This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research

Volume Title: Annals of Economic and Social Measurement, Volume 6, number 5

Volume Author/Editor: NBER

Volume Publisher: NBER

Volume URL: http://www.nber.org/books/aesm77-5

Publication Date: December 1977

Chapter Title: and Price Controls in a Flexprice-Fixprice Model

Chapter Author: Donald Schlagenhauf, Franklin R. Shupp

Chapter URL: http://www.nber.org/chapters/c10540

Chapter pages in book: (p. 501 - 519) i/(n(:l22/ I:t on,iflli anti .octa1 .tit'asurenent. 155

INII.AIION jN1) PRI('1 (ONTROI.S IN\ }:il

13v DON F.Sc!lI.AuINIIAUI ANt)FRANKlIN It. Siitpp i1:'l ,r(zper (icr c/op a ample piirir'/ u/ i,iflatioit /or an etanom 2jaratttri:,sl hi 1tli lie', - priee ((liii /15 price output settor.',. !ntlian i,ro,'utaIe.sttiiii e Set Ideiiiaitd(II(it/U'!Itt KIlT. and ii Ic traminined il(rosc seet0rli,is trait Itnullan process rineiher aitit an injiationari e.vpeclation Jii'iotItesiv .custain.s the in/la firm even in the ahcenee a! all verilltiflhllng('.52122 demand. i/ic inflation generated hi this prott'I Ii suhjertt'd to a age and proc eonir,,IsPar- t/tutor attention vsi!iit'Pl to the 5(11(21 201'iti/it' iiptoirul control rule lot the nun/elnit! ii) i/it' qucs f/on a! al/inst/ic efloienrr. Iquit v and terminal titiTus are a/la (Oil %uii'rOl

1. INI RO1)U(i IoN This paper has two purposes.Firstitdevelops a simple analticaIlv tractable model of inflation for an ccononlv characterized h two output (flexprice and lixprice) markets and one input (labor) market. The model incorporates most of the major elements of' short run inflationtheory and demonstrates, at least in a stylized way. how inflation can hetransmitted and sustained. Second, the study imposes a set of temporary wageand price controls on the model. The impact of these controls is examined to identify the circumstances under which controls might. and also might not, be appropriate, and also to suggest how controlsmight be designed to satisfy certain allocation, equity. and termination criteria.

2. Tit E INn.1vr10N MOl)F i. Price and behavior is examined in a simple economychar- acterized by two output markets and a single labor (input) market.Prices in one output sector are determined primarily in auction-typemarkets. while prices in the other sector are largely administered. The first market- type is representative of agricultural and commoditymarkets in which prices are determined largely by excess demand considerations.The sec- ond market-type is typical of many manufacturing industries inwhich prices are largely determined by some mark up strategy.Gordon [3). Hicks [51 and Moroshinia [6] refer to the former as the /k'.vpricemarket and the latter as the /ixprice market. Okun [7] prefers tocall them the auction market and the customer market,respectively.

tthe authors are particularly graietui to the referees of this journal tartheir t houghi- ful and very helpful conlnients. fhev would also like to acknocs edgelinaiicial support or Insesiors in this siudprovided by the Graduate School (An/aria State University) and Business Education (University of liii iois). I In this simple CCOAOO1Y the labormarket is mation equation in which specilied bya wage wage increases arcassumed to for- increase expectatioflS and toexcess demand respond toUrice considerations ket. Price increase expectatiOnsare assumed to he in thatmar. are related to past price increases forriedtdtptiI in bothoutput markets output prices and wagesinfluence costs, the both of the tIxprice sector postulatedmark up raises prices in thatsector, and these strategy feedback into increasedwage demands. increases intur changes in relative prices of Furthermore,the the two sectorsimply a shift resulting position of demand(even if one in thecorn. is held constant assumes that nominal or is determined aggregatedemand cxogenouslv). andthis too inflation process. In thisstudy aggregate feeds the demand andsupply tions are, in fact, assumedto he determined considera. model can be readily exogenously. adapted to allow However,the br theimpact of monetary policies. tIscaland/or

A. The Flexprice(A uction) Market In this market it is assumed thatthe dominant movements arcoutput excess demand determinant ofprice to be essentially considerations. unrelated to Prices areassumed short-run changesin costs; cause in many ofthese commodity possibly be. relatively or auction markets, unimportant. labor costsare The demandfunction appropriate given by to the flexprice (auction) marketis (I) = where e = income elasticity of demand price elasticityof demand = cross price elasticity of demand The quantitysupplied is trolled by the assumed to be vagaries of the given exogenousl)and is con- other domestic weather andby the OPEC and international ministers and/or ply function is cartel of the form managers. Consequently, thesup- (2) I-Is VA? =,--IS Finally it is assumed thatprices respond (3> to excess demandas given by = where k= elasticity of = P.0(l price adjustment,and ± p= the trend flexprice whichinsures some long run price parityfor the Combining(I), (2), fiexprice sector. and (3)yields

502 V" DID (f kD e 1 A(s+I) t 4j (tLV4, Equation (4) can easily he rewritten as (5) PA , =kyp-t- k/p1 ±e Y where n ct= kiv, -kq + p and P4(:+I,is the percentage change in >, v,isthe percentage change in Y,, etc. It should be clear from (5) that inflation can he initiated either bya contraction in the quantity supplied in the flexprice market or by an increase in demand resulting from an increase in national income Y,.

