The Un-Natural Rate of Unemployment

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American Economic Association

The Un-Natural Rate of Unemployment: An Econometric Critique of the NAIRU HypothesisAuthor(s): David M. GordonSource: The American Economic Review, Vol. 78, No. 2, Papers and Proceedings of the One-Hundredth Annual Meeting of the American Economic Association (May, 1988), pp. 117-123Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/1818108

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CHALLENGINGOMECONVENTIONALWISDOMSABOUTTHELABORMARKETt

The Un-NaturalRate of Unemployment:An Econometric Critique of the NAIRUHypothesisBy DAVID M. GORDON*

Few ideas have taken such firm hold inneoclassical economics as the concept of a"natural rate of unemployment" (see my1987 paper). The transformation of the pre-vailing wisdom is compactly illustrated bythe evolution of the profession's exemplaryelementary textbook, Paul Samuelson's Eco-nomics. In his 8th edition, Samuelson de-fined "full employment as a condition where96 1/2 percent of the labor force are em-ployed, rather than where only 94 or 95percent are employed" (1970, p. 801). By the12th edition in 1985, reflecting the new con-ventional wisdom, Samuelson (with WilliamD. Nordhaus) reports: "Modern mainstreammacro says that there is a natural rate ofunemployment -today around 6 percent-below which the economy cannot go withoutrunning the straits of inflation" (p. 766).Reporting on work-in-progress, I arguethat this "modern mainstream macro" viewis unwarranted. (See my 1988 paper for amore complete presentation.) I concentratehere on only two strands of the argument. Ifirst present econometric evidence that, evenon its own terms, the natural rate hypothesisdoes not provide a convincing explanation ofthe deteriorating tradeoff between inflation

and unemployment in the United States fromthe 1960's to the 1980's. I then suggest thatthe basic models underlying that hypothesis,upon which the hoary visions of acceleratinginflation are grounded, themselves providesubstantially incomplete representations ofthe dynamics of wage and price determina-tion and consequently suffer from under-specification bias. Once one takes account ofstructured mediations of capital-labor con-flict and dynamic interactions between eco-nomic growth and pricing strategy, pre-vailing conclusions of a vertical tradeoffbetween unemployment and inflation beginto dissolve.I. The Econometrics of a Rising NAIRU:Where's the Beef?

Some argue that the natural rate of unem-ployment has increased simply because thedemographic composition of the labor forcehas changed. This argument is incompleteand essentially tautological, since by itselfit embodies no stochastic tests of the linkbetween these demographic changes andchanging dynamics of wage and price de-termination.I have therefore concentrated on directstochastic applications of models of the nat-ural rate hypothesis, focusing on notions ofan "equilibrium" or "non-accelerating-infla-tion" rate of unemployment (NAIRU). (SeeG. E. Johnson and P. R. G. Layard, 1986,for a general review.)This method is most compactly sum-marized for a reduced-form inflation equa-tion in which the dependent variable in anominal wage-change equation is substitutedas an independent variable into a price-

tDiscussants: Orley Ashenfelter, Princeton Univer-sity; Marvin Kosters, American Enterprise Institute;Robert Topel, University of Chicago.*Department of Economics, Graduate Faculty, NewSchool for Social Research, 66 W. 12th St., New York,NY 10011. I am grateful to Robert J. Gordon forsharing his data and to members of the Center forDemocratic Alternatives Macro Working Group forhelpful discussion. This work was partly supported by aresearch grant from the National Science Foundation.

