Why Do We Think That Inflation Expectations Matter for Inflation? (And Should We?)

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Why Do We Think That Inflation Expectations Matter for Inflation? (And Should We?) Jeremy B. Rudd 2021-062 Please cite this paper as: Rudd, Jeremy B. (2021). “Why Do We Think That Inflation Expectations Matter for Inflation? (And Should We?),” Finance and Economics Discussion Series 2021-062. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2021.062. 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.

Why Do We Think That Inflation Expectations Matter for Inflation? (And Should We?) Jeremy B. Rudd Federal Reserve Board* September 23, 2021 Abstract Economists and economic policymakers believe that households’ and firms’ expectations of future inflation are a key determinant of actual inflation. A review of the relevant theoretical andempiricalliteraturesuggeststhatthisbeliefrestsonextremelyshakyfoundations,anda caseismadethatadheringtoituncriticallycouldeasilyleadtoseriouspolicyerrors. *E-mail: jeremy.b.rudd@frb.gov. Theanalysisandconclusionssetfortharemyownanddonotnecessarilyreflect theviewsoftheBoardofGovernorsorthestaffoftheFederalReserveSystem.

Nobodythinksclearly,nomatterwhattheypretend. ...That’swhypeoplehangonsotighttotheirbeliefs and opinions; because, compared to the haphazard way they’re arrived at, even the goofiest opinion seemswonderfullyclear,sane,andself-evident. DashiellHammett,TheDainCurse(1928) I Introduction Mainstream economics is replete with ideas that “everyone knows” to be true, but that are actually arrant nonsense. For example, “everyone knows” that: • Aggregateproductionfunctions(andaggregatemeasuresofthecapitalstock)provideagood way to characterize the economy’s supply side; • Over a sufficiently long span—specifically, one that allows necessary price adjustments to be made—the economy will return to a state of full market clearing; and, • The theory of household choice provides a solid justification for downward-sloping market demand curves. None of these propositions has any sort of empirical foundation; moreover, each one turns out to be seriously deficient on theoretical grounds.1 Nevertheless, economists continue to rely on these and similar ideas to organize their thinking about real-world economic phenomena. No doubt, one reason why this situation arises is because the economy is a complicated system that is inherently difficult to understand, so propositions like these—even though wrong—are all that saves us from intellectual nihilism. Another, more prosaic reason is Stigler’s (1982) equally nihilistic observation that “it takes a theory to beat a theory.” Isthisstateofaffairseverharmfulordangerous? Onenaturalsourceofconcernisifdubiousbut widely held ideas serve as the basis for consequential policy decisions.2 In this note, I examine one such idea, namely, that expected inflation is a key determinant of actual inflation. Many economists view expectations as central to the inflation process; similarly, many central banks consider “anchoring” or “managing” the public’s inflation expectations to be an important policy goal or instrument. Here, I argue that using inflation expectations to explain observed inflation dynamics is unnecessary and unsound: unnecessary because an alternative explanation exists 1Forausefulbriefagainstproductionfunctions,seeFelipeandFisher(2003);forthecaseagainstcapitalaggregates,seeBrown(1980). Theideathattheinherentstabilityoftheeconomyisaconcomitantofgeneral-equilibrium theoryisdifficulttoentertainseriouslyaftergivingFisher(1983)closestudy;seeGrandmont(1982)forsomerelated macroeconomicarguments. Finally,Hildenbrand(1994)providesasoberingcorrectivetofirst-yeardemandtheory. 2Ileaveasidethedeeperconcernthattheprimaryroleofmainstreameconomicsinoursocietyistoprovidean apologeticsforacriminallyoppressive,unsustainable,andunjustsocialorder. 1

thatisequallyifnotmoreplausible,andunsoundbecauseinvokinganexpectationschannelhas nocompellingtheoreticalorempiricalbasisandcouldpotentiallyresultinseriouspolicyerrors.3 II Why do we think that expectations matter—and why should we care if they do? I’malwaysalittledubiousaboutanappealtoexpectationsasacausalfactor;expectationsarebydefinitionaforcethatthatyouintuitivelyfeelmustbeeverpresent andveryimportantbutwhichsomehow you areneverallowedtoobservedirectly. R.M.Solow(1979) The usual argument for viewing expected inflation as a key driver of actual inflation goes something like this. 1. Theoretical models (such as those developed by Phelps, Friedman, and Lucas, along with the more-recent new-Keynesian Phillips curve) all incorporate a role for expected inflation thatis either intuitivelyappealing (becauseit rules out a stateof persistent moneyillusion) or microfoundedinasensibleway(inthatthepresenceofstickypricesshouldinduceaconcern about future costs or demand conditions). 2. Models like these also help us explain the observed instability of the Phillips curve and changes in measured inflation persistence over time, especially the U.S. inflation experience from the late 1960s through the mid-1980s and the shift toward a mean-reverting inflation process that appeared to take place around the mid-1990s. 3. Inlightofthestrongpriorinducedbytheory,andwiththecasualempiricismofpoint2(coupled with the formal empiricism obtained from tests of the new-Keynesian inflation equation), it seems sensible to grant a central role for inflation expectations in inflation determination. If correct, such a view has important practical and policy consequences. For an inflation forecaster, observed (imperfect) measures of expected inflation might usefully inform inflation projections and permit one to explain past inflation developments. For a central bank with a pricestabilitymandate,monitoringmeasuresofinflationexpectationscanprovideanimportantgauge of how well the monetary authority is meeting its goal, while attempts to shape the public’s inflation expectations through central bank communications and policy actions will represent time wellspent. Inparticular,totheextentthatpost-1990inflationdynamicsreflecttheeffectthatthe conductofmonetarypolicyhashadoninflation,thereshouldbeanactiveattemptbypolicymak- 3Iwillhavenothingtosayaboutwhatdeterminesinflationexpectations—eitherinprinciple,orinthecontextofthe varioussurveyandfinancialmarketmeasuresthatwecanobserve. (Myhopeisthatanyreaderswhofinishthisnote willnolongerfindthatquestionterriblyinteresting.) 2