B.The Fixprice (Customer) Market The dominant market clearing mechanism in this sector is a quantity adjustment process. Accordingly, prices are essentially independent of short runexcess demand considerations and are instead largely cost de- termined as firms employ a mark up strategy. The three inputs employed are customer goods, auction goods and labor. The mark up relationship can be written in lagged form as (6)

+ I) =ij[(OPc + + + (I - )(Opc.r 1 - + I + (I -i)2(Op.,2 + 1//P4(g_2 + 1t_2) 4- where i', is the percentage change in unit labor costs, defined as theper- centage change in nominal , w,, minus the percentage change in long-run productivity, p',. After a Koyck transformation this yields

(7) Pc(t+I=(I - + i9)p, + 1?1'p, +11t

In this equationrepresents the response coefficient, with a larger iim- plying a more rapid pass through of costs. The coefficients 0,', and sum to one and represent the relative intensity of use of customer goods, auc- tion goods and labor in the production process. It should be evident from (7) that price increases in the fixprice market are notdirect/vapected by changes in short run aggregate demand. However these prices are indi- rectly influenced by aggregate demand through the corresponding tight labor market.

C.TheLahor Market The labor market is assumed to be characterized by a combination of 'administered' pricing and excess (input) demand considerations. In 503 'I j

particular it is assumed that employees liv 10 obtain a 'lair' moneywa increase hich covers both mv productivity increase and anCpCcte(l price increac. The actual increase is also intluenced hexcess deniatiti in the labor market This relitiionsh ip ;s tti yen by

ii',i - P':.= P/I!: Ii + i(L, --1 7). wherepr1 = the percentage change in labor p10(1 uctivily = the unemployment rate. L'7 the natural unemplovnicnt rate, and = the expected percentage change in overall prices.

The actual percentage change in overall prices isaveighted sum of the percentage change in customer and auction prices. That is, p,, = VP.: f (I -

where p = the fraction of final output comprised ofauction goods. In addition we assume that expectionsare formed adaptivelv so that + (I p>1+> = -- )p, + (I 2> + ''i. Substituting (9) and (10) into (8) and usinga Kovck transformation yields (II) = ( I - ,')p., +z'p,-i-(I- ; .- where

(1=ô( L', L7 )- ô (1 )( L, -.(17

D. The ('omp/ete Model

The complete inflation model is thus specilied by equations(5), (7). and (II). To Illustrate the basic dynamics of the model, plausibleparam- eter values were appioxirnated from estimates reported in other studies. These parameter related estimates include: k=6, =I, = .7, .55. and p 'y = = .01 for equation (5): z= .3, 0 .2. = .1. and 5 = .7 for equation (7) and.' = .1, .55 and = .3 for equation (II). As a check the three reduced form equations, (5), (7) and (Ii)were also estimated directly, and these estimates correspond surprisingly wellto the parameter values obtained fromother sources The direct .334 and k estimates include ky= = .430 for equation (5): (I- + O) = .766, andØ = .205 for equation = .028, (7): and(1 - v)= .495. (I-) = .450 for equation (II). e .055 and Four simulation results for the inflationmodel are presented in In th s contevi in h ich aggregate dern rid rs deter:ired ekogeno uslthe adaptive espectarion hpoihcsr5 is prohablsuperior to the rational fliore. br the ssage controloption the a age espectatiori hptheI5 Further- hthe con roller Increase IrflIat,i,i ion () K 0' errittden

51)4 'C lABEl. I d 1-II ISIARKIl P1(1(1 I( RI A(l11(AJIiIi)RiI ',IN III-l!\IIiiCi_II I\I'klii M091 I 10

A F,.!,i,hr,.On ( hg' wth 0Or, Fl*.pr'-e Suppk Shri:(' 1) .3 with ,j= .3

Period P, P '4 P1 P ii Pi

1.500 3.000 I .650 1.650 .500 3.001) .650 1.650 2 1.572 .3(17 1.65)) 1.455 .572 2.60)) I .651) I .67-I 3 1.549 I .4)19 1537 1.543 .6)5 2.414 1.663 I .695 4 1.543 .973 1.540 I .46)1 .646 2.126 .6)11 t .695 5 1.524 1.193 1.510 1.491 .665 I57)1 I .6)15 I .656 6 1.50 .092 1.5(5) I .468 .674 I .608 I .687 1.667 7 1.494 1.130 I .482 I .458 .673 1.345 I .676 .650 8 1.479 1.150 1.469 1.442 .662 (.076 I .656 1.603 9 1.465 1.113 1.454 1.430 .642 l.lss 1.627 1.596 10 1.451 1.106 1.441 1.416 .624 1.133 1.61)) 1.573 II 1.437 1.104 1.427 1.404 .605 1.151 1.59) .559 2 1.424 1.101 1.414 .391 .587 1.137 1.574 .542 C. 10, Flexprice . I).I0'I lexprice SuppI Shortage I, ExceDemand. j = .3 with = .6

