 0.91∗∗∗ 0.20∗∗∗ 0.97∗∗∗ t−1 (0.01) (0.04) (0.01) (0.03) (0.04) (0.02) Infl −0.00 −0.14∗∗∗ 0.00 −0.13∗∗∗ −0.05 −0.05∗ t−12 (0.01) (0.04) (0.01) (0.05) (0.04) (0.03) J2J 0.17∗ −0.07 0.17∗ −0.07 0.14 −0.00 t−1 (0.10) (0.16) (0.10) (0.17) (0.09) (0.03) J2J −0.04 −0.16 −0.04 −0.21 −0.07 −0.03 t−12 (0.06) (0.17) (0.06) (0.18) (0.06) (0.04) UE 0.00 0.02∗ 0.00 0.01 0.00 0.00 t−1 (0.01) (0.01) (0.01) (0.01) (0.01) (0.00) UE 0.01∗ 0.01 0.01∗ 0.00 0.01∗ −0.00 t−12 (0.00) (0.01) (0.01) (0.01) (0.01) (0.00) Obs 319 319 319 319 319 319 Adj. R2 0.15 0.88 0.15 0.88 0.18 0.93 Notes: ThemeasureusedforInfl isCPIyear-to-yearinflationincolumns(1)and(2), inflationsurprisefromSPFforecastsincolumns(3)and(4),andSPFforecastsincolumns(5)and(6). Columns(1), (3),and(5)havetheJ2Jrateattimetwhiletheothershavetheinflationmeasuresattimetasthedependentvariable. AllvariablesareseasonallyadjustedandHP-filtered. ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Source: Fujitaetal.(2024);U.S.BureauofLaborStatistics,CPI;authors’calculations. 60

Table13: VAR(2)EstimateswithDummiesfortheCOVIDPeriod J2JRate CPIInfl J2JRate SPFInflSurprise J2JRate SPF1-yrAheadInfl (1) (2) (3) (4) (5) (6) Infl 0.02∗∗∗ 0.89∗∗∗ 0.02∗∗∗ 0.90∗∗∗ 0.20∗∗∗ 0.97∗∗∗ t−1 (0.01) (0.04) (0.01) (0.04) (0.04) (0.02) Infl 0.01 −0.12∗ 0.01 −0.10∗ 0.00 −0.03 t−12 (0.01) (0.06) (0.01) (0.06) (0.04) (0.02) COVID −0.00 −0.00∗ −0.00 −0.00∗ −0.00 −0.00∗∗ (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) J2J 0.18∗∗∗ −0.10 0.18∗∗∗ −0.15 0.14∗∗ −0.03 t−1 (0.06) (0.17) (0.06) (0.19) (0.06) (0.03) J2J 0.05 0.02 0.06 −0.03 0.01 −0.04 t−12 (0.05) (0.14) (0.05) (0.15) (0.06) (0.03) Infl ×COVID 0.02 0.06 0.02 0.07 −0.05 −0.04 t−1 (0.02) (0.07) (0.02) (0.07) (0.07) (0.04) Infl ×COVID −0.02 −0.09 −0.02 −0.11 −0.10 −0.18∗∗∗ t−12 (0.02) (0.07) (0.01) (0.07) (0.11) (0.06) J2J ×COVID 0.11 0.46 0.12 0.48 0.21 0.17∗ t−1 (0.18) (0.60) (0.18) (0.67) (0.18) (0.09) J2J ×COVID −0.04 −0.09 −0.04 −0.24 −0.04 0.15 t−12 (0.14) (0.42) (0.14) (0.45) (0.17) (0.10) Obs 319 319 319 319 319 319 Adj. R2 0.13 0.89 0.13 0.89 0.16 0.93 Notes: WedesignatetheCOVIDperiodasMarch2020onward. ThemeasureusedforInflisCPIyear-to-year inflation in columns (1) and (2), inflation surprise from SPF forecasts in columns (3) and (4), and SPF forecasts in columns (5) and (6). Columns (1), (3), and (5) have the J2J rate at time t while the others have the inflation measures at time t as the dependent variable. All variables are seasonally adjusted and HP-filtered. ∗p<0.1; ∗∗p<0.05;∗∗∗p<0.01. Source: Fujitaetal.(2024);U.S.BureauofLaborStatistics,CPI;authors’calculations. 61

