Interest Rates and Price Level Changes, 1952~69*

Transcription

1 Interest Rtes nd Price Level Chnges, 1952~69* by WILLIAM P YOHE nd DENIS S KARNOSKY Our economy hs been experiencing n ccelerting infltion during the pst five yers At the sme time, mrket interest rtes hve risen to extreme ly high levels. The cuses of infltion re reltively well-known, but the resons for high interest rtes ccompnying infltion re not. The following rticle investigtes primrily this ltter sitution. Infltion develops when, t high level of resource utiliztion, totl spending on finl goods nd services (GNP) rises t rte fster thn the rte t which productive potentil grows Such hs been the cse in thu country since erly 1965 Totl spending hs risen t n 8 per cent nnul rte nd rel product t 4,4 per cent rte. As consequence, the overll puce level hs risen t 36 per cent nnul rte The mjor cuse of the current infltion hs been the stimulus to totl spending provided by n excessive rte of expnsion in the money stock, From erly 1965 to the end of 1968, the money stock, on blnce, grew t 5,2 per cent nnul rte, compred with 2 per cent trend rte in the preceding decde. Rpid growth in the money stock ccompnied by high nd rising mrket interest rtes hs ppered prdox to mny observers. According to modern Keynesin economic theory, n ccelertion in the rte of monetry expnsion will provide lower mrket interest rtes. However, this pprent prdox cn he explined by the economic theory developed by Irving Fisher round the turn of the century. According to Fisher, nominl (observed) interest rtes consist of two components the rel rte of interest, to which rel sving nd investment respond, nd premium bsed on expected chnges in the price level. The following study uses this Fisherin nlysis to quntify the effect of infltion on movements in interest rtes from 1952 to The principl finding is tht pst price movements exert mjor effect on nominl interest rtes, with the effect lrgely mnifested within two yers. Consequently, most of the rise in mrket interest rtes since 1965 cn be ttributed to the current infltion. This finding hs n importnt impliction for mrket interest rtes s n indictor of the thrust of monetry ctions on economic ctivity. High mrket interest rtes do not necessrily indicte monetry restrint. Insted, they most likely indicte excessive monetry ese, (s mesured by rpid expnsion of the money supply) which results in rpidly expnding totl spending nd eventully infltion. Willim P. Yohe is currently visiting scholr with this bnk nd is lso Professor of Economics nd Director of Grdute Studies in Economics t Duke University. He is the uthor of numerous publictions, primrily in monetry economics. Deni-s S. Krnosky is n economist with the Federl Reserve Bnk of St. Louis. Pge 18

2 IN SUMMARIZING his mny yers of work on the subject, Irving Fisher cited four empiricl reltionships between interest rtes nd price levels:1 (1) Interest rtes tend to be high when prices re rising nd low when prices re flling. (2) Interest rte movements lg behind price level chnges, which obscures the reltionship between them. (3) There is mrked correltion between interest rtes nd weighted verge of pst price level chnges, reflecting effects tht re distributed over time. (4) High interest rtes ccompny high prices, nd low interest rtes ccompny low prices. The first of these reltionships derives from the fct tht, if lenders nd borrowers could perfectly foresee future price level movements, the former would hedge ginst chnges in the rel vlue of their lon principl by dding the percentge chnge in prices over the life of the lon to the interest chrge; the ltter, expecting money income to chnge in proportion to prices, would redily ccept the higher rte. Fisher ttributed the second nd third reltionships to imperfect foresight bout future prices nd the resulting inclintion to extrpolte pst price chnges into the future in order to djust interest rtes for expected chnges in prices. He devised the concept of the distributed lg to explin the wy informtion bout the pst ffects expecttions of the future. Fisher thought the fourth reltionship, frequently clled the Gibson prdox, ws n ccidentl consequence of the other three. 2 Wht is prdoxicl is tht the theory prevlent in