Period P Pa Pi P P Pi

I 1.500 3.00(3 1.65(1 1.650 1.500 3.000 I .651) 1.630 2 I .572 2.600 1.950 1.674 1.653 2.600 I .650 1.747 3 1.676 2.414 1.963 1.750 1,708 2.441 I .7(13 1.781 4 1.754 2.147 2.011 1793 173(1 2.1-IS 1.746 1.791) 5 1.816 1.905 2.056 1.823 1.772 1.904 1.770 1.785 6 1.865 1.647 2.094 1.843 )779 1.632 1.778 1.765 7 1.903 1.392 1.821 1.852 1.770 1.37(1 1.771 1.730 8 I .869 I. 132 1.838 1.796 1.746 I .098 I .748 1.681 9 1.840 1.233 1.815 1.779 1.708 1.21)7 1.712 1.638 10 1.815 i.I:O .795 1.751 1.680 1.147 .682 1.626 II 1.794 1.194 1.771 1.731 1.649 1.163 1.651 1.60)) ed 12 1.71)7 1.180 1.749 1.708 1.621 I .16(1 I .623 1.573

or table I- All four simulations assume the same initial conditions, i.e., first ck period quarterly inflation rates of 1.5",,, 3.0,, and 1.65°,, respectively in ed the fixprice, flexprice, and labor sectors. In the first simulation, no addi- e r tional excess demand considerations are introduced. Nevertheless after 12 periods a quarterly inflation rate of approximately 1.40,, persists. In the 8, second simulation reported the only inflationary stimulus is a 10",, short- nd fall in supply in the flexprice (auction) sector. This shortfall is assumed to persist for six quarters. A substantially higher rate of inflation obtains n both in the short run and at the end of the planning horizon. In the third live simulation in addition to the 10",, supply shortfall in the flexprice sector a icr- I"., increase in aggregate demand is introduced. The resulting inflationar\ ilen trajectories are given in table IC. The fourth simulation reported uses

505

-I I

the same economic environment as the second: however, the passthrougi) coefficient ;j has been doubledIrOn] .3 to The sensitivitof the mocj to this particu!ar parameter has been explored because thereappea to he some evidence of a :/zre.v1w/1 e//t't! which dlaii,aticallv increases thespeed with which cost increasesare recouped when the rate of inflation a certain level. One should not, however, infer exceeds from thissensitivity es- perirnent that the parameter values eriiploved in this studyare ojjered as anything other than plau.rib/e estimates.

3. Wx;i ANI) Pki(-j; CONTROLS Income policies of any form are conlroversiil and directcontrols are particularly suspect. Twoquestions arise rather naturally in Is it possible to identify this context any circumstances under whichcontrols are ap- propriate? How should controls hedesigned to satisfy certain and equity properties? These aIlocatiJ,I are not really separate questionsbecause the economic arguments against controls are typically couched interms of in- duced misallocation and of induced inequitablercdistrihutitsn of inconle Proponents of controlsacknowledge these shortcomings they maintain that in However some circumstances controlspermit the use of stimulative monetary and/or fiscal measures whosepositive ml pacts more than ofliset any negativeimpact of controls. This tested in the model outlined argument can not be fully above, because in it sumed to be determined aggregate demand isas- exogenousf However, the model to estimate the potential can he used for induced misallocatiol]and income redistrihu tion. It can also be usedto derive control rules tive features. which mmml i/c thesenega-

A. The CriterionFu,zc't ion

Four argumentsappear to he germane propriate to the simple to a criterion functionap- model outlined above.These provide for duction in priceinflation to some (i) a re- acceptable level, (ii)an equitable dis- tribution of anyrestraining impact on wages and profits, (iii)minimal interference svithmarket allocation, and (iv) terminalcharacteristics which minimize thepossibility of an explosive wagepricespiral following the suspension ofcontrols. A criterion these objectives lUnctionconstructed to achieve when it is mininiizedis given by (I 2) T D= + 1p,j +U2!p(.1 * PA,-- + 113p, - l + U p, + S * I Pt, POTII P1(J +

.SO6 ugh The first term of this function. u,n, - pt. is designed to insure odtI that the percentage price increasep,, does not differ substantially from he the targeted price increase pt which may be set equal to sonic historical )eed norm. 'eds The second term of the welfare function, ii',- p , is designed to protect the purchasing power of the wage earner or salaried employee, and iii us to guarantee that the burden of stopping the inflation is borne by both wage earner and property owner. It is evident from this term thai whenever the increase in money wages adjusted for productivity gains fails to compensate for price changes, a penalty is incurred. Conversely,a penalty is imposed whenever the relative share of property income are deteriorates. CXL. The most severe critics of incomes policies typically focus on price controls' potential for disrupting the allocative function of the market, It Lion is obvious that imposed uniform price and wage increases eliminate this he function completely. Therefore, it is important to design policymeasures Iin- so as to preserve some relative price flexibility in response to market le. pressures. The third, fourth and fifth terms of equation (12) are intended to achieve this objective. For example, the third term is given by of ore p7, U2 1'(, - h,, ised where the price ratio p7,/'7 represents the relative price increase which bu- would have prevailed in the absence of controls. Deviations from this ga- ratio are penaliied because the controlled price relatives may transmit ertoneous signals. A final important characteristic of any temporary control is that the termination of the control should be more or less automatic, and that this suspension should not induce a wage-price explosion such as occurred in 1 197374. Wage controls, for example, can only be readily abandoned whenever the restraining impact of the control is minimal, i.e., whenever the control rule grants most of the wage demand. Further- 11 more, whenever this condition prevails, no substantial pressure for a tics wage-price explosion exists. ing It is evident from the analysis in the previous section and, inpar- icve ticular, from equation (8) that asPi( + approaches p7, adjusted wage increases, induced by market forces will stabilize at p7. From(7)it lollows that market induced price increasesp, will also stabilize at p7. Consequently a major objective of any control strategy is to reduce the price increase expectation PiT*ii to Pir+i,. The last term of the cri- isdesigned terion function. uP(T+ 1 - PT4 , I to accomplishthis objective. The first and fifth terms of (12) can be combined using the relation- ship - relationship ts u, = u + (I-- This derived from(10) The critertonI ti[lctiOfl (12)an then he replaced h the (BOretractable / quadrahc structureof (13)given below.2 13. i'/ze ('o,iirof ilteoreije io,-,nu/aiw,z of the I'roble,n A formal statement of the wage-price control model i iopossible The objectiveisto niinimite