Table14: VAR(3)Estimates J2JRate CPIInfl J2JRate SPFInflSurprise J2JRate SPF1-yrAheadInfl (1) (2) (3) (4) (5) (6) Infl 0.03∗∗∗ 0.90∗∗∗ 0.03∗∗∗ 0.89∗∗∗ 0.22∗∗∗ 0.96∗∗∗ t−1 (0.01) (0.04) (0.01) (0.03) (0.04) (0.02) Infl 0.00 −0.15∗∗∗ 0.01 −0.15∗∗∗ −0.01 −0.04 t−12 (0.01) (0.04) (0.01) (0.04) (0.04) (0.02) Infl −0.00 −0.04 0.00 −0.05 0.03 −0.05 t−24 (0.01) (0.03) (0.01) (0.03) (0.03) (0.04) J2J 0.24∗∗∗ 0.04 0.25∗∗∗ 0.03 0.19∗∗∗ 0.00 t−1 (0.07) (0.16) (0.07) (0.17) (0.06) (0.03) J2J 0.01 −0.03 0.02 −0.11 −0.04 −0.03 t−12 (0.04) (0.13) (0.05) (0.14) (0.05) (0.04) J2J −0.01 −0.10 0.00 −0.15 −0.02 0.01 t−24 (0.05) (0.18) (0.05) (0.20) (0.05) (0.02) Obs 307 307 307 307 307 307 Adj. R2 0.14 0.88 0.14 0.89 0.19 0.93 Notes: ThemeasureusedforInfl isCPIyear-to-yearinflationincolumns(1)and(2), inflationsurprisefromSPFforecastsincolumns(3)and(4),andSPFinflationforecastsincolumns(5)and(6). The columns(1), (3), and(5)havethejob-to-jobtransitionrateattimetasthedependentvariable, while theothershavetheinflationmeasuresattimet. AllvariablesareseasonallyadjustedandHP-filtered. ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Source: Fujitaetal.(2024);U.S.BureauofLaborStatistics,CPI;authors’ calculations. 62

Table15: VAR(2)EstimateswithAlternativeMeasures J2JRate PCEDeflator J2JRate PCEexc.FE J2JRate MSC1-yrAhead J2JRate MSCSurprise (1) (2) (3) (4) (5) (6) (7) (8) Inflt−1 0.03∗∗∗ 0.93∗∗∗ 0.08∗∗∗ 0.93∗∗∗ 0.07∗∗∗ 0.78∗∗∗ 0.02∗∗∗ 0.88∗∗∗ (0.01) (0.03) (0.02) (0.04) (0.01) (0.05) (0.01) (0.04) Inflt−12 0.00 −0.13∗∗∗ −0.00 −0.12∗∗∗ −0.00 −0.02 0.00 −0.13∗∗ (0.01) (0.05) (0.01) (0.03) (0.01) (0.04) (0.00) (0.06) J2Jt−1 0.26∗∗∗ −0.03 0.25∗∗∗ 0.03 0.27∗∗∗ 0.08 0.29∗∗∗ −0.13 (0.07) (0.11) (0.06) (0.06) (0.07) (0.12) (0.07) (0.21) J2Jt−12 0.08 −0.00 0.07 0.05 0.07 −0.18 0.08∗ −0.04 (0.05) (0.09) (0.05) (0.06) (0.05) (0.16) (0.05) (0.17) Obs 319 319 319 319 319 319 319 319 AdjR2 0.15 0.90 0.17 0.88 0.16 0.61 0.14 0.82 Notes: ThemeasureusedforInflisPCEdeflatorinflationincolumns(1)and(2),PCEdeflatorinflationexcludingfoodand energyincolumns(3)and(4),inflationsurprisefromMSCforecastsincolumns(5)and(6),andMSCinflationforecastsincolumn (7)and(8). Columns(1),(3),(5),and(7)havethejob-to-jobtransitionrateattimetasthedependentvariable,whiletheothers havetheinflationmeasuresattimet.AllvariablesareseasonallyadjustedandHP-filtered.∗p<0.1;∗∗p<0.05;∗∗∗p<0.01.Source: Fujitaetal.(2024);U.S.BEA,PCE;authors’calculations. Table 16: Summary Statistics on Monetary Policy and OilPriceShocks Variable Mean SD Min Median Max BC 0.031 0.716 -2.931 0.000 3.260 GK -0.013 0.052 -0.345 -0.002 0.112 BLM -0.001 0.064 -0.537 0.000 0.367 NS 0.000 0.036 -0.243 0.000 0.099 NSFFR -0.009 0.056 -0.413 0.000 0.125 RR -0.004 0.143 -0.588 0.000 0.437 SZ -0.131 1.111 -4.813 0.118 1.974 OilSurprise -0.002 1.378 -9.901 0.000 7.906 Notes: Each row represents the source used for the monetary policy and oil price shocks. The values are before the HP filtering. See Table 17 for the time coverageofeachvariable. 63