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118 AEA PAPERS AND PROCEEDINGS MA Y 1988change equation, resulting in a reduced-forminflation equation in which current inflationis a function of expected inflation, a de-mand-pressure variable, and a variety ofother "supply-side" influences on wage-pricedynamics. Relying on Robert J. Gordon'selaboration and notation (1985, pp. 267-71),this reduced-form equation for price changeover time can be written as(1) p=pe+m(v)+(l/a+b)[hgX+z],where time subscripts are suppressed, lower-case letters designate time derivatives, P isthe product price; pe is the expected prod-uct price; M is the markup expressed as afunction of V, measuring conditions of ex-cess demand in the commodity market; X isa measure of excess labor-market demand(for example, of "excess" unemployment); Zis a vector of other supply-side influences; aand b are, respectively, the real-wage elastic-ities of labor demand and supply; g is thecoefficient of dynamic labor-market adjust-ment to the gap between demand and supply;and h is the proportion of domestic inputsin total final product. As written, the coeffi-cient of 1.0 on pe indicates that equation (1)satisfies the conditions of perfect adjustmentof current to expected rates of price change.The definition of the NAIRU follows di-rectly from (1). At a constant level of excessdemand (v = 0), inflation accelerates (p >pe) whenever X is positive and decelerateswhenever X is negative. If we (i) use the rateof unemployment (U) as a measure oflabor-market demand pressure and designateU* as the NAIRU; (ii) allow a constant (cl)to appear in the equation; (iii) denote[- hg/(a + b)] = C2; and (iv) impose the re-striction that p = pe, we can then use (1) tosolve for U*:(2) U*= [cl(a+b)+z]/-hg;or U*=C1/C2 whenz=0.

If z were equal to zero, we get whatR. J. Gordon calls the "no-shock" naturalrate (hereinafter abbreviatedas NAINORU),or U*N. If supply "shocks" are manifest

(and, therefore, accommodated), we get whatI would call the non-accelerating-inflation,shock-accommodating rate of inflation(NAISARU), or U*s.Gordon has provided what appear to bethe most robust estimates of these relation-ships for the United States (see 1985 andreferences to other work therein). Accordingto his specification and estimation, theNAINORU increased from roughly 4.5 per-cent in the 1950's and 1960's to roughly 6.0percent in the 1980's. In order to set aside(as much as possible) issues of variable defi-nition and data commensurability, I havebased all of the discussion in this section onGordon's data and specifications.It is worth stressing at the outset that arising natural rate of unemployment doesnot follow automatically from this approach.Most concretely, if we use the measuredaggregate unemployment rate as the directmeasure of labor-market demand pressure in(1) and assume that there are no supplyshocks, then the NAINORU is constant bydefinition, with U* = C1/C2, and can there-fore not have increased during the period ofestimation.

Working within this approach, however,one might still find at least three alternativekinds of econometric evidence for a risingNAIRU.A. A Weighted UnemploymentRate

Instead of the actual rate of unemploy-ment as a labor-market demand-pressurevariable, some use an unemployment rateweighted for changing demographic com-position (U W) on the grounds that the labormarket works more or less smoothly depend-ing on the (weighted) "quality" of the laborforce. If UW is substituted for U in (1) and(2), then an estimate for U*w can be derivedfrom (2), still necessarily constant over time,while a variable estimate for U* is thenderived by an algebraic transformation basedon the variable difference between the actualand weighted unemployment rate: U* = U*w+ (Uw - U). This is the basis for Gordon'sestimate of a rising NAINORU since themid-1950's, since it does turn out that (UW- U) itself increased.


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VOL. 78 NO. 2 CHALLENGING CONVENTIONAL WISDOMS ABOUT THE LABOR MARKET 119