ers to preserve the relevant features of this policy regime. But what real evidence do we have for this view? III How strong is the theoretical case? Pure economics has a remarkable way of pulling rabbits out of a hat—apparently a priori propositions which apparently refer to reality. It is fascinating to try to discover how the rabbits got in; for those of us whodonotbelieveinmagicmustbeconvincedthattheygotinsomehow. J.R.Hicks(1946) Twooftheearliesttheoreticalargumentsforassigninganexplicitroleforinflationexpectationsin aPhillipscurverelationarefoundinPhelps(1967)andFriedman(1968). Inaddition,Lucasand Rapping (1969) derived an aggregate supply function in which a correlation between inflation and real activity would arise through a price expectations mechanism, while Lucas’s imperfect information model (which was described opaquely in a 1972 article and somewhat more accessibly in a 1973 paper) implied an inflation equation in which a change in (rationally) expected inflation would pass through one-for-one into the intercept of the Phillips curve. Finally, a later generation of rational expectations models that started from the assumption of less-than-fully flexible prices or wages gave rise to the so-called new-Keynesian Phillips curve, which differed from previous models in assigning a role to the current expectation of next period’s inflation rate (as opposed to last period’s expectation of the current inflation rate). What are the merits of each theoretical approach? Phelps simply asserted that the intercept of the Phillips curve would shift one-for-one with expected inflation; to the extent that a theoretical argument was vouchsafed, it was based on the notion that “...the supply of labour [should be] independentoftherealandmoneyratesofinterestandhenceindependentoftheexpectedrate ofinflation,”as“...otherwise,everysteady-stateoffullyanticipatedinflationwouldbeassociated with different ’levels’ of output, employment and the real wage.” Hence, Phelps’s argument was basicallyfoundedontheideathatnominalvariablesshouldnotpermanentlyaffectrealvariables, though here the real variable in question was the real interest rate. Friedman’s derivation was superficially simpler than Phelps’s—unlike the latter’s paper, Friedman’s paper contains no equations—but was arguably better grounded in theory. Specifically, Friedman posited that workers entered the wage bargain with a concern over anticipated real wages (the concern with real wages is of course a reasonable one if money illusion is absent) whilefirms’hiringdecisionswerebasedonactualrealwages(nodistinctionwasmadebetween the consumption and product wage). Hence, by reducing the ex post real wage, a surprise increase in prices could yield higher employment. But a fully anticipated price increase would 3

be fully reflected in nominal wages, thereby leaving the real wage (or any other real variable) unchanged. Lucas and Rapping formulated a model in which price expectations affect labor supply by influencing households’ substitution between goods and leisure across time. Specifically, the model assumesthatarisein(expected)realinterestratesboostslaborsupplytoday(thecostofcurrent leisure, in terms of foregone future consumption, goes up). Critically, the model also assumes adaptive expectations in the price level, along with less than one-for-one adjustment in nominal interest rates. A little later, Lucas (1972) constructed a model in which agents use observed market prices in order to assess how much of a given disturbance is “purely monetary” as opposed to having resultedfromashocktoarealvariable. Thebasicideaistiedtothenotionthatproducersmight mistake an absolute (money) price change for a relative price change; the theoretical problem that the paper attempts to solve is why one producer’s mistake in a particular direction isn’t simply offset in the aggregate by a different producer’s mistake in the opposite direction. (The paper does so by appealing to a sort of “islands economy” that is similar to a modelling strategy employed by Phelps in other work.) What is often called the “Lucas supply function” or “Lucas surprise supply function” refers to an aggregate supply or Phillips curve relation of this form.4 Finally, the subsequent development of the new-Keynesian Phillips curve represented an attempt to integrate rational expectations into a model where some sort of exogenously specified contractingmechanismortheassumedpresenceofadjustmentcostsyieldednominalrigidities. Given the models’ assumed competitive structure, these nominal rigidities would in turn cause current inflation to depend on expected future inflation.5 Even without appealing to empirical arguments (that will be done in the following section), it is clearthatnoneofthesemodelsmakesastrongorevenespeciallyplausibletheoretical casefor including expected inflation in an inflation equation. • ThePhelpsassumptionisessentiallyadhoc;takenliterally,Phelps’sjustificationforitrequires ignoring effects that fully anticipated inflation can have on current real income (for example, through capital losses on wealth) as well as on perceived permanent income, either of which should affect labor supply to the extent that leisure is a normal good. 4Though not as far as Lucas himself is concerned: He views the “Lucas supply function” as equivalent to the Lucas–Rappingmodel(seetheintroductiontoLucas,1981). 5In fairness, motivating a role for expected inflation was not really the original concern of these models; rather, theirgoalwastoshowthatanominalshockcouldyieldpersistentrealeffectsunderrationalexpectations. Thatsaid, Isuspectthatonereasonwhysome(notall)economistsrearedonthePhelps–Friedmantraditionweremostlywilling to accept the new-Keynesian Phillips curve was because the presence of an expected inflation term in the new- Keynesianinflationequationresembledsomethingthattheyalreadyfoundreasonablewhenthinkingaboutinflation dynamics. 4

• Friedman’sderivationassumesthatfirmsarealwaysontheirlabordemandcurveeventhough workersarenotontheirlaborsupplycurve,whichisaknife-edgecasethatimplicitlyassumes that the goods market always clears. • Both the Phelps and Friedman assumptions can be viewed as trying to ensure that money illusionisabsent,thatpurelynominaldisturbancescannothavepermanentrealeffectsonthe economy, or both.6 These are, of course, a priori assumptions that rule out the possibility of path dependence in the economy (for example, hysteresis effects in the labor market); that money illusion or inflation insensitivity could actually exist at low rates of inflation; the effects that high rates of inflation might have on the economy’s supply side (a possibility that Friedman,1977,himselfacknowledgedandthatisapredictionofaclassofsticky-pricemodels with nonzero steady-state inflation); or the possibility that the economy might function more smoothly at nonzero rates of inflation.7 • On a deeper level, both the Phelps and Friedman approaches are grounded in the idea that there is a “real side” of the economy that eventually makes its influence felt after any sort of (nominal) disturbance, which again falls prey to Fisher’s (1983) criticism that there exists no compelling theoretical proof of the stability (as opposed to the existence) of a general economic equilibrium.8 • TheLucas–Rappingaggregatesupplymodelhingesontheassumptionthatexpectedinflation declineswhenthereisanunanticipatedincreaseincurrentinflation(thisassumption,whichin turn only obtains because of the specific adaptive expectations formulation that they employ, is what causes the real interest rate to increase).9 • The usual criticism levelled against the Lucas surprise model is that it should not be all that difficult to determine whether there has been a change in the absolute price level (apparently thereexistfreelyavailablestatisticsonthatsortofthing);also,themodel’spredictionthatonly randomandtransitorypolicyshockscanaffectoutputseemsunappealingonapriori grounds. • Finally, the channel through which expected inflation enters the new-Keynesian Phillips curve is especially contrived. In the canonical version of these models, the nature of the contracting 6Even if one does think that monetary neutrality is a feature of the real world, it would be an example of Aristotle’s twelfth logical fallacy (affirming the consequent) to argue that the presence of monetary neutrality therefore necessarilyimpliesaroleforexpectedinflationinpriceorwagedetermination. 7SeeAscariandSbordone(2014)foranew-Keynesianmodelwherehigherratesof(perfectlyanticipated)trend inflationactlikeanegativeproductivityshock. Thesecondnotion, whereinflation“greasesthewheelsofthelabor market,”isusuallyattributedtoJamesTobin. 8Forexample,Friedman(1968)describesthenaturalrateofunemploymentas“...thelevelthatwouldbeground outbytheWalrasiansystemofgeneralequilibriumequations.” 9ThisflawwasrecognizedbyLucasandRappingintheirpaper,whichcontainsalengthy(andstrained)defenseof thenotionthatthissortofprice-levelexpectationformationisreasonable,alongwithanappealtoempiricalevidence (thatbasicallyinvolvesquotingIrvingFisher)tojustifytheirimposedassumptionthatnominalinterestrateswouldnot moveinsuchawayastoleavetherealinterestrateunchangedfollowinganinflationchange. 5