(13) p*)2 13 = u(p, + (u', p,)2+ u2(p7, . )2 -f-I /7

2 + u (p * - + 4 n 7p subject to either one ortwoofthefollowingprice andwage equations increase

P4t +I) = '.'f(, /%/4 + t,

Is = (I - 7/ + iO)p5-1 + ?j/i, f- 1)i3O, = ç( I -, + + (I - fl it-, + , % tb P, +(I i')ii /7= P7/W7m7= p,/t7aridn7 Itshouldbe clear from (5). (7) and = (II)that any inflationinthis economy can be brought under control either byemploying mand policies including aggregite de- nionetarv and fiscal measures 'hichalter c, and ci,.orbycontrolling either wageor price increases. If the policy selected is to override the option wage formation equation (II),i.e., to impose threci wage contmtc,the price formation equations(5)and(7)govern the inflationary process, and thecontrol variable is;, of' equation (7). This choice does not necessarily preclude price controls hutPrices niust only be controlled at a level Consistent with thosegenerated by market k)rccS, 2An ahtcrn,Itise iormalation of the criterionhjflct!ofl nould replace the';isth (12) ssith p p rhis formulation terni of (age of iovusiiig directl appropriate Ii) s;ige controlshas the adsan- on the basic ohjectie of thecontrols shich is to align creases adj usted for prod netI is gains with the forcied si.ige in- tseen this term rate ol inflation- 1 he trade oil he- and the second terni of(!2). shicfi is designed creases ith the i'urrgizj rate of to align adjusted uage in- inflation in order topreserve labor's share of national Is Ifl]fliediatels apparent Theinclusion of the term income. for the twa! period also ohs sitesthe need expectation terni. because itforces p7 earls !i] the planning and therefore to approach 'non/onthis assures that p of this forriiu(atioiiis that equaiiiig p r p - The dkadiantage inonc\ uppk targetj, 'hich and i s auI'I!ir'fr)e5/ji,(. ohpcct iSe (flu us-h prosides no U/U,,Uj,i. utjljts like a This .ilteri],itne for its attainment formulation dues nutina(erjall toresaniple equations alter the major lindine'ssit this studs (16) and (t7( heloInipIs a control rule polics coefficient Thisfinding also obtains for cliaracteni/ed hs a sari,ihle us hat more suhstantil the aIter,i,itjveciiterion Function.\ sone- as i, rnodfjc,ttofl i_s required for i/2(p+f( -(n/2)A equation tt sulmichi must he ressrituen euuitahle a age control role Ii ihus implies amore vigoroth .umd sonueishau less Oj. i.e., by equations (5)and (7),Alternatively, the price increase trajectories ihle generated by these equations can be interpreted as guidelines. Conversely, the decision maker may elect to control prices direetli'. In this case he would either override (7) and use p, as the control variable or possibly choose to control both pr-, and p,.

C. Some A na/rile Results with Direct J'age Controls

The wage-price control problem outlined above with direct wagecon- trols can be formulated in terms of a discrete time Pontryagin minimum principle problem with i', as the control variable. Thenecessary and sufficient conditions for an optimum are given by:

'ase (14i)n = [p -I- U2: i'C: + u3imi7p4, - I + U7 + 1437117

011 *1 (l4ii) A(-, = u,(l - v)[p, - Pit]-+- (I - v)Fp,,-

(4*2 * ' + u2,J)( --17i,) + u4(n$ pç, - ',EAt)

+ (I 1] +u10)Aclr+i)+ ky4(,fl, this *1 de- (I 4iii)A4, = = U,PL pit Pirj + i'[p, - iv,] + u3( PA: 2,n7',) and tiofl + U4(pA, -fl7pcz)-4- L'AC(,I) -ki3A41, ose OH (I4iv) P1,ti) = (I 17 f170)Pcz+ ip,t'p4, + iti',, the OAC(i+ I) Fhi s and only rces, OH (14v) p4 = kyp-, - kI3PA! + cii. (1 + Ii:UI that'.- 'e in- Given the proper boundary conditions these five difference equations be- can be solved for the optimal trajectories oF the control variable i', and 'Cti- the corresponding trajectories OfCI.Ai, A, and A41. oflIC. It is also instructive however to examine separately the individual need roh equations. To facilitate this examination we set u2 = = 0. Under these ntage circumstances the wage control rule (14i) reduces to ik a (15) tud). p0 - IJAC1I+I1. ri a hi e onIe- The critical variable inthis expressionisthe time varying shadow lit (en price Ac(,i). Using (14i) through (l4iii),itis possible to show that this it Ies shadow price is given by