There are two principal problems with thismethod. First, the weighted-unemploymentrate, following George Perry's lead (1970,especially pp. 439-40), is itself constructedby using relative wages as weights for ag-gregating individual age-sex groups' share ofthe total labor force. This presupposes that(a) relative wage rates accurately and mono-tonically reflect differences in relative pro-ductivities; (b) those relative weights are sta-ble over time; and (c) relative labor marketdemand does not adjust sufficientlysmoothlyto (or, indeed, even partly cause) shiftingage-sex labor-supply composition so thatlabor-market friction can be taken to be adirect function of the demographic composi-tion of the labor force. All of these presump-tions seem sufficiently problematic that oneshould avoid their purely axiomatic presup-position and therefore not lean exclusivelyor too heavily on this particular variableconstruction.Second, this tactic implies that theweighted-unemployment rate is a bettermeasure of labor-market slackness than theactual unemployment rate-presumably be-cause the latter is more fraught with errors-in-variable than the former. But the econo-metric evidence supporting this estimatingtactic is weak at best. In the reduced-formspecification of (1), the explanatory power ofan equation using UW is empirically indis-tinguishable from one using U. (In a test fordifferences in the residual sum of squares ofthe two equations, F


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120 AEA PAPERS AND PROCEEDINGS MAY1988

II. The Dynamics of Perfect Adjustment:Where's the Vertical Line?

All the foregoing discussion reflects solelyon the evidence for a rising natural rate ofunemployment over a specific period of his-tory. It does not yet address the centralmicrofoundations of the idea of a naturalrate. Even if the preceding econometric evi-dence suggests that we have been operatingabove a constant NAIRU over the past 15years, with inflationary pressures from othersources, this in no way compromises theprevailing expectation that a reduction in theunemployment rate below the NAIRU,whatever its current level, would imme-diately trigger accelerating inflation.I therefore arrive at the theoretical punch-line of the natural rate proposition: it isbased on the notion that there is full adjust-ment of prices to wages (and vice versa) withno long-run tradeoff between inflation andunemployment.One of the strongest strands of empiricalevidence for a vertical long-run tradeoff be-tween inflation and unemployment, indeed,was that earlier Phillips curve equations hadbeen underspecified, inattentive to a varietyof additional supply-side determinants ofwage-price adjustment; the early Phillipscurve coefficients, normally falling signifi-cantly below 1.00, apparently suffered al-most fatally from underspecification bias.The econometrics could hardly have beenbetter scripted if Milton Friedman orEdmund S. Phelps had generated the datathemselves.But are more recent models of wage-priceadjustment any less vulnerable to such com-plaints?Upon reflection, it would be surprising ifit were not possible to improve upon prevail-ing accounts. In the NAIRU literature, mostempirical treatments of price adjustmentbuild from the sparest of markup models.And almost all analyses of nominal wagechange begin and end with only the faintestnod toward structured bargaining models orthe dynamics of capital-labor conflict. Butthe issue for my current purposes is not somuch the simplicity of prevailing specifica-tions as the robustness of their empiri-

cal estimates of the unemployment-inflationtradeoff when confronted with more texturedanalyses.Reporting on work-in-progress,I concludethat recent estimates supporting no long-runtradeoff between unemployment and infla-tion suffer from the same disease as theirearlier Keynesian predecessors: they are con-taminated with underspecification bias. Con-strained by space limitations I summarizehere only the most skeletal outlines of analternative account of wage and price de-termination-reviewing just enough of itsresults to suggest the shakiness of the pre-vailing NAIRU perspective. (See my work-in-progress both for more detail of argumentand for references to the literature on whichthis analysis builds.) Compared with morefully articulated models of wage and pricedynamics, it appears the vertical Phillipscurve begins to look like the leaning tower.

A. Wage DeterminationPrevailing mainstream models of wage de-termination seem incomplete along theoreti-cal, institutional, and historical dimensions.