mechanism is such that producers are required to supply as much output as is demanded at thefixedcontractprice.10 Giventheimperfectlycompetitivemarketstructureofthesemodels, firms are therefore concerned with their current and expected real (that is, relative) price, since a future decline in their relative price will result in additional demand that could be less profitable to meet at the previously contracted nominal price. When these individual pricing decisions are aggregated, the result is a dependence of current economywide inflation on expected future inflation. It should also be pointed out that all of these models give pride of place to short-run expected inflation, in the sense that current inflation is influenced by a one-period-ahead expectation (the main difference across models is whether the short-run expectation is last period’s expectation of the current inflation rate or this period’s expectation of next period’s inflation rate).11 This fact sitsuneasilywiththeobservationthatinpolicycircles—atleastintheUnitedStates—muchmore attention is paid to long-run inflation expectations, as it is the “anchoring” of these expectations that is viewed as being the wellspring of desirable economic outcomes and (as an empirical matter) as the source of important changes in U.S. inflation dynamics over the past 50 years.12 Moreover,whileitturnsouttobepossibletoappendanadaptive-learningmechanismtoseveral of these models in order to derive an inflation equation where long-run inflation expectations do play a critical role (see section V, below), such a mechanism turns out to carry subtly different policy implications. IV How strong is the empirical case? Don’tinterferewithfairytalesifyouwanttolivehappilyeverafter. F.M.Fisher(1984) It is an irony of history (or perhaps a testimony to the power of pure thought) that, when Phelps andFriedmansoughttojustifytheirproposedtheoreticalspecifications,theywerefacedwiththe uncomfortablefactthatempiricalPhillipscurvesappearedtoberemarkablystable. Thesensible explanationthat bothauthorsadvancedwas thatthis seemingstabilitywasactually theresultof existing models’ having been estimated over a period in which actual and expected wage and price inflation had remained within a relatively narrow range. (Oddly, neither author appealed to the gold standard to make his case.) While one could quibble with the view that inflation (and 10Similarly,modelswithwagecontractsrequireworkerstosupplyasmuchlaborasisdemandedatthecontracted wage. Suchassumptionsviolatetheprincipleofvoluntaryexchange(andcommonsense). 11Evennew-Keynesianmodelsthatexplicitlyincorporatetime-varyingtrendinflationrates(usuallytoallowforthe possibilityofachangeinthemonetaryauthority’sinflationtarget)predictthatshort-runexpectationsofinflationwill haveanimportantinfluenceoncurrentinflation. 12SeeYellen(2015)foroneexample. 6

otherinfluencesoninflation,liketrendproductivityandunemployment)hadactuallybeenallthat stable over the first part of the 20th century, there was no question that the sustained inflation increases of the 1960s and 1970s appeared to be associated with outward shifts of estimated Phillips curves. Ex post, these developments were seen as a stunning victory for the prediction that expected inflation was an important determinant of actual inflation.13 It is worth noting, however, that the direct evidence for an expected inflation channel was never very strong. Most empirical tests concerned themselves with the proposition that there was no permanentPhillipscurvetradeoff,inthesensethatthecoefficientsonlaggedinflationinaninflationequationsummedtoone14 Relatedly,theinvocationofanadaptiveexpectationsmechanism in numerous theoretical contexts led many to simply associate the presence of lagged inflation terms in empirical Phillips curves models with a role for “expectations” in some loose sense.15 Perhaps the closest (and, for the time, most econometrically sound) attempt at a direct test was made by McCallum (1976), where he used instrumental variables techniques to assess the role of expected price inflation in a wage equation.16 (These techniques are similar in spirit to those employed in the 1990s to estimate new-Keynesian models; hence, they suffer from the same sorts of problems—discussed below—that attend empirical estimates of those models.) In addition, the various theoretical models that assumed a role for expected inflation tended to carry other empirical implications that were clearly at variance with the data. For example: • Friedman’s derivation of the expectations-augmentedPhillips curve implies that the real productwageshouldbestronglycountercyclical(recallthatinthismodelfirmsarealwaysassumed 13Morerecently,Clarida,Gal´ı,andGertler(2000)haveattemptedtoexplainthesubparmacroeconomicoutcomes ofthelate1960sand1970sbyarguingthattheFederalReserve’sfailuretoadheretotheTaylorprinciplepermitted self-fulfilling expectations of inflation—“sunspots”—to influence macroeconomic outcomes, while also leaving the economymoresusceptibleto“fundamental”shocks. However,eveniftheFed’spolicyreactionfunctiondidhavethis property—aviewthathasbeenquestionedbyOrphanides(2004)andbySimsandZha(2006),amongothers—the Clarida, et al. interpretation of the 1970s stagflation requires that period’s food and energy price shocks to have resultedinalargeandrapiddeclineinthelevel ofpotentialoutput. (Hadnon-fundamentalinflationshocksbeenthe sourceoftheGreatStagflation, outputwouldhavebeenabove potentialthroughoutthisperiod.) Suchadeclinein potential seems highly unlikely in the case of a food price shock; in addition, as Blinder and Rudd (2013) discuss, neoclassicalsupplytheorypredictsthattheeffectonpotentialoutputfromashocktoenergyprices(orotherimported commodityprices)isrelativelysmall. 14Empirically,thisunitsumbecameeasytofindaroundthemid-1970s—seeGordon(1976)foracontemporaneous account,andMcCallum(1994)foraretrospectiveone.Itshouldalsobenoted,however,thatKingandWatsonargued as late as 1994 that it was surprisingly difficult to reject the hypothesis of no long-run tradeoff in U.S. data without simplyimposingitthroughthe“monetarist”assumptionthat“...long-runinflationisastrictlymonetaryphenomenon” (thoughseeEvans,1994,foranalternativeview). 15Itisanotherironyofhistorythatoneoftheearliestusesofadaptiveexpectationsinempiricalworkwasnotinthe contextofamodelof“normal”inflationdynamics,butratherinCagan’s(1956)hyperinflationstudy. 16Several other studies from the 1970s and 1980s tried to use survey-based or commercial inflation forecasts to disentangletheseparaterolesof“inertia”and“expectations”inunionwagesetting;seeKaufmanandWoglom(1984) for one example as well as for a useful literature review. (As one might expect from the vantage of hindsight, the Kaufman–Woglompaperfound“surprisinglysmall”differencesbetweenspecificationsthatused“direct”expectations measuresandspecificationsthatsimplyusedlaggedactualinflation.) 7