509 S

(16) A.,,1 - (1 - °)1l --pJ -+v1,

i&ii7[p, FZ7C,i A

for the .r,peeial'a,S'ein which the economy has no flexpricesect)1 i.e.,for sshieh = = = = 0, equation (16) further rc(Juccs to (I?) = A0, -- U,(Pi, It follows ni mediately from (17) that A, < A whenevor I)uring a period of controls this p, ,' would almost certainly bethe case This result together with (15) implies that u', approachesPh as t i', policy rule compensates the I e., th employee for an increasingfraction 0! price increase Over tiflle. airs Alternatively the policy rulecan he written as (18) i'i' = (;,, where the variable policycoefficient (I, increases over time andapproaches I towards the end of thehorizon, This isa "cry desirable property it slates that in the last few because periods of the controlprogram the enipl'ee isl'ull' compensated for all price andproductivity increases quently, there should he minimum Conse- pressure for awage-price e.spls when the controlsare terminated3 I-or the moregeneral niodel which includes theflexprice sector, the optimal wage control ruleis governed by (I S) and (16). Asabove, a smooth transition fromwage controls hackto the market minimally thatt'T requires, p1, i.e., that A015approaches zero as 7'. This obviouslyimplies that iapproaches < Ar,. As can he seen from(16) this inequalitholds when is quite small, p,, > p, the third andfourth terms of the r.h.s. of'(16) are also small,and A, conditions all hold. However > 0. Typically these a separate exaniinatioii of in for in at I ye. each condition is The first condition derives !'roni the factor17(1 nj) which applies to the entire r,hs of(16) and is therefore parameter i potcntijlly very disruptive.The is the adjustnienitor pass through coeflicient cost of producing for any increased fixprice goods. A largen could prove damaging it implies thata high flexprice inflation because rate would more quickl imbedded in theprice of lixprice become that a wage commodities However, italso implies increase controlledat a low level is also and this servesto improve the quickly passed on. pact of increasing performance of thecontrols The net im- j from .3 to .6 isstudied below, The impact ofthis factor 17(1 eter - ) is also dependenton the param- which measuresthe input intensjt' of the flexpricegood. The value is. ol 'our truethat at decreases ( 0 nseq the beginning ottheCl )Fi trot period I;i hors share uen I R, a iirico me Ia ol income rebate propo rio Ira I t h Controls more to Iss 0 ) ul d ni ok e 'rare equitable arid morepalatable

10 ofis approximately I. if this should increase sigmlicantly either because of a higher relative cost for Ilexprice goods or because of a more flexprice intensive technology, the eflicacv of wage-price controls would he under- miii ed. tor, The second condition, that p,, > p. has been discussed previously. to It imposes no real restriction since temporary controls will only be Con- sidered in periods characterized h' an inflation which exceeds the tar- geted rate. * The smooth functioning of a wage control program also requires his that the third term on the r.h.s. of (16),v[ Pu -']be small. This ob- the viously derives from equity considerations, but exists independently only ii fly for a non-zero flexprice market. The parametervmeasures the fraction of national product comprised of Ilexprice outputs. A plausible estimate here is .1Again any substantial increase in this fraction would impede an orderly reduction in the level of the shadow priceA(r.and therefore h es obstruct the operation of a wage-price control program 'use Similarly, efficient operation of the control program requires that )Vee the fourthterniof ther.h.s.of 16).114117 [pA, -- n7p,).besmall. use- The bracketed tern) captures induced allocative inefficiency as measured Oil by the deviation between the controlled and market determined relative price trajectories. From (16) it follows that an\ increase in the deviation the interferes with the smooth dampening of X(r. The extent of this inter- e. a ference also depends on the relative size of the allocation weight144.Too ires, great an emphasis on allocation could prove so disruptive as to lead to a ches rejection of all controls, as is shown in the simulation studies reported in this the next section. urth In summary it should he clear from all of the above that the intro- hese duction of a flexprice sector into the model complicates any control pro- )fl iS gram. The control rule is then governed by equations (14)and (16) in- stead ofby the more simple equations (15) and (17). Nonetheless, in both plies cases the rule can be written in the general variable policy coefficient for- The mat of (l8). Furthermore for the plausible parameter estimates used in a se d this study. the controls for the more complex economy still appear to be ause relatively smooth and efficient. This is demonstrated b' the simulation re- onie sults presented in the next section. plies I on, 4. SiuiiioSTuDIIs 01-Diirci WAGECoNTRo1s 1111- To illustrate the basic arguments outlined above, eight simulation ran) - studies of direct wage controls are reported in this section. The first four aloe focus on the allocation question and its implications for direct controls. in- Iiorfle 4Wc note that the impitcit seihr br this term in the criterion bunction is I..\n crease in this relatise sseighi s oubd ohviousby also increase the negatise influenceof ihl\ .ige term SI I The next three experiments analvie diflerent approaches to a'ojdjnga 'age-price CXpI()SiOfl once controls arc suspended. The final simulatjoii Lests the robustness of the earlier findings by van ing the costpass through cueflicictit, which appears to he the most sensitive parameter in the svsteni. The model used in these siniiilations is the liexprice_fixprice model constructed in Section 2. The economic environment is that appropriate to the price movements presented in table I B. This implies aninherited inflation characterized by first period quarterly pricechanges of 3",,y and I .65",, respectively in the flexprice, fixprice and labor sectors ad- dition a 10",, shortfall in supply in the flexprice sector is posited forthe first six quarters of the planning horizon.

