Rational Expectations, the Real Rate of Interest, and the Natural Rate of Unemployment
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THOMAS J. SARGENT University of Minnesota Rational Expectations, the Real Rate of Interest, and the Natural Rate of Unemployment THE INTERACTION OF EXPECTED INFLATION and nominalrates of interest is a topic that has receivedits share of attentionsince Milton Friedman gave IrvingFisher's theory a prominentrole in his presidentialaddress to the AmericanEconomic Association in 1967.1The relationshipbetween interestand expectedinflation depends intricately on the interactionsof the real and financialsectors of the economy, so that the subjectof this paperlies in the domain of macroeconomicanalysis. Partial equilibrium analysiswon't do. Therefore,even thoughmy mainsubject is the relation- ship betweeninterest rates and expectedinflation, there is no way to avoid such mattersas the natureof the Phillipscurve, the way expectationsare formed,and, in some formulations,the sizesof variousinterest elasticities: those of the demandand supplyfor moneyand those of aggregatedemand and its components. Note: The researchunderlying this paper was financedby the FederalReserve Bank of Minneapolis,and earlier researchthat was an indirect input was supportedby the National Bureauof EconomicResearch. Neither institution is responsiblefor the paper's conclusions.I benefitedfrom discussionswith Neil Wallace,Arthur Rolnick, Christopher A. Sims, and membersof the Brookings panel, none of whom, however, can be held responsiblefor any errors.Thomas Turnerprovided valuable help with the calculations. 1. Milton Friedman,"The Role of Monetary Policy," AmericanEconomic Review, Vol. 58 (March 1968),pp. 1-17. One statementof Fisher'stheory can be found in Irving Fisher. The Theoryof Interest(MacMillan, 1930), pp. 399-451. 429 430 Brookings Papers on Economic Activity, 2:1973 Thus, considerIrving Fisher's theory. In one interpretation,it asserts that an exogenousincrease in the rate of inflationexpected to persistover a given horizonwill producean equivalentjump in the nominalyield on bonds of the correspondingmaturity. That assertionconcerns the way the whole economyis put together;in particular,it is aboutthe reducedform equationsfor nominalrates of interest.If it is to hold, variousrestrictions mustbe imposedon the parametersof the structuralequations of a macro- economicmodel, which in turnimply important restrictions on the reduced form equations for endogenousvariables besides the interest rate-for example, aggregateincome and prices, variablesthat properlyconcern policy makersmore than do nominalinterest rates. For example,in stan- dardIS-LM-Phillips curve models,2 the responseof the interestrate to an exogenous shock in expectedinflation, like the response to any other shock that affects aggregatedemand, is distributedover time.3 A once- and-for-alljump in expectedinflation eventually leaves the real rate of interestunaltered, but in the shortrun drives it down and outputUp.4 Only in the specialcase in whichthe LM curveis vertical,the IS curveis hori- zontal, or the short-runPhillips curve is vertical(price adjustments being instantaneouswhenever employment threatens to deviate from full em- ployment)does an increasein expectedinflation produce an immediate, equivalentjump in the nominal interestrate.5 These special sets of pa- rametervalues obviously impart a very monetaristor classical sort of behaviorto the model. On this interpretationof Fisher'stheory, all of the parametersinfluenc- ing the slopesof the IS, LM, and Phillipscurves are pertinent in evaluating its adequacy.Conversely, evidence that the theoryseems adequate contains indirectimplications about the parametersof the macroeconomicstruc- ture, and thereforemight have some clues relevantfor evaluatingthe relativeefficacy of monetaryand fiscalpolicies. 2. See, for example,Martin Bailey, National Incomeand the Price Level: A Study in Macrothieory(McGraw-Hill, 1962), especiallypp. 49-54, which contains a good exposi- tion of Fisher'stheory from the standpointof the standardmacroeconomic model. 3. This point has been made by EdwardJ. Kane, among others.See "The Rasche and AndersenPapers, A Commentby EdwardJ. Kane,"Journal of Money,Credit and Bank- ing, Vol. 5 (February1973), Pt. 1, pp. 39-42. 4. Some of Keynes'views about the effect of an increasein expectedinflation on in- terest and employmentare containedin John MaynardKeynes, The GeneralTheory of Employment,Interest and Money (Harcourt,Brace, 1936), pp. 141-43. 