to be on their labor demand curves). In particular, Friedman states as a matter of fact that “...selling prices of products typically respond to an unanticipated rise in demand faster than pricesoffactorsofproduction,”whichwouldinturnimplytheempiricalpredictionthattheprice Phillips curve is steeper than the wage Phillips curve. However, in U.S. data this prediction is completely at odds with the evidence: Conventional price and wage equations imply that the tradeoff between wage inflation and activity is much steeper than that for price inflation (put differently, the aggregate real wage is procyclical). • The Lucas–Rapping model assumes that inflation follows a trend-stationary process (deviations from this assumption lead to a Phillips curve with the “wrong” sign). In addition, this model cannot yield large fluctuations in real activity (employment) without assuming a large elasticity of intertemporal substitution. • The Lucas “surprise” model depends on the arbitrary exclusion of the current aggregate price levelfromtheinformationset. Moredirectly,Ball,Mankiw, andRomer(1988)arguethatakey prediction of this model—specifically, that the standard deviation of inflation should matter for the size of the output-inflation tradeoff—receives no support in the data. Similarly, thedocumentedempiricaldeficiencies ofthenew-KeynesianPhillips curvearelegion. • The canonical new-Keynesian inflation equation implies a long-run tradeoff between the output gap and inflation. Attempts to remedy this problem by simply imposing a zero long-run tradeoffeitherimplythatrealdevelopmentsmillionsofyearsinthefuturehavethesameeffect asdevelopmentstodayorthatinflationismostlygovernedbysunspots;ortheyyieldthecounterfactual prediction that the first-difference of inflation is strongly positively autocorrelated.17 • In addition, most standard tests of the new-Keynesian Phillips curve suffer from such severe potential misspecification issues or such profound weak identification problems as to provide no evidence one way or the other regarding the importance of expectations (much the same statement applies to empirical tests that use survey measures of expected inflation).18 17See Rudd and Whelan (2006) for a discussion of the latter point in the context of a “hybrid” new-Keynesian Phillips curve. The dependence on far-future events arises in the “pure” new-Keynesian Phillips curve when a unit coefficientonEπ isimposedbecauseeachexpectedfutureoutputgaptermintheclosed-formsolutionmakesthe t t+1 samecontribution to currentinflation; alternatively, a role for sunspots arises becausethe terminal inflation termin theclosedformnevervanishes. 18SeeRuddandWhelan(2005)foradiscussionofthemisspecificationissue. Theweakidentificationissueaffects thehybridnew-KeynesianPhillipscurve(andwasoneofseveralmotivationsforthealternativetestsofthemodelthat RuddandWhelan,2006,considered);itarisesbecausethevariablesthatareusedtoinstrumentforexpectedfuture inflationEπ willonlybeabletotiedowntheinfluenceofthistermifalargeportionofthepredictablevariationin t t+1 inflationisunrelatedtolaggedinflation. (SeeMavroeidis,Plagborg-Møller,andStock,2014,foradetaileddiscussion oftheestimationissuesthatariseasaresult.) 8

• Versions of the new-Keynesian model that allow for time-varying trend inflation imply that the effect of real activity on inflation should be smallest in periods like the 1970s, when trend inflation is high (see Ascari and Sbordone, 2014). However, as shown in figure 1, the response of price inflation following a shock to real activity was largest in the 1970s, and smaller thereafter.19 Furthermore,astheaccompanyingtableindicates,thisfindingalsoobtainsifwefocus on the short-run inflation response: Integral multipliers for the four- or eight-quarter period following the shock also become smaller after the 1970s.20 • Finally, versions of these models that impose realistic contracting mechanisms (specifically, modelsthatrequirelabormarketstobecharacterizedbyvoluntaryexchange)lookverydifferent from the canonical model and do extremely poorly in fitting the data.21 Leavingasidetheresultsofeconometrictestsofparticularmodels(andgiventhatthereisgood evidence that many prices actually are sticky), doesn’t it seem intuitively plausible that firms fixing their price over some period would worry about future costs or demand conditions—that is, about any relevant developments that could materialize over the period in which their price is held constant? Perhaps, but perhaps not. • What little we know about firms’ price-setting behavior suggests that many tend to respond to costincreasesonlywhentheyactuallyshowupandarevisibletotheircustomers,ratherthan in a preemptive fashion (see Blinder, et al., 1998). • Similarly, the idea that sticky prices would necessarily result in a dependence of aggregate inflationonaggregateexpectationsseemsalittleunintuitive: Mostoftheobservedvariationin prices appears to be idiosyncratic (suggesting that cost increases are as well), and it seems likely that price stickiness itself is endogenous (in that firms that face relatively more stable costs are more likely to enter into “fixprice” arrangements). • It is highly unlikely that something like a Dixit–Stiglitz competitive structure—where everyone competes with everyone else to some extent—actually exists; rather, competition for inputs or customers probably has an important local or industry-specific aspect. That would tend to weaken the need for firms to be focused on their future real prices (defined relative to the 19TheseestimatesareobtainedfromVARmodelswithtime-varyingparametersandstochastic volatility, andare takenfromPeneva(2019); seePenevaandRudd(2017)foradetaileddiscussionoftheestimationprocedureand data. Impulseresponsesforlaborcosts—alsofoundinPeneva(2019)—implyamuchgreaterdegreeofstabilityfor thewagePhillipscurve(afindingthatisalsoobtainedusingconventionalempiricalwageequations). 20Theintegralmultipliersaredefinedastheratioofthecumulatedn-quarterimpulseresponseofpriceinflationto the cumulated n-quarter response of the unemployment gap. Calculations such as these are useful because they accountforanytimevariationintheresponseoftheunemploymentgap. 21SeeHuoandR´ıos-Rull(2020). 9