I postulate an expanded model of wagedetermination which seeks formally to in-tegrate four main additional analytic con-cerns: 1) At the most general level, em-ployers set a target nominal wage in order toachieve the optimal level of labor intensity,while workers seek to achieve a target rate ofreal wage increase. 2) The relative influenceof these respective objectives is mediated bythe "reserve army effect," by the relativedisciplinary effectiveness of external labor-market conditions. 3) Structured wage bar-gaining, primarily in enterprises featuringunion representation, is additionally condi-tioned by the specific dynamics of labor-management expectations-in the UnitedStates, for example, primarily by the systemof "productivity bargaining." 4) The trajec-tory of wage bargaining in the United Stateswas critically affected after the early 1970'sby increasingly intensive "employers' offen-sives," themselves spurred by the profitsqueeze of the late 1960's.These four elements can be unified into asingle operational model of the determina-


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tion of nominal wage change. Estimated forthe United States over the postwar period,the model appears both to receive empiricalconfirmation for each of its constituent ele-ments and significantly to improve the ex-planatory power of mainstream models ofwage determination. The implications ofthose empirical results are summarized be-low.

B. Price DeterminationI have also sought more fully to elaboratemodels of price determination. Beginning asin many prevailing mainstream accounts

from a foundation of markup pricing, I haveattempted further to incorporate two ad-ditional dimensions of determination. 1)Traditional markup models pay insufficientattention to the richness of both short-termand longer-term influences on variations incompetitive pressure and therefore on thelevel of the markup over unit costs. 2) Tradi-tional markup models have paid too littleattention to target pricing models and, as aresult, to interactions between price deci-sions and expected market growth.It is possible to attend to these concernswithin the general framework of markuppricing models and thus to compare theirrelative importance with somewhat morestandard approaches. I have also estimatedsuch an extended model for the postwarUnited States; it also appears to receivestrong confirmation in the data.

C. The Long-RunTradeoffI shall review here only one aspect of theempirical results of these models: their im-plications for estimates of the long-runtradeoff between inflation and unemploy-ment. As noted above, the natural rate hingescritically on the coefficient on expected infla-tion-wage change in the relevant wage-change, inflation, or reduced-formequations.What happens to that coefficient in morefully specified models?Table 1 presents a compact report. Twoequations are summarized:an inflation equa-

tion, with expected nominal wage change asan independent variable; and a nominal

TABLE 1-THE EFFECTSOF ALTERNATIVE PECIFICATIONOF INFLATIONAND NOMINALWAGE-CHANGE

EQUATIONS: RESULTSFOR THE UNITED STATES,1954:II-1986:IIIInflation WageEquation Equation

Stage of Estimation &18/3pe1) Original Model 1.021 1.135Technical Modifications2) Adjust control vars. 1.053 1.0873) Adjust behav. vars. 1.012 0.777Substantive Modifications4) Long-run competition 0.8485) Expected demand growth 0.6836) Short-run bottlenecks 0.4157) Firm target wages 0.6218) Worker target wages 0.5439) Union bargaining 0.358

10) Surplus labor effects 0.33011) Management offensive 0.553

wage-change equation, with expected infla-tion as a right-hand side variable. For easeof interpretation, the equations begin withthe precise specifications deployed byGordon in his work, now estimated through1986, and then report on the effects of aniterative sequence of reestimated equations,with each iteration additively and cumula-tively modifying the previous specification.1The first stage reports on a series of techni-cal modifications necessary to translate fromthe benchmark models to specifications war-ranted by my own alternatives. The secondstage reports on the effects of each of thesubstantive behavioral additions outlinedabove. The rows report on each sequentialphase of model modification, while the single

'The specifications reported in the table as the"original model" differ from those reported in Gordon(1985) in a few minor respects: they report on estima-tions for separate wage-change and inflation equationsrather than the single reduced form; they are estimatedthrough 1986:III on Gordon's data (incorporating NIPArevisions) instead of through 1984:IV; they use poly-nomial distributed lags on the expected inflation andwage-change independent variables instead of step rec-tangular lag distributions; and they incorporate theactual unemployment rate as the demand-pressurevari-able in both equations. None of these changes signifi-cantly alters the results for the original model.