A. ill isa/location and ('onlro/.v In the first sini u lation St udv the criterion functionisdefined b U = .5, u = = = 0 and u 100. This implies thatany indUced misallocation is costless. The results of thisexperiment are recorded in table 2A and figure I and are generally very satisfactory.By the end of the 2 quarter horizon the inflation rate in all three sectorsapproaches the targeted level of I",, per quarter. The shadow price A(414of equation (15) diminishes over the horizon and approaches zero, and thepolicy Co. efficient G, of equation (18) converges on one. These trajectoriesare con- sistent with the findings of section 3 thata variable coefficient policy is optimal. At the rule same time, they imply that age earners and salaried employees are almost fullycompensated for all price and changes in the last few productivjt. quarters of the control horizon. Thisnear com- plete compensation reduces the pressure to recapture lostwages once the controls arc suspended.5 This is an important finding and is one possibleexplanation for the failure of previous inconlespolicies. These policies have fixed policy coeflIcient all been of the variety. A lixed coefficientpolicy rule does not compensate fulls for price and productivits increaseseven in the final periods. Consequently substantial latentpressure exists to right induced distributional inequities. This pressure is capable of triggeringa wage. price explosion, similarto that of 1973 74. which gains of the controls. can negate most of the The seco,,d .VfIflUiCtfojjexperiment recognizes the allocation The criterion cost of induced mis- function is definedby u1 = .5, = .3 and Uç = 100. and the ,, = 0, control rule isgoverned by equation (16)

conserOenLe esen more pr000ujicedss hen eiiher creased The formeritophes iht prices in is increased or isdC cre,tsec sshjle the latter implies the tisprice Secior adanimore rapidis to cosi in- rapid con serSeiice thai the sue of iheIlespriec seCtor is diniinished pros dcs t>r a sf1001 her The more reejlir\ into the free iii a rkei l2 CD CD TABLE 2 At.i.o A1iVi EFFICLNC i OPTIMAL. PRLCE INCREASE. SHAU0w PRIcE, AND Poi." COELFICIL,NT TRAJECTORLF.S U3= U4 u3 A. SmulatIon PC PA t:u1 = .5.u, P1 '-O.u5 X 00 B. Simulation 2'u1 PC P.4 So, = P1 =0,u4 = .3u C100 = Pe nod w C = /p Period I 2 (.500 3.000 .650 1.123 2.785 2 1.500 3.000 .650 1.174 . 2.555 .712 S43 1.419 .465 2,0762.3782.600 1.515 .442.578 1.0191.060t .088 2.231 2.4002.582 .706.699,60.689 543 1.437 .394.475 2.0812.3822.600 1.5321.587 .463 .050102 38 2.1062.2032.333 .718.7 7 I 1.808 1.367 .978 2.072 .715 3.342 1.814 .389 997 23120 718 9876 1.261I.7l .078.l8201[41) 1.0(31.2451.523 .962 1.0761.122 .287 .897.205 .870.90(1.936 .908 I1.495 .234 .722 .775 .834.746.727 9876 I1.220 .0851.154 .284 1.066 .966.250.528 1.2231.308 .085.335 .899.899.944865 1.785 .589 .762 1.3211.923 .735.721828 II10 2 1.0141.039.1105 1.0001.014 .999 u1 1.0051.0141.035 1.0(14 .973.926 44 .203.525.881 .999.959.891 12II10 1.0071.0181.046 1.01)0 .0)5.00 1.042 1.006 .0)8 .005.970921 .232.590964 .99).952883 Perod (. SimuIatin 3: p P4 .5. u' - Pi - .l.0 ,\' 00(I = I'/p/ Period 1). SirnuLuii'n 4: u Do PA .5. u,To ' " = = .3. us = .8<' ID)) G Pi I .51)1) 3.000 .650 .249 2.879 .756 1.5(8) 3.000 .650 1.366 3.10! .827 432 1I 423 46(149)) 2.9872.3872000 1.4891.5531.6)11 1.0931.197 .154 2.6252.6992.78(1 .734.743.737 432 1.514 .476.51)) 2.3952.60(1 1.538I 623 590 1.259 1.1561.307 3.2353.!723.122 .7.79).8)15 I 8675 1.2)17I1314I3'3 70 .53625782) 1.2481.3(1) .4)8 .9)13.963.1)3)) 2.4452.545 .726 .71(8 756 1.433 1.834.370 2.097 .55(1 13)121473 .393 1.1)121.104 32983.253 .726.749 '1)5 9 I.I (1 .1)7).Y'2 1.0991.156 854 .578 2.0731,1941.767 .738 9 I .4 .305 .s5.1)51.27) I .20') 133 .947.923 32293 (4' .Th 0 i5 .004 1.049 .91(1 1.345 .799 II) 1.139 08)) 1(112 1)173 .864 2211(12.709I 52% II 1.1)1(11.1)23 1.18)1) I.1II7 1.0)191.1)22 I .979(124 .407.57) .985.857.946.3 II 1.1)21)1.1)38 1.00311)22 I .036 11)8 1055 .9(1)889 s2571 I Free Market Free Market