economywide price level), which is how expectations of aggregate inflation enter the new- Keynesian Phillips curve.22 • Finally, even if one is willing to entertain the idea that in some vague, mushy sense concern over costs and demand by individual firms facing fixed prices leads to a dependence of aggregate inflation on expected inflation, we are still left with the conclusion that short-run expectations should be the ones that are most important. This last point is particularly important given that one of the few shreds of empirical evidence that we do have suggests that it is long-run expectations that are most relevant for inflation dynamics. As figure 2 demonstrates, there is a suggestive low-frequency correlation between an estimate of inflation’s long-run stochastic trend and survey measures of long-run expected inflation.23 The stability of inflation’s long-run trend after the mid-1990s—more precisely, the fact that the trend appears almost completely invariant to changes in economic conditions—is perhaps the most remarkable feature of the U.S. inflation process at present; at a minimum, it representsasignificant departurefromtheexperienceofthe1970sand1980s(seethedashed line in figure 3, which plots the stochastic trend for price inflation over a longer period).24 Of course, the correlation that is apparent in figure 2 provides, at best, only circumstantial evidence of a causal relationship in which expectations determine the long-run properties of inflation; it could equally well reflect a situation where respondents to these surveys are making reasonably plausible inflation forecasts in response to observed changes in actual inflation. In addition, further evidence against a causal relationship is provided by the fact that in recent years, movements in these survey measures (as well as in long-run inflation expectations from TIPS yields) appear not to be mirrored by changes in trend inflation (this casual observation is confirmed by Rudd, 2020, using more-formal estimation techniques).25 A reasonable reader’s reaction to the preceding discussion might be: “So what? No model is goingtodescriberealityallthatwell,andaconvincingtheoryofaggregatesupply—orofinflation 22Unsurprisingly, what little evidence we have suggests that firms pay little attention to forecasts of aggregate economicconditions,includinginflation(Blinder,etal.,1998). 23ThetrendestimateisobtainedfromtheVARmodelusedforfigure1. 24SeePenevaandRudd(2017)andRudd(2020)fordiscussionsofthesepoints. 25The characterization of inflation dynamics implied by the flattening of the price Phillips curve and the nearconstancy of inflation’s long-run trend imply an explanation for the so-called “missing disinflation” of the late 2000s thatisdrasticallydifferent—butmuchmoreplausible—thantheoneadvancedbyCoibionandGorodnichenko(2015). Inparticular, thatstudystartsfromapricePhillipscurvethatimposesaunitcoefficientonlaggedinflation(orona measureofshort-runexpectedinflationthatiscloselyrelatedtolaggedinflation). Asaresult,theinflationequation thattheyuse,whichisessentiallyanaccelerationistPhillipscurve,ignorestheempiricalfactthatinflationessentially became a mean-reverting process after the mid-1990s. As Peneva and Rudd (2017) note, such a model of inflation“...generatesamisleadingbenchmarkforhowwewouldhaveexpectedinflationtobehavefollowingthe2007 businesscyclepeak.” 10

dynamics generally—has eluded students of macroeconomics since the field’s inception. So your criticisms really just amount to ill-tempered pettifogging.” WhatIbelievesucharesponsemissesisthatthepresenceofexpectedinflationinthesemodels provides essentially the only justification for the widespread view that expectations actually do influence inflation. In other words, rather than simply serving as a plausible postulate that, once invoked, allows a theorist to analyze other interesting questions, the expected inflation terms in these models have been reified into a supposed feature of reality that “everyone knows” is there. And this apotheosis has occurred with minimal direct evidence, next-to-no examination of alternatives that might do a similar job fitting the available facts, and zero introspection as to whetheritmakessensetousetheparticularassumptionsorderivedimplicationsofatheoretical model to inform our priors (particularly when the ancillary assumptions of the model are so incredible and when the few clear predictions it makes are so wildly at odds with the available empirical evidence). V An alternative interpretation of inflation dynamics Itisfar,farbetterandmuchsafertohaveafirmanchorinnonsensethantoputoutonthetroubledseas ofthought. JohnKennethGalbraith(1958) If expected inflation isn’t a key determinant of actual inflation, how might we try to explain the observed evolution of postwar U.S. inflation dynamics? First, consider figure 4, which plots inflation’s stochastic trend (the black dashed line) together with the estimated stochastic trend for unit labor cost growth (the blue line).26 The similar contoursofthetwolinescertainlyseemstoindicatethatthelong-runbehaviorofpriceinflationand labor cost growth is linked. Second, the fact that inflation’s stochastic trend manifests its last persistent level shift after the 1990–1991recessionalsoseemsrelevant,inthatitsuggeststhat“whateverhappened”toinflationmightbemorerelatedtoitsactuallevel’shavingbeenkeptlowratherthantoany“credibility” thattheFedgainedasaninflationfighterfollowingtheVolckerdisinflation. Putdifferently,atrend inflation rate of around four percent was associated with highly persistent inflation dynamics— both in the late 1960s and in the 1980s—while a two-percent trend inflation rate was not. 26Moreprecisely,themeasureshownisfor“trend”unitlaborcostgrowth,whichusesameasureoftrendproductivity growth (obtained separately with a bandpass filter) in lieu of actual productivity growth—see the data appendix of Peneva and Rudd (2017) for details. Hence, the line in the figure is the stochastic trend for trend unit labor cost growth. 11