Table17: IVEstimates,withControls BC GK BLM NS NSFFR RR SZ BS (1) (2) (3) (4) (5) (6) (7) (8) Infl 0.095∗∗∗ 0.057∗∗∗ 0.076∗∗∗ 0.104∗∗∗ 0.080∗∗∗ 0.090∗∗∗ 0.070∗∗ 0.072∗∗∗ t−1 (0.031) (0.015) (0.015) (0.021) (0.020) (0.029) (0.028) (0.015) Infl 0.067∗ 0.017 0.022 −0.006 −0.011 0.021 0.007 0.013 t−12 (0.034) (0.033) (0.018) (0.030) (0.034) (0.030) (0.041) (0.017) UE 0.004 0.014∗ 0.015∗∗∗ 0.017∗∗ 0.019∗∗ 0.012∗ 0.014 0.012∗∗∗ t−12 (0.007) (0.007) (0.005) (0.007) (0.007) (0.006) (0.011) (0.004) Range ’95-’08 ’95-’12 ’95-’20 ’95-’14 ’95-’14 ’95-’08 ’95-’03 ’95-’23 Obs 131 179 278 200 200 125 68 308 AdjR2 0.054 0.168 0.088 −0.139 0.033 0.138 0.125 0.061 Notes: Eachcolumnrepresentsthesourceusedforthemonetarypolicyshock. Theinstrumentsare1to 24-monthlagsofmonetarypolicyshocks. ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01. Source: Fujitaetal.(2024);U.S. BureauofLaborStatistics,CPI;authors’calculations. Table18: IVEstimateswithMPSandOilPriceShocks BC GK BLM NS NSFFR RR SZ BS (1) (2) (3) (4) (5) (6) (7) (8) Infl 0.057∗∗∗ 0.050∗∗∗ 0.040∗∗∗ 0.062∗∗∗ 0.038∗∗ 0.055∗∗ 0.073∗∗∗ 0.036∗∗ t−1 (0.020) (0.014) (0.012) (0.016) (0.018) (0.022) (0.024) (0.014) Infl 0.034 0.035∗∗ 0.039∗∗∗ 0.047∗∗∗ 0.034∗∗ 0.035∗ 0.025 0.041∗∗∗ t−12 (0.023) (0.016) (0.012) (0.014) (0.015) (0.020) (0.026) (0.014) Range ’95-’08 ’95-’12 ’95-’18 ’95-’14 ’95-’14 ’95-’08 ’95-’03 ’95-’18 Obs 131 179 245 200 200 125 68 245 AdjR2 0.133 0.106 0.027 0.029 0.081 0.121 0.110 0.020 Notes: Eachcolumnrepresentsthesourceusedforthemonetarypolicyshock. Thecontrolsarethe unemploymentrateandtheunemployment-to-employmenttransitionrate. Theinstrumentsare1to 24-month lags of monetary policy shocks. See Appendix B for the data sources and details of how eachvariableisconstructed. ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01 64

Table19: SummaryStatisticsforSearchEffortandOutcomes Variable N Mean SD Min Median Max SearchedM 20709 0.23 0.42 0.00 0.00 1.00 HoursSearchedW 4752 3.44 4.52 0.00 2.00 25.00 NMethodsTried 4758 3.45 2.38 0.00 3.00 12.00 EmpApplied1M 1167 2.71 3.64 0.00 1.00 15.00 EmpHeardFrom1M 1168 1.25 2.05 0.00 1.00 10.00 NInterviews1M 1111 0.31 0.60 0.00 0.00 2.00 NOffersReceived1M 1023 0.29 0.63 0.00 0.00 3.00 NOffersReceived4M 3254 0.51 1.00 0.00 0.00 5.00 Notes: Eachrowrepresentsadifferentmeasureofjobsearchactivity. SeeAppendixBfordetailsonhoweachmeasureisconstructed. Table20: SummaryStatisticsforMacroeconomicExpectations Variable N Mean SD Min Median Max inflrate 20680 0.05 0.05 -0.03 0.03 0.20 higherstock 20704 0.42 0.23 0.00 0.49 1.00 higherint 20702 0.33 0.26 0.00 0.30 1.00 higherunemploy 20702 0.37 0.23 0.00 0.38 1.00 Notes: Each row presents expectations of a different economic aggregate. The inflation expectations are continuous, while the rest are binary, indicating whether the economic aggregate is expected to be higher (=1) or lower(=0) than the previous year. See AppendixBfordetailsonhoweachmeasureisconstructed. 65