\ Rith Allocation 1.4 L4 Penalty

With Allocation Penalty 1.2 1.2

.-. \ 1.0 4,o No Allocation .1' Penalty No Allocation Penalty

Free Market Fr.. Market

WiLI Allocatjonl.ô Penalty tith Allocation Penalty

8 10 12 2 4 Figure I:Inflaion Pathsih- above. Beca use of the allocalive pressure. age controls are pursued somewhat less vigorousIand the terminal characteristics ire marginall less attractive. See table 2R. Nonetheless, the intlatioii is suppressed and good coil Velgeiluc Is obtained iii the pulics cuellIcieiu The third simulation experiment also focuses on the allocative !ssue. While no increase in the aggregate penalty for misallocation is introduced, the criterion function has been modified to redistribute the penalty so as to penalize any deviant price relative. The loss function is defined by u= 5. = u= u=.1 and u = 100. The simulation results are presented in table 2C and figure1. In this instance imposed wage constraints are markedly less severe at the beginning of the control horizon: still alt price targets are approximately met by the twelfth period. The sliados price decreases monotonically, while the policy coellicient (1, declines from .756 to .708 in the sixth period before beginning its 5105% rise to one. This unevenness in the policy coellicient trajectory lessens the intuitive ap- peal ol the control rule and therefore reduces its chance of adoption. However, the overall results of the policy appear reasonably satisfactory and closel' parallel those of the first two simulations. In the fourth .cwzulaiwn experiment, the weights on the allocatvc terms are tripled. The results are recorded in table 2D. The controls again meet the targeted inflation rates bthe tss ehith quarter. 1-lossever. the 12 shadow price and policy coefficient move so very slowly towards their respective targets that a successful reentry into the free market appears to be marginal, at best. A longer control period may he indicated: or pos- et sllth' under these circumstances the inflation should be moderated with more conventional demand management policies, or with more selective measures. n B. Variations on a Theme It should he clear from equation (17) that the variable coellicient policy rule is consistent with a time invariant u,. However, any increase over time in u1 amplifies the variability, and a large Uc, the weight of the price expectation term in the criterion function, leads to such an increase. In all of the above simulations studies. us is set equal to tOO. In the li/i/i simulation, u is reduced to 10, and the other weights are given by u =

V .5 and u2 = = u = 0. The results of this experiment arepresented in table 3A. These should be compared with those ol' the lIrst simulation run recorded in table 2A. From this comparison itis evident that while the indicated controls of this fifth simulation are some\s hat less vigorous and 12 the targets slightly underachieved, all trajectories are quite similar to those which obtained using u= 100. It follows that while the control results are indeed sensitive to the relative emphasis placed onthe terminal ex- pectation term, a wide range of emphases is quite acceptable.

515 StNSD'JVii STUDI AND Oprj TABLE 3 SHADOW PkI('L.. A, Simulauon 5 u .5,u2 = U4 = O,uç = Prc', J' 0 B. Simulation 6' t, Pot Icy Cot FIC!INT TRAfl( u1 .5, u = 04 O.0 U)RftS 5,,, Period 1 p. p p Ac C = WITh Period Pc' p G 4 32 1.4271.500.456.483 2.0862.3842.6003.000 1.4931.650 .548.594 1.1931.2011.25 -- . - c /pj 8765 1.3071.3531.392 1.5411.823 267 1.3031.372 435 9 1.196I .255 1.091) .9 1.187 .228 1110 2 C. SImulation7'01_5020 I1.113 088 151 1.0211.0391.027 1.0811.139.105 1.172 1.1091.145 1.065 1.012 .986.998 2.130' .753 2 I 500 3.000 6Sfl .745.931 .785.777 3 1.447I 396 2.3722.600 I 560 .594 1.4241.577 .289 .817.808.797 7654 I 233I1.3101.352 271 1.24815222.071 .804 1.424 1.0571.167 .921 .865.842.824 098 1.123I .193152 I .971 77 1.074 .009 .472.746 .93.913 12II 1.083I 101 1.0191.0341.018 I 359 I 296 .235 1.114I 1.171 45 1.094 I 042 1.0561.054.054.,,.05!046 I 077 I 031 I 033 I.4( .00

I 1030 031 3,29 - 1.033 I .605463961772173 .19307826734Y 32 668 703 777740 8(3 846 902880 924 942 Pcriod pç PA P1 w D. SImuIatjofl8:jij_ 959 o 2 1.50(1 3.000 ,00 I l.uZ,5s Ac i C = w/p Period p' PA S.U2U)U4IUSIJ \ C 43

5 6 II) 87 II I 451I 481 12 1.419 1.2011346 .305.384 1.215 1.183 2.3482.601) I I So 30 2.0851539 .266821 1.1)93 .988 i 0171.032 !.53 - - I 032 1.544 1.486 1.2341.3(111.428 .365 1.2(12 1.168 1.182 .175 1.1051.1261.160.080.145 I 1,0771.083 -, I 145 25 1.1061.493 .928.294 I 079 .762 I O4 .607 .385.747 .177.280 .741 .050 .781.761 .825.801 .849 .922.90.875 2 I I 495 500 2.6003 003,) .606 S(I .942 654 1.34!I 454 .406 1.81720842.388 98 7 I l.28oI 113 89 I 958245527 ,9<,4 I2 0 i10171.1142 .1)03 (8)2 ),IH)()I III))990056 .574

