SSc I he Nadtri u was obtained direcilfrom him and has beenused by h - PDF document

SSc: 'I he Nadtri u was obtained direcilfrom him and has beenused by hintrecent work on factor demands. The ('oenc came lrom his paperpNadiri uses a long-term government bondrate as he base for userCost, Coen theAAA bond yield. Nadiri adjusts tor thelnvestnieiit tacredit in962 and l)63hutadjustments for theI 94 and mid-changes in(Ieprecjatjctntuidelincs, C'oen does adjust for changesdepreciation guidelinesthe text, the Coen series is shorter titan thesample used in theregressio,ç in thispapet not using the Coen series, and Was crudelyconverted to a quarterlybasisthe purposesthis paper.Wage: Seasonally adtistedwage for manufacturingproduction workersadjusted for overtinle hours andinterindustry shifts (availableon NBER datahank. Original source in part BLSpublications

, though hack datafor seasonaiI'seriesas vet tinpublished).R.EFEREN( 'ES\ kaite, Fl. (I 967. "Some Pro blenisin the Application of the (ross-Spectra I Mcthod." fl01k edon Sp'tal -malt',,of Jon,' .S','ri,'. B. I larris. e,l, J Wiley afld Sons. N YA rne,1)i,i, 1. a rid W. A. I tiller (I 967) "A ('orfiparati;e Sin dv of Alternative Estimators ina i)isi,t_ag Model.'' Lionam,'iri,-i. Vol.35. No. 34, pp. 509 529Bischofl, C. (I 969) "I lypoliresis lestineand the Demand for Capital Goods"Rri,', o/ E onono,.i andStatism-s. Vol. Li. No. 3. pp. 354 368Coeri, R. M .I 96$. ''Effects ol Tax Policyon tn vestment in NI antufacturing,'''lit-i,-,,,, L,in,,nn,,Rrrnew (l'rae,','djng.,j Vol. 58, No. 2,pp. 200 211.I)hr)meS, P. J. )l969f 'A Model ofShort-Bun Labor Adtustment''in T/i' Brook-

,ns .%!odc/Sum,'Fr,lu'r R,'si,lj,, J. S. Duesenberry.ii al.. cd., Rand McNally, ChicagoEckstem 0. and T. A. Wilson 11964)."Short-Run Produetiiity Behaviorin U S Manufacturing"Rt'n'i,i,' o/ L,'on. and Stat,'ol. Xi.Vl, No. t, pp 41 54Eisner R and M. I. N,tdiri (1968)."InSeslnlncflt Behavior and theNeoclassical Theory," R'i'i'ii'oj&omiand Stat. Vol. 1.. No. 3.pp. 369382.Granget, C. W. J. (l969"Iris estigating Causal Relationsby Econometric Modelsand Cross-SpectralMethods," Eco,non,e,rjc,, Vol. 37, No.3, pp 424 438Hall. R F. and D. W. Jorgenson(1967). "Fax Policy and InvestmentBeha lOr," .100'rjcan Lcw,o,5,R,'i"j'\'ol. lvii, No. 3,pp 391 414Hannan, F. J.19631. "Regression for Time Series,'in i1n' Set-its .'lnalryjs.Murray Rosenbiatt ed,John Vile' and Sons, N.Y.I Iultgren,

l'hor(1965) Costs,Prue.s, amid Profits- i'/i('ir Co-lit-a!Relations. National Bureau ofEconomicResearch, New York.1967). "Estimatinga l.anged Regression Relation,'' Bionnetrjka,Vol 54. PP 409 4lJorgenson, I). W. (1963). "Capitall'heory and Investment Behavior,".'Imn&'ri,'a,n E,'o,n'n,ii,' Re,'i,',r(Proceedois( Vol. S3, No. 2,pp. 247- 259-(1969) "issues in the l)eelopmentof the Neoclassical Theoryof Iilsestrnent Behavior."P.i'u'iv of E,'on. mu! Stat., Vol.Li, No. 3. pp. 346 .253Kuh, F (1965), "('sclicai andSecular Labor Productivityin U.S. Manufacturing" Rt'rie'tcofJco,,andSuit., Vol. XLVII, No. I,pp. I- !2.Nadiri, M Iand S. Rosen 1)969)"Interrelated Factor I)enna nil I-uOct ion :'.,n,'ri, -anRm'r-u's- Vol. l.I.X. No. 4,pp. 457 421Nerloe, NI N (l97O. "OnLags in Ecoiio