Another way of stating this point is that an important feature of inflation dynamics after the mid- 1990s appears to be the lack of a strong wage–price spiral (or of any significant year-to-year feedbackbetweenwagegrowthandinflation). Thisistruedespitelarge(butultimatelytransitory) increases in actual inflation—for example, headline PCE inflation averaged 3 percent over the threeyearsleadinguptothe2007–2009recession.27 Itseemsunlikelythatwell-anchoredlongruninflationexpectationsweretherootcauseofthisstability,inasmuchasthisbeliefalsoleadsto theconclusionthatworkerswerewillingtoignorenoticeable(andreasonablysustained)changes in the cost of living when deciding on the wage rate that they were willing to accept, simply because they believed that eventually inflation would return to some long-run average pace.28 An observation about the actual nature of the “wage bargaining process” is helpful at this point. Outside of a few unionized industries (which now account for only about 6 percent of employment), a formal wage bargain—in the sense of a structured negotiation over pay rates for the coming year—doesn’t really exist anymore in the United States. In a world where most employment is “at will,” changes in the cost of living will enter nominal wages as part of an employer’s attempttoretainworkers: Ifemployerspaytheirworkersawagethatfallstoofarbehindthecost of living, they will start to see more quits, which will in turn force them to raise the wages they pay to existing workers (and those they offer to new hires). But there is no real scope for direct negotiation.29 Insituationswhereinflationisrelativelylowonaverage,italsoseemslikelythattherewillbeless ofaconcernonworkers’partaboutchangesinthecostofliving—thatis,asmallerproportionof quitswillreflectworkers’attemptstooffsethigherconsumerpricesbyfindingabetter-payingjob. But this is a story about outcomes, not expectations: Workers don’t behave this way because theyexpecttoseelowinflationinthefuture,butratherbecausetheydon’tviewtheirrecentwage increases as appreciably lagging actual changes in the cost of living.30 On this latter point the experience of the 1960s and 1970s is telling. As one study of wage determination over this period argued, “there appears to be some threshold at which the rate 27Wecanmakeareasonablecasethatreactionsoflaborcoststoactualinflationwereanimportantfeatureofthe inflation process in the 1970s. In particular, without this channel’s being present, it is nearly impossible to explain whymovementsinfoodpricesleftadurableimprintoncoreinflation—unlikeenergy,whichcanplausiblybeviewed asabroaderinputtoindustry,changesinagriculturalpricesshouldn’tactlikeacostshocktofirmsoutsidethefood sector. 28Ontheotherhand,perhapspeopleactuallydoexpect(say)thataperiodof3percentinflationwillbefollowedby acorrespondingintervalof1percentinflation,leavingthefive-to-ten-yearaveragearound2percent. ButIdoubtit. 29Likewise, the survey evidence on why people dislike inflation reported in Shiller (1997) indicates that a major concern is that their wages won’t keep up with price increases—which certainly doesn’t suggest that they view themselvesashavingmuchbargainingpowerwiththeirexistingemployer. 30Similarly,firmsmightalsostillbeveryconcernedwiththeircosts,butarelativelysmallportionofthesecostswill co-move with economywide inflation (beyond those induced by changes in import prices) given that wages are not closelytiedtoactualinflationandgiventhat—withtheexceptionoflaborandimports—onefirm’sinputcostincrease isanotherfirm’soutputpriceincrease. 12

of change in living costs becomes a pervasive factor of which account has to be taken in wage decisions,”andthat“[i]tiswhentheupwardmovementofpricesquickens,andextendssubstantiallythroughoutthewholerangeofconsumergoodsandservices,thatwagesbegintorespond directly to price movements.” That threshold was apparently reached around the mid-1960s, whentherateofincreaseintheCPImoveduptoaround3percent,with“theadvanceextending to most of its components” and with the food at home component rising by 5 percent.31 Hence,thecurrent(post-1995)stateofinflationdynamicscouldreflectasituationwhereinflation simply does not enter workers’ employment decisions—people no longer (or don’t often) quit a job because their wages aren’t keeping up with the cost of living (which is not to say that they won’t do so if they believe that they can get higher pay elsewhere—money is money, after all—and especially when conditions in the labor market reduce the likelihood of undergoing a prolongedspellofunemploymentbeforefindingabetter-payingjob). Thissituationisdifferentto one where an adaptive expectations channel is operative—under the alternative interpretation, expectations are irrelevant in the sense that there is no attempt to leapfrog or make up for anticipated inflation “in advance” by negotiating a higher nominal wage. Rather, the current period represents one in which inflation isn’t on workers’ “radar screens” anymore (or is at least is only a very tiny blip), which in turn yields an outcome where current price inflation does not respond(much)topastinflation(becauseinflationisnotamajorfactorinwagedetermination).32 Even if one is not willing to concede that inflation expectations are utterly irrelevant, it is still necessary to explain why it would be that long-run expectations appear to be the ones that pin down actual inflation. It turns out to be possible to come up with an explanation along these lines, but it takes a bit of doing. First, assume that the “true” inflation equation has a role for short-run expected inflation (say becausetheseexpectationsinfluencewage-settingbehavior—orsimplytakeyourpickfromone ofthetheoreticalmodelsdescribedinsectionIII).Specifically,assumethattheworldisdescribed by a version of a Phelps–Friedman Phillips curve: π t = β(U t −U t ∗ )+(1−φ)π t−1 +φE t−1 π t +ζZ t +e t , (1) whereπ denotesinflation,(U −U ∗ )isameasureofrealactivity(forexample,theunemployment t t t 31SeeDouty(1975). Thisstudyalsofindsthatcontractsconcludingin1974thatdidnotcontainexplicitescalation clauses tended to see larger average wage increases over the contract period than did contracts with escalation provisions,andnotesthatthisevidencemightbeconsistentwiththeideathatanticipated inflation—thatis,short-run inflation expectations—might have started to enter into wage contracting around this time. However, this evidence isalsoconsistentwiththenotionthatthelackofanexplicitescalatorprovisionwouldintroduceaninsurancemotive intowageagreements;mostlikely,itreflectsthefactthatexplicitescalatorclausescontainedcapsorotherprovisions suchthatonlyabouthalfofagivenincreaseintheCPItendedtoshowupasacost-of-livingadjustment. 32IfthissituationsoundslikeformerFedchairAlanGreenspan’s(2002)definitionofpricestabilityas“...anenvironmentinwhichinflationissolowandstableovertimethatitdoesnotmateriallyenterintothedecisionsofhouseholds andfirms,”that’sbecauseitbasicallyis. 13

gap), Z is a vector of supply shocks, e is an error term, and where the relevant expectation is t t E t−1 π t (that is, last period’s expectation of the time-t inflation rate—a short-run expectations concept). Note also that the coefficient values are such that a permanent change in expected inflation eventually passes through one-for-one into actual inflation. Now assume that that agents use the following inflation forecasting rule to formulate their oneperiod-ahead inflation expectation: E π = c +c π , (2) t t+1 0,t 1,t t or equivalently (lagging one period), E t−1 π t = c 0,t−1 +c 1,t−1 π t−1 . (3) Here, the presence of the time subscripts on the rule’s parameters reflects the possibility that agentsmightupdatetheirforecastingruleovertime—forexample,ifsomekindofleast-squares learning process were at work where agents revise the parameters of the rule by applying a gain to realized forecast errors. (Absent any forecast errors—or absent forecast errors that are sufficiently persistent or outside a certain range—agents are assumed to keep the coefficients of their forecasting rule fixed.) When the forecasting rule has c < 1, so agents assume mean- 1 reversion in inflation, long-run expected inflation at t −1 will equal πLR = c 0,t−1 . (4) t−1 1−c 1,t−1 (Of course, agents could instead assume that inflation follows a random walk—leaving us with an accelerationist Phillips curve—but in that case, there would not be an interesting distinction between long- and short-run expectations.) Substituting the forecasting rule (3) into the Phelps–Friedman specification (1) yields π t = β(U t −U t ∗ )+(1−φ)π t−1 +φ[c 0,t−1 +c 1,t−1 π t−1 ]+ζZ t +e t , (5) which, after a bit of manipulation (and again using the fact that long-run expected inflation will equal the unconditional mean of the forecasting rule) gives us π t = β(U t −U t ∗ )+(1−φ+φc 1,t−1 )π t−1 +(φ−φc 1,t−1 )π t L − R 1 +ζZ t +e t . (6) The expectation of long-run inflation in this sort of world will likely be self-fulfilling: With a zero unemployment gap and no supply shocks, actual average inflation will equal the long-run mean obtained from the inflation forecasting rule. If correct, such a description of the world would carry two important implications. 14