1 .474 I 098I .294 95 I 206 239 I 1.015I 043 (1)12004 1098I 155 10001044 966 1 097I 264 . 77 I 0023 3)04 988979 1(112400595911 2)11 757772 800 79 9I I1) I 097 The two sets of simulation results given in tables 3D and 3C assume the use of the alternative criterion function described in footnote 2. Inthis criterion lunction, the fifth or terminal expectation term isreplaced by a iIc% term dcsigiicd to align adjusted money wageincreases in each period with the targeted inflation rate. This is a rather conventional approach to the design of measures, and corresponds loosely tothe structure of the Nixon controls of 197! 73. Inthe first of these simula- tioris the criterion function is defIned by a = .5, ii, = = U4 = 0, u = .5 and u = .5. In the second simulation allocativecriteria are considered and the function is defined by u1 = .5.a = = .1 , = .5 and a6 .5. The coefficient 116 isassociated with the equity term which inall previous simulations had an implicit weight of one. The sumof the co- ellIcient of the two equity ternis in the alternative function, u-and a6, also equals one. The results in tables 3B and 3C should be comparedwith those given in tables 2A and 2C respectively. As is evidentfrom this comparison, the alternative specification is less attractive onall counts: inflation control, equity, and terminal or reentry considerations. In the final sunulaiwn. the cost pass through coefficient ij of equation (7) is doubled. This allows an analsis of the sensitivityof the control measures to variations in this parameter. Fromequation (16) it appears that an increase ini should reduce the elThctivcnessof the controls be- cause this increase implies thatprices in the fIxprice sector adapt more quickly to the 'destabilizing' impact of volatile auction sector prices.This is true. However, this adverse impact is more thanofFset by the more rapid adaption of price in the fixprice sector to co,itrolled wage increases.Con- sequently as shown in table 3D and figure 2. the simulatedinflation re- sponds very quickly and equitably to wage controls. Thecriterion func- tion used in this simulation is given by = .5, 142 = u = u4 = .1and u = 100. and corresponds to that of simulation 3 above.Table 3D should therefore be compared with 2C. The control results ofthis last simulation are significantly better on every count.This is particularly impressive since the model with = .6 generates asomewhat higher rate of inflation on the free market. ComparetablesI B andI D. This sensitivity testis obviously illustrative. Nevertheless, since it focuses onwhat was believed a priori to be the most sensitive parameterin the system. this experiment suggests that the control conclusions derivedabove may be rather robust.

5. Cosci.csioN An alternative to direct wage controls is direct pricecontrols. No analytic or simulation results for direct price controls arepresented in this paper. However, the results obtaining from direct pricecontrols in the tixprice market are analogous to those of direct wagecontrols, with the qualification that severe iluctuations in auction market prices are more Sf7 PC Free Market ree 'nrtpt

l.Rt.

1.6 1.6 \

\ ith Allocation 1.4 Peilty With Allocation Penalty

1.2

10 -.. - No Allocation Penalty No Allocation Penalty

6 6 8 12 4 12 w Free Market 3.0 Free Market 1.8

With Allocation 1.6 Penalty With .11ocatjon Penalty 2.0 1.4 \. \ 1.2 .\.

1.0 No

No AllocationPenalty

2 4 6 8 10 12 2 4 6 8 10 12 I j'ure 2: InttatIn Pathsith , - annoying for priceControls than icr controlling prices in both wage controls. On the otherhand. the fiexprice andtixprice sectors provedmore or less UnworkjbIe Thisis not surprIsin Direct controlsarc most ctlee- tive in combatinginflation induced in an primarjlby inflationary expeclations econofl)charac(erj,ed by mark_up pricin.Controls are least ctlec- live in dealing with excess demand inflation. Because of this, auction markets have historically been exempted from controls. [he study is obviously incomplete as several major questions reiflalil iinaiiswere.d. These include:I low much relative price movement can he tolerated before wage controls must yield to direct intervention in see- toral markets'? At what point do allocation considerations require the substitution of direct controls by restraining monetary and fiscal mea- sures? How serious are the consequences of introducing a heterogeneous labor force? What is the implication of introducing a quasi rational ex- pectation hypothesis? These are all subjects for a continuing study. A rizona State L'nit'i'rsiti', leFnpe 1:nit'er.si,v o/ illinois, L'rhana-('/iatnpaig,i

R ii FR I: N (IS

[I],\oki NI.. Oj'iinroi (niroIand .5r'le,nlh'orinDin,inruiiio,i'nrzu-i ,u,Ir:ir,\rrierr- can F!se icr, NeYork, I 976. U Cheu G .I naii.osnd ('witral of I) riuiniji !:c000lnu .Si.ren,i. 55 iles . N en York, 973. Gordon, R -J., "A!iernaave Responses o FternaI Suppls Shocks,'Brook in'i Pajur iPILi'oniinti''i 410113,I 975. I3 2134. Gordon. R. J., "The Impaci at Aggregate Demand on I'rices," flruokmgs /'aj)eri WI i:'eonomi' -iiIi'it i' 3.I 97, 613 625 3 Hicks, J -, i/re C risi in Fsei-nriiwi Li-anouri ,Basic Rooks, N en York I974. NIorsh ma. Ni..Tire Eeoninnir-1 heoriof Modern SW-ic! '.(,'ani bridge V n i' e [sits Cambridge. 976. 7] Okun, ANI..''Intlatron:Its Mechanics and \Se!iarc Costs,'' Br,k'ns Pper in Econmiic .4ctiriIv2,975. 351 395. Sh upp, F.. ''Optima! Poires Ru ks br a Tem porarvI ncorneI'ohc, '' /cj ol I'co. nornic Siudie.i, 13, June 1976. 249 260.

alty

12

hand, iliore effic- iii On S dice- l9