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122 AEA PAPERS AND PROCEEDINGS MAY 1988

column for each equation reports the sum ofthe estimated coefficients on the terms forexpected nominal wage change and inflation,respectively.Minor changes are involved in the phaseof "technical modifications." The adjust-ment of independent variables (row 2) in-volves some cleaning out of insignificantvariables from the original specifications andsome tranformation of a few other supply-side variables. The adjustment for "behav-ioral variables" (row 3) consists primarily ofchanges in the wage and productivity vari-ables from detrended indices for all em-ployees to measures expressed for produc-tion workers which are not detrended. Withthe exception of the "behavioral variable"adjustment in the wage-change equation,these technical modifications do not havemuch impact on the performance of theequations and in any case account for noneof the change in the expected-wage coeffi-cients in the inflation equation and only partof the corresponding change in the nom-inal-wage equation.Once one moves to the "substantive mod-ifications" (rows 4-6 and 7-10), one findsthat the estimated coefficients on expectedwage change-inflation drop markedly. Themodels' explanatory power also improves:the (unreported) adjusted R2 increases from.822 for the original inflation equation (row1) to .899 in row 6 and from .846 for theoriginal wage-change equation (row 1) to.911 in row 10.Why do these estimated adjustment coeffi-cients now fall so far below 1.00? Thesemodels and results are very preliminary and,at this stage, little more than exemplary. ButI nonetheless reach some provisional conclu-sions about their internal dynamics. In theinflation equation, wages are only partlypassed on for two main reasons: when de-mand growth is rapid, firms limit price in-creases in order to hold on to or expandtheir market shares; and when demandgrowth is slow, supply-side bottlenecks de-velop which either reduce competitive pres-sure or increase effective unit costs. In thewage-change equation, two factors seem toplay the largest role in moderating the effect

of price changes on wage changes: 1) Firms'target wages are defined solely with respectto labor extraction strategies and not withrespect to expected product prices; whileworkers' target real wage demands are likelyto moderate if recent real wage growth hasbeen especially rapid; and 2) wages in theunion sector both appear to exhibit someinertia and are modulated by fluctuations inthe real wage share through "productivitybargaining."

III. ConclusionMany if not most mainstream economists

have believed for some time that rising levelsof unemployment in the United States werewarranted by and largely reflected a "risingnatural rate of unemployment." The per-vasiveness of these beliefs has reflected inpart the widespread fascination with "newclassical" presumptions about instantaneousadjustment in product and labor markets.But their widespread acceptance has alsoreflected, to some large degree, a broadeningacceptance of econometric studies alleging tosupport the NAIRU hypothesis.The research summarized in this paper,although still provisional, would appear tocast considerable doubt upon those econo-metric foundations. And without such econ-ometric support, the belief that we cannotreduce unemployment in the United Statesbelow 6 percent (without "running the straitsof inflation") would appear to reflect littlemore than revealed and entirely contestabletheoretical preference, not hardened and un-yielding empirical fact.

REFERENCESGordon, David M., "Six-Percent Unemploy-ment Ain't Natural: Demystifying the Ideaof a Rising 'Natural Rate of Unemploy-ment'," Social Research,Summer1987, 54,223-46.___,"'But the NAIRU Has No Clothes':Institutions, Expectations, and the Infla-tion/Unemployment Trade-off," paper in

progress, New School for Social Research,


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1988.Gordon, RobertJ., "Understanding Inflationin the 1980s," Brookings Papers on Eco-nomic Activity, 1:1985, 263-99.Johnson, G. E. and Layard,P. R. G., "TheNatural Rate of Unemployment: Explana-tion and Policy," in 0. Ashenfelter and R.Layard, eds., Handbook of Labor Eco-

nomics, Vol. II, New York: North-Hol-land, 1986, 921-99.Perry, George L., "Changing Labor Marketsand Inflation," Brookings Papers on Eco-nomic Activity, 3:1970, 411-41.Samuelson,PaulandNordhaus,WilliamD., Eco-nomics, New York: McGraw-Hill, 8th ed.,1970; 12th ed., 1985.

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