nuic Behavior:'unpublished paper presentedas the SchultzLecture at the 1970 WorldCongress of the Economen,rjcSocietySargent, T J. (197i. "InterestRates and Pricesin the Long Run: A Studs of the GibsonParadox."unpuhlishd paper presentedat the May, 1971 meeting oftheseminarirn tinieeriesan,Idjstrihutedlags of the NBER-NSJ:Conference on Mathem,itrcalEconomics and EcononienricsSin,s. C'. A. )l97tj,"Money, Income .'rnd ('ausality"nhimco.Vahha G969) "Est,iiuiijon of theCoeljjcicnts in a Multi-l)iipensj0r,.ilDistrihutd Lag Model,"Eco:nonietrjca Vol. 37, No.3pp. 398407Waud, R. N (1968"Manhour Behaviorin U.S. Manufacturjiig- ANe(clacsic,l Inerpretatnon."Jourmnaj of Poll to',,! Ecoino1.Vol. 76, No. 3.pp. 407 427.* v(t) - ant1) + hy(: - 2).2. Definitions of Variables and Data So

urcesSurreyCurrent Business)Business StatisticsEmploymentiiiand Earnings).Business StatisticsEmplovineniand Earnings).reBusiness StatisticsCurrentr-Industrial Reports. Series M3-I, Manufacturers Shipments, Inrentories,and Orders)a 0/yields results alniost identical to those obtainedwith publishedseasonall adjUstdata.As can he seen by comparing Chart VIIwith Charts IlltIRI V. USC ofCon-sistcntIadtusted data has the expected cflectof fCi11O' ing theSeasonal patternfrom the sales on manhoursrcgressii.1i estimates. ihe flatterlag distrihtiti0obtained with the consistently adjusteddata for manhoursOn sales wouldheexpected if manhours not only weremore flexibly deseasonalj/e(lthan Sales, hutretained relatively more residualpower at the seasonal than safesIn terms of thefreq

uency doniain, the latter resultsuggests that the officialprocedures multiplymanhours by a function which hasa broad dip near seasonalfrequencies butwiththe dip not approachingzero as nearly as the correspondingdip for salesadjust.ment. Since the manhours series is obtainedfrom separatelyadjusted e11]ployzieand hours series, such "imperfect''seasonal adjustmentseems not at allunlikely.6. CONCI.USIONWe can recapitulate thispaper's results in orderoi increasing deLlreeofconflict with the assumptions ofpast research. First, the practiceof treating salesor output as exogenous in time seriesestimates of distributedlag acceleratormodels of investment has beenconfirmed as reasonableSecond doubts havebeen raised about thepractice of treating factor-pricevariables asexogenous

infactor-demand equations, at leastat this level of aggregation,At the very least,estimates of price efi'ects shoti Idbe accompanied bytests of the exogeneityassump-tion. Third. the practiceof treating salesas exogenous in labor demandfunctionshas been strongly rejected.There is evidence thata better approach to findingtheshort-run relation betweenlabor inputs andoutput is to estimateshort-runsingle-factor "productionfunctions," in which laborinput variablesare treatedas exogenous,L' lllrer,sjj V 0/A PPENJ)tXThe frequency domainestimation method appliedin this study is t-lannan'sinefficient procedure,as described in, e.g., \Vah ba(1969;. This method takestheestimated lag distributionforregressed on x as the inverseFourier transformof S 'S, whereSis a consistentestimat

e of thecross-spectral density ole andx and S is a consistentestimate of the spectraldensity matrix ofx. Theseestimateshave (under certainconditions on the lagdistribution, theautocovariance functionfor x andv, and the choice ofestimator for S and S)an asYmptotically normaldistribution withautocovarjince function givenby the inverse Fouriertransformof(l/T)s; 'Sn. whereS is the spectraldensity of the regressionresidual and Tissample size.The HannanineffIcient estimatorhas the greatadvantage that the estimatefor an individualcoefficient is independentof how ma,iother lagged values areincluded in theregressioii Thus thereis no need forrepeating the estimationprocedure several timeswhen the length ofthe lag distribution isnot well-deter-mined a priori. Themethod also cans

ave absolutely oncomputation time, evenfora singleregression estimate,because it exploits thefact that the sample variance-34S IIII /71'ISiS l()RIS i)"10LCIOOfl1)05!: Coeftcient15tLAo DisiRinurtoN FUR SMFS ON ttPLOYs1tNT ANt) WORKWFFKSales oi employmentSales ott .orkweekCocH cent3025201.51005 /2DISIRJnI;uuiN 10kIS (IN MANIIOUL1SITutu &IeS nFl lolut in i:eiipinrs012340678LdF;stuirters30ILI020 88.28*550.23* 0.1CIFwui050.40.3020CHART IvI.A(;ION lOR t'.t1l.()Y\fINl (SN SAl ISW((kI1.K ((N SAlS(S VeilIWorkweek on saies-3-2-10I2345670Lags in quartersCoeft iciest0.1-0.10.20 JL_L L-4-3-201234567 ITARLI 4EsrisiAlir) LM; DIs1kJfl1jNs tok INvEsrfI:NrON S&t isNote: See note to Table I. Exceptfor r:ght-han&I.tiis column,all these lag distrihu-uons are Iront trequency-dcmainestimate

squalification to all the resultsreported in this Section isthat the standarderrorof the residuals declinesby a factor ofapproximately two between theearlier andlater portions of thesample. The elects ofthis heteroskedasticityon the teststatistics are hard to judge.Probably there isno general bias, but probablynullhypotheses are too easilyrejected (degrees of freedomin the regressionsareexaggerated)The estimated lagdistributions for investmenton sales (see Table 4) accordwith the theory ofa distributed Jag accelerator.Coefficients are positive,and of theright order ofmagnitude. The fact that forthe two well-determineddistributions.total manufacturingand durables, thesum of coefficients over lags0 through 8 isclose to two andsignificantly greater thanone might seem sur

prising.However,the really longrun elect of outputgrowth on gross investmentworks entirelythrough depreciationIt seemsreasonable that for the firsttwo years output in-creases induce more thanproportionate increases ingross investment and thatthe negativecoefficients which bringthe total effect hackto unity are so spreadout over a long tailto the lag distributionthat they do not showup as significantin these estimatesThese results differfrom those ofsome previous investigatorsin finding thatthe largest individualcoefficients are on thezero'th or first orderlags, and thatthe entire positiveeffect of salesappCars spent within five quarters.Labor demandfunctions also giverelatively clear-cut results,but here thepattern is lesscomforting in itsimplications aboutprevious re

search. Chart IIIdisplays lagdistributions formanhours of productionworkers regressed on26SManuticiuriiig(ocllicientsI)urablesNldurthlcsLeast Squares87-0.0714-0.0795--0.015402957Ii0.14920.049)0.06640.846:5-- 0.0037-00062--0.0l4'0052040.35990.2450.2000().9300.32360.22830.15160711220.21300.2767-003120.8887I0.44070.37260.24660,902500.69780.35600.4577118180.30980.40670.10420,42s--20.08510.08600.032!02172- $- 0.021)90.1606-0)16100l2-40.19390.1178- 0.11980 6848Standard error of0.05220.1)2820.0649-(1.0390coe)1i's0.1240.1020.0850279 toSure of0coeli.'s50311Standard error of2.42I XISIi(56.2540.0890.1220 169 S(IN IN1VLSIMI:Ni I050.40.3020-I0-0.1-0.2Note : Smallest and Targcl st:tnda id errors for least ;q uIre CoflteienIs tre dopla', ed as vertic,Ilote,jove or belosI correp&indt

iig coelleli-Olaid stan:l:trd error for spectraleo!lieiet., are at theright hand side of the cia rt.Co&hcient0.40.30.2//0-4-3-2's_ ia coet i-c writsLersi squares coeft-ceitsTotal ale on total 000trIrentSalesIN) on investment (N)/Saes(D) on rrvestrnerlt(o)_j//////I'-II234Lags in quarters678-ri01-0.2ICoet0.4- 03020.1-0.1-0.20.3 rntti.:The above argument does not apply to demand for labor, except nsolaraslabor behaves like a capital good. Both labor and capital equations, though.aresubject to a variant of the classical son of identification problem fora demandequation. In static competitive theory it is sometimes approprhite In take factorprices as determined outside any single indi.ixtry In empirical work, thesame kindof reasoning may justify using prices as exogenous v

ariables in cross-sectionalorlong run historical studies. But ii' quarterly time series analysisa considerableportion of variance in factor demands is likely to be cyclical, and hence willcorrespond to cyclical variation in factor prices. Unless industry-specific patternsof variation in factor demand dominate the dependent variable, the fact thatanalysis is at an industry level does not make it legitimate to ignore classicalidentification problems.''4. Rnsuis WITH FACTOR D1IANI) REI.ATI]) TO SAI.ES AioN1In comparison to the results for the price variables, results with sales aloneas explanatory variable are clear cut. In the equations for gross investment, salesbehaves like an exogenous variable. Chart I displays lag distributions for grossinvestment on sales for aggr