0.10 0.05 0.00 −0.025 0.000 0.025 0.050 Inflation Surprise t−1 (SPF) esaercnI egaW reyatS sv rehctiwS Figure 9: J2J Wage Increase and Inflation Surprises Each point represents a quarter in the U.S. from2000Q3to2023Q1.Thesolidlinerepresentsthelinearregressionline,withacorrelationcoefficientof 0.3.TheswitcherandstayerwagegainsarefromtheLongitudinalEmployer-HouseholdDynamics(LEHD) explorer by the U.S. Census Bureau. Inflation Surprises are constructed as the discrepancy between the realizedinflationandthe1-yearaheadSurveyofProfessionalForecasters(SPF)forecasts. 66

0.05 0.00 −0.05 1980 1990 2000 2010 2020 Year (w t - w^ t- 2,t ) w^ t- 2,t i t - ^ i t- 1,t Figure10: TheDiscrepancyBetweentheSPFForecastandRealizedInflationThedashedred line represents the difference between the realized inflation (i ) and the 1-year ahead SPF forecast ( ˆi ) t t−1,t inpercentagepoints. Thesolidlinerepresentsthecumulativerealwageloss(asafractionoftheintended wage(wˆ ))foraworkerwhosignedhiscontracttwoyearsagoaccordingtotheSPFforecasts. t−2,t 67

0.10 0.05 0.00 −0.05 1980 1990 2000 2010 2020 Year (w t - w^ t- 2,t ) w^ t- 2,t i t - ^ i t- 1,t Figure 11: The Discrepancy Between the MCS Forecast and Realized Inflation Thedashed red line represents the difference between the realized inflation (i ) and the 1-year ahead forecasts by the t MichiganSurveyofConsumers( ˆi )inpercentagepoints. Thesolidlinerepresentsthecumulativereal t−1,t wageloss(asafractionoftheintendedwage(wˆ ))foraworkerwhosignedhiscontracttwoyearsago t−2,t accordingtotheMichiganforecasts. 68

0.4 Data Model s 0.3 r e k r o w fo 0.2 n o itc a r F 0.1 0 1 2 3 4 5 6 7 8 9 10+ Job Tenure (Years) Figure12: JobTenureDistributionintheModelandtheData NoteThelinesrepresentjobtenuredistributionsoftheemployed. Thesolidlineisthedistributioncalculated from the 2005 Current Population Survey Occupational Mobility and Job Tenure Supplement. The dashedlineisthedistributionsimulatedfromourcalibratedmodel. 69

higherint higherstock higherunemploy #Apply (1M) #Heard (1M) #Interviews (1M) #Methods #Offered (6M) #Offers (4M) Hours (1W) Search (1M) −1 0 1 −1 0 1 −1 0 1 Coefficient Estimate Model Without Controls With Controls Figure 13: Job Search and Expectations of Other Economic Conditions Notes: Eachcolumn of plots represents expectations of a different economic aggregate. Each expectation is binary, indicating whether the economic aggregate is expected to be higher (=1) or lower(=0) than the previous year. The independent variables are represented by rows and include job search activities and outcomes. The bars indicate99%confidenceintervals.Allregressionshavesurveydatefixedeffects.Theadditionalcontrolsare naturallogarithmsofage,tenure,andannualearnings,dummiesforsexandmaritalstatus,fivedummies for race, four dummies for education, and fixed effects for state, job start-year, and two-digit industries. Thestandarderrorsareclusteredattheindividuallevel. SeeAppendixBforthedatasourcesanddetails ofhoweachvariableisconstructed. 70

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