5. For example,see ThomasJ. Sargent,"Anticipated Inflation and the Nominal Rate of Interest,"Quarterly Journal of Economics,Vol. 86 (May 1972), pp. 212-25. ThomasJ. Sargent 431 While the precedingstatement of Fisher'stheory may be of interestin highlightingits macroeconomiccontent, the theory can be stated in an alternativeand less confiningform, whichprobably comes closerto what modernadherents to Fisher'sdoctrine have in mind. This statementis less confiningbecause its truthdoes not requireany restrictionson the magni- tudes of the slopes of the IS, LM, and short-runPhillips curves. Further- more, it does not involvepursuing the implicationsof an exogenousjump in expectedinflation. Instead, expectations of inflationare assumedto be endogenousto the systemin a veryparticular way: they are assumedto be "rational"in Muth'ssense6-which is to say that the public'sexpectations are not systematicallyworse than the predictionsof economic models. This amountsto supposingthat the public'sexpectations depend, in the properway, on the thingsthat economictheory says they oughtto. Beyond this, the alternativestatement of Fisher'stheory assumesthat the Phelps- Friedmanhypothesis of a naturalrate of unemploymentis true, and thus that no (systematic)monetary or fiscal policiescan producea permanent effecton the unemploymentrate.7 Given these two hypotheses(which are relatedto one another,since it seems impossibleto give the naturalrate hypothesisa properformal statement without invoking the hypothesisof rationality),it follows that the real rate of interestis independentof the systematic,or foreseen,part of the money supply,which therefore can in- fluencethe nominalrate only througheffects on expectedinflation. The notion that the real rate of interestis independentof the systematic part of the money supplyembodies the key aspect of Fisher'stheory ap- pealedto by Friedmanin his presidentialaddress. To obtainthis property for the real rate requiresno assumptionsabout the slopes of the IS, LM, and short-runPhillips curves, for rationalityand the naturalunemploy- ment rate hypothesisare sufficientto supportit. From this point of view, then,the importantthing is not the responseof the systemto an exogenous shift in expectedinflation. It is importantto determinethe relationshipthat the standardway of empiricallyimplementing Fisher's theory bears to the precedingstatement 6. John F. Muth, "Rational Expectations and the Theory of Price Movements," Econometrica,Vol. 29 (July 1961), pp. 315-35. Some very important implications of assumingrationality in Muth'ssense in certainkinds of models of forwardmarkets were pointed out by Paul A. Samuelson in his "Proof that Properly Anticipated Prices FluctuateRandomly," Industrial Management Review, Vol. 6 (Spring 1965), pp. 41-49. 7. See EdmundS. Phelps, InflationPolicy and UnemploymentTheory: The Cost-Benefit Approachto MonetaryPlanning (W. W. Norton, 1972), pp. 35-43. 432 Brookings Papers on Economic Activity, 2:1973 of the theory.Irving Fisher and most of his followers8have implemented the theoryby estimatinga model of the form =p + 7r + ut n T= wwi (pz -Pts-1)3 i=O wherert is the nominalrate of interest,p is a constant,7rt is the unobserva- ble expectedrate of inflation,pt is the logarithmof the pricelevel, wi and n are parameters,and ut is a randomerror assumedto be distributedin- dependentlyof past, present,and futurevalues of p. Thesetwo equations have typicallybeen combinedto yield the equation n -=E (A-4 + Ut + P3 i=O wi Pt-i-1) whichhas been estimatedby a variantof the methodof least squares.The wishave been interpretedas estimatesof the distributedlags by whichthe publicforms its expectationsof inflation.(Some of Fisher'sfollowers have addedsome regressorsin an effortto improvehis equation.9) Generallyspeaking, the resultsof estimatingthis equationhave reflected poorly on the model. For data extendingover very long periodsof time, estimatesof the wis depictextraordinarily long distributedlags, much too long to be useful in forming predictionsof inflation.Consequently, the estimatedwis do not seem to providea plausibledescription of the way peopleform expectations of inflation-at least if they do so in an informed way.'0 For this reason, Fisher'sempirical results have often been viewed with suspicion." 8. For example, see William E. Gibson, "Price-ExpectationsEffects on Interest Rates," Journalof Finance,Vol. 25 (March 1970), pp. 19-34, and WilliamP. Yohe and Denis S. Karnosky, "InterestRates and Price Level Changes, 1952-69," Federal Re- serve Bank of St. Louis, Review,Vol. 51 (December 1969), pp. 18-38. 9. For example, see Martin Feldstein and Otto Eckstein, "The FundamentalDe- terminantsof the InterestRate," Reviewof Economicsand Statistics,Vol. 52 (November 1970), pp. 363-75. 10. This point has been madeby PhillipCagan in Determinantsand Effects of Changes in the Stock of Money, 1875-1960 (ColumbiaUniversity Press for the National Bureau of Economic Research, 1965), pp. 252-59. 11. Nerlove has proposed comparingregressions of dependentvariables (like rt) on currentand lagged proxies for psychologicalexpectations (like pt, pt-i, . .) with the distributedlags