egate manufacturing and the two suhaggregates. Inall three lag distributions, coefficients on future sales (the coefficients with negativetime index) are noticeably smaller than those on current and past sales, and thetests shown in Table 1 confirm that in each distribution, coefficients on the firstfour negative lags are insignificant as a group.'2TABLE ITESTS FOR SIGNIFICANCE OF GROUPS OF CoEFFIcIENTS, INVESTMENT23y2(9)= fli-LAo DISTRIIIIJTIONsquares coel1icints arc diplayeiIas erlcjlines above or below coriesponding coetlicients, andstandard error lr spectralCOCII!CjCffls are It theright hand side of the chart.Coefficient0.8\I-0.61Spectral coefficients-- -- Least squares coefficientsTotal investment on total sales /'\F/.'/F/,Investment (Dl on sleslD)I'I'I1.0IIA0.8I

Investment (NI on salesINI,I %,Lags in quartersCoeffcie0a 2(9)Coen's annual data (actually semiannual for one sear when a mator tax changeoccurred atmid-year) was converted to a quarterly basis by simply repeating each observation four times.This ofcourse introduces a spurious seasonal in the data. However, bythe argument in another paper of mine)l971(. excess seasonal variance ill an independent variable has the effectof "deseasonalizing" theestimated lag distribution, so unless the true lag distribution has a seasonal pattern,the resulting biasshould not be large. Iagenous variable instead of on the autocovariance function of the residuals8 Theprocedure has substantial computational advantaL'cs over least squares regressionespecially where several possible lengths o

f lag distribution are COfltempliteditalso makes seasonal adjustment easy and aulomitticallv takes account ofcomcated patterns of serial correlation in residuals in computing test StatisticsBoththese latter characteristics are important for this paper because: (a) as Ipointedout earlicr(l97l), seasonal adjustment of dependent and independent variables bydifferent methods can cause serious bias in distributed lag estimates andIb) wewill be making tests on groups of coefficients about whose sizes, signs, andinter-relations we have little a prior: notion, so that unbiased test statisticsare a centralconcern.The Hannan inefficient procedure has disadvantages too, howeverMostobviously, it is less than fully efficient. Also, it requires relatively longseries inorder that it

not be contaminated by "end effects." which arise because themethodtreats series as infinitely long, either periodic or filled out withzeroes. Laggedvalues of exogenous variables at the beginning of the sampleare implicitly eithertaken as zero or taken as values from the end of the sample. Themethod alsodraws its computational advantages from the assumption ofstationarity. Henceit will fail on data which show very different patterns of variationin differentperiods or which have many gaps. And, finally, the method doesnot allow exacttest statistics, even if normal errors are assumed. All testsmust he based onasymptotic distributions.Because of these possible probletns with the frequency-domainestimates.most of the main results of the paper were verified with leastsqua

res regressiontechniques.3. RESULTS WITH FACTOR DEMAND RELATEDWith one marginal exception,every equation with both sales and priceasindependent variables showed eitheran insignificant price variable or significantcoefficients on future values of priceor sales. Experimentation with the form of theprice variable, while considerable, didnot cover every formulation which hasappeared in the literature. Itwas decided not to proceed further with the searchfor a valid exogenous price variable,however, because: (a) an explicitly stochasticapproach to the theory of factor demandleads to doubt that any single variablecan summarize the influence of price and(b) the fact that positive resultsappear inequations without price variablessuggests that such equations have valid in-terpr

etations as causal reduced formseven if price is excluded.Two forms of the cost ofcapital variables, c, were tried. Onewas taken fromprevious work by Nadiri9 andthe other taken froman article by Coen (1968).Both are based on interestrates (rather than returns on equity) and bothuse thestandard formula foruser cost, as presented in, e.g., Hall andJorgenson (1967).Coen, however,corrects for the effects of changes in depreciationguidelines, whiletlannan(19f,3) pointed out theequivalence of hiseltIcient procedure with his inetlicientprocedurewhen the residuals and theexogenous sariabIhave the same spectral densities. Arnemiya and Fuller11967) showed the equivalence ofthe efficient procedure toeneraIi/ed least squaresSupplied to me by ProfessorNadir).20 S BY CHRIsToPhERvI.