• First,eventhoughtheunderlyingpricingequationdependsonshort-runexpectedinflation,the full inflation equation that obtains will manifest a dependence on long-run expected inflation and actual past inflation (with coefficients that sum to one). Moreover, if agents continue to updatetheirforecastingrule,bothlong-runexpectedinflationandinflation’slong-runmeanwill themselves be time-varying.33 • By contrast, if this updating process were to stop—for example, if in a learning framework the gain on realized forecast errors were to go to zero—then long-run expected inflation (and inflation’s estimated stochastic trend) would be constant. Whatthissecondpointsuggestsisthattheobservedstabilityofbothobservedlong-runinflation expectations and inflation’s stochastic trend is consistent with a situation in which agents no longer update their perceived law of motion for inflation (put differently, a gain close to zero will weaken the statistical evidence for a unit root in actual inflation). This state of affairs will in turn be reasonable so long as the forecast errors that result from setting expectations in this manner are relatively small—or, if large, not very persistent. It also doesn’t preclude continued attention to inflation on the part of households—they are still making forecasts—but rather requires them to see no pressing need to revise or update the “parameters” of their forecasting rule. Finally, a situation like this is also not at odds with actual inflation developments playing a limited role in workers’ employment decisions, since “on average” a steady rate of nominal wage increases (evenonethatimpliesapaceofrealwageincreasesthatlagstrendproductivitygrowth)willstill ensure that workers’ earnings won’t fall too far out of line with the cost of living. Importantly,thisexplanationlinesupwithanothersalientfact: Agents—specificallyhouseholds— stillappeartopayattentiontoinflationinothercontexts. Inparticular,thereisastrongcorrelation between consumer sentiment and actual inflation, even since the mid 1990s; likewise, actual inflation appears to influence short-run expected inflation (and even long-run expected inflation to a more-limited degree).34 Again, these observations are consistent with the notion that agents see no reason at present to make large changes to their view of the inflation process (“updates to their forecasting rule”), but they also hint at the mildly disturbing possibility that inflation might not be quite as far off households’ radar screens as we might hope.35 33Ifagentsonlyupdatetheinterceptoftheforecastingrule(butnottheirassessmentofinflationpersistence),the coefficientsonπ t−1 andπ t L − R 1 inequation(6)willbeconstant. 34The relationship between consumer sentiment and inflation is a well-known and long-established stylized fact amongconsumptionforecasters,asistherelationshipbetweensentimentandmeasuresofrealactivityandhousehold wealth. (Of some possible interest for thinking about wage determination, there does not appear to be an economicallyorstatisticallysignificantrelationshipbetweenchangesinthequitrateandchangesininflationoverthe pasttwentyyears.) 35Whatthesefactsseemtobeinconsistentwith,however,isanexplanationbasedonstrictrationalinattention: In astandardmodelofthatsort,agentswhodidnotconsiderinformationaboutinflationtobeimportantwouldsimply ignoreitcompletely;bycontrast,oncetheypaidattentiontoitinonecontext(sentiment),therewouldbenoreason 15

VI Possible practical implications Fewthingsarehardertoputupwiththantheannoyanceofagoodexample. MarkTwain,TheTragedyofPudd’nheadWilson(1894) Atpresent,aninflationanalystgeneratinginputstopolicydecisionsshouldbemainlyconcerned with the possibility that inflation’s stochastic trend is once again starting to react to changes in actual economic conditions, as such a situation could be a harbinger of a return to a regime with high inflation persistence. However, if the preceding description of inflation dynamics is correct, movements in measures of short-term or long-term expected inflation will probably not provide a very accurate real-time indicator of whether this situation is starting to emerge—and, byextension,whether actualinflationisstartingtobecomeamaterialfactorinagents’ decisionmaking.36 Similarly, statistical estimates of inflation’s long-run trend are likely to suffer from the usual endpoint problems that plague filtering exercises. So is there anything else that analysts or policymakers might try to monitor? Onedevelopmenttowatchforwouldbeanyevidencethatarenewedconcernwithpriceinflation was starting to affect wage determination—either in statistical form (for example, if reducedform models of wage growth that assumed a stable long-run trend were to see errors emerge that appeared to be correlated with actual inflation) or in the form of anecdotes. To the extent possible, we might also try to determine whether quit rates were starting to rise in a manner that was less tied to the state of the labor market and more correlated with consumer price developments,orwhetherwageincreasesfornewhireswerestartingtoriseappreciablyrelative to wage increases for workers in continuing employment relationships (the argument being that wages for new hires are more flexible and hence more responsive to economic conditions). Unfortunately, these are developments that would probably only become clear over a span of several years, not over a few months or quarters. Another practical implication is rhetorical. By telling policymakers that expected inflation is the ultimate determinant of inflation’s long-run trend, central-bank economists implicitly provide too muchassurancethatthisclaimissettledfact. Advicealongtheselinesalsonaturallybiasespolicymakers toward being overly concerned with expectations management, or toward concluding that survey- or market-based measures of expected inflation provide useful and reliable policy toignoreitinanothersphere(employment)unlesstheyfounditsignificantlymoredifficulttounderstandor“process” theimplicationsofchangesininflationinthelattercontext. Itshouldalsobepointedoutthatthejustificationgiven hereforthepresenceoflong-runexpectedinflationinthePhillipscurvecan’tsayanythingaboutanotherimportant observedchangetotheinflationprocess—namely,whythepricePhillipscurvehasflattenedovertimeeventhough thewagePhillipscurvehasnot. 36As noted, movements in measures of expected inflation—which even today can be relatively large and persistent—donotappeartocontainmuch(orany)informationaboutinflation’sstochastictrend. 16

guideposts. And in some cases, the illusion of control is arguably more likely to cause problems than an actual lack of control. VII Possible policy implications Interviewer: Whatwasyourintention? R.Crumb: Idon’tknow. IthinkIwasjustbeingapunk. ThomasMaremaa,“WhoIsThisCrumb?” NewYorkTimes,October1,1972 Related to this last point, an important policy implication would be that it is far more useful to ensure that inflation remains off of people’s radar screens than it would be to attempt to “reanchor”expectedinflationatsomelevelthatpolicymakersviewedasbeingmoreconsistentwith their stated inflation goal.37 In particular, a policy of engineering a rate of price inflation that is high relative to recent experience in order to effect an increase in trend inflation would seem to run the risk of being both dangerous and counterproductive inasmuch as it might increase the probability that people would start to pay more attention to inflation and—if successful—would lead to a period where trend inflation once again began to respond to changes in economic conditions.38 Thissortofconcernisnotmerelyacademic. EmpiricalestimatesofPCEpriceinflation’slong-run trend typically yield point estimates that are slightly below the Federal Reserve’s stated longerrun target of two percent (Rudd, 2020). Hence, even if anchored long-run inflation expectations actually are the reason that trend inflation is currently stable, it appears that the level at which they are anchored isn’t fully aligned with the Federal Reserve’s policy goal. A related issue is more pragmatic. In some ways, the situation that arises from a focus on long-term inflation expectations is similar to one in which a policymaker seeks to target a single indicator of full employment—for instance, the natural rate of unemployment. Like the natural rate, the long-run expectations that are relevant for wage and price determination cannot be directly measured, but instead need to be inferred from empirical models. Hence, using inflation expectations as a policy instrument or intermediate target has the result of adding a new unobservable to the mix. And, as Orphanides (2004) has persuasively argued, policies that rely too 37Evenifapolicymaker’stargetforactualinflationisinformedbyacarefullydetermined“optimal”levelofinflation, it seems plausible that the loss to policymakers from having actual inflation persistently average slightly above or belowthattargetwouldbesmallerthanthelossthatwouldobtain(fromanoverallstabilizationstandpoint)byhaving inflationbehaveinamorepersistent,“accelerationist”manner. 38Likewise, the single observation that we have suggests that returning to a regime where trend inflation is once again invariant to the state of the economy would be difficult and costly: Even the Volcker disinflation wasn’t able to achieve this outcome, since inflation’s long-run trend persistently moved lower once again after the 1990–1991 recession. 17

heavily on unobservables can often end in tears. One might also be uneasy about policymakers’ relying too heavily on the assumption that inflation’s long-run trend will remain stable going forward so long as measured long-run inflation expectations do. Even if every one of my preceding arguments is judged by the reader to be completely unconvincing, it nevertheless remains the case that we have nothing better than circumstantial evidence for a relationship between long-run expected inflation and inflation’s longrun trend, and no evidence at all about what might be required to keep that trend fixed (beyond that it might involve keeping actual inflation from moving up too much above two percent on a sustained basis). Given the huge boon to stabilization policy that results from a stable long-run inflationtrend,actionsthatmightjeopardizethatstabilitywouldappeartofaceanunusuallyhigh cost-benefit hurdle. VIII A closing thought Thebestlackallconviction,whiletheworst Arefullofpassionateintensity. W.B.Yeats,“TheSecondComing”(1920) Consider the following Gedankenversuch. Say you had never heard of Phelps or Friedman, and only knew that the stochastic trend for inflation (and labor costs) last shifted noticeably following a recession that occurred after a period whenactualinflationhadbeenrunningatfourpercent. Youthencameacrosssomesurveymeasures of long-run expected inflation that roughly showed the same one-time level shift. Would you be convinced enough by this evidence to conclude that long-run inflation expectations were an important factor driving inflation dynamics? Or would you be skeptical of this conclusion because it is basically derived from a single observation (with later observations providing no evidence at all), and because one could just as easily explain these facts with an appeal to the notion that agents were simply making forecasts of inflation that were roughly correct on average? How would you also explain that a recession permanently reduced trend inflation when actual inflation was four percent, but never did so thereafter? Or would you justify the view that expectations “matter” by pointing to the inflation experience of the1960sand1970s,eventhoughthatperiodprovidesnoactualevidencethatworkersorfirms tried to boost their wages or raise their prices in anticipation of future price or cost changes? After all, history really only tells us that lags of actual inflation seem to enter inflation equations toagreaterorlesserdegreeovertime,notthatexpectationsdoordid;thinkingthattheselagsof 18

inflation are present because they are a proxy for some kind of forecast is more a habit of mind than anything solidly grounded in fact. Alternatively,ifyouviewthetheoreticalargumentsasdispositive,exactlyhowwouldyouexplain to a fellow economist why it is that you see an important role for expected inflation in inflation dynamics? Would you make a halfhearted appeal to Phelps and Friedman? Would you feel a little guilty doing so, knowing that these authors either assumed such a role for expectations (Phelps)ormotivateditwithatheoreticalmechanismwhosebasicpredictionsareclearlywrong (Friedman)? Ifnot,thenhowwouldyouexplainthat,inreality,onlylong-runinflationexpectations seem even vaguely related to actual inflation? And if you tied your explanation to some sort of “wagebargaining”mechanism,whatexistinginstitutionalfeatureoftheeconomywouldyoupoint to in order to justify it? Would you instead try to fall back on the new-Keynesian Phillips curve, whose theoretical derivation is even harder to take seriously and whose empirical justification is close to nonexistent? And would you feel the slightest bit nervous (or chagrined) about any of it? 19

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1. Response of Core Inflation to an Unemployment Gap Shock 0.25 1975 Integral multipliers 0.20 1985 0 to 4 0 to 8 1975 0.32 0.45 1995 1985 0.23 0.28 1995 0.19 0.19 0.15 2019 2019 0.14 0.16 Note: Cumulated IRF for inflation 0.10 divided by cumulative IRF for unemployment gap over quarterly span shown in column header. 0.05 0.00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Quarter after shock Note: Percentage point deviation from baseline; core inflation defined using market-based PCE price index. 2. Long-Term Inflation Expectations and Long-Term Trend Inflation Percent 9 8 Professional forecasters 7 (blackline) 6 5 4 Households (redline) 3 2 1 Estimated long-term trend (dashed line) 0 1980 1985 1990 1995 2000 2005 2010 2015 Note: Household expectations are median long-term expectations from the Michigan survey (University of Michigan, Survey Research Center, Surveys of Consumers, http://new.sca.isr.umich.edu/). Expectations for professional forecasters are derived from the Survey of Professional Forecasters, Federal Reserve Bank of Philadelphia. 24

3. Total and Core PCE Price Inflation Since 1960 Percent 14 12 Total (redline) 10 8 Core (blackline) 6 4 2 Estimated long-term trend (dashed line) 0 -2 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Note: Inflation computed as four-quarter percent change (total or core PCE price index via Bureau of Economic Analysis). 4. Stochastic Trends for PCE Price Inflation and Trend ULC Growth Percent 9 8 7 6 PCE price inflation (black, dashed) 5 4 3 Trend ULC growth (blue, solid) 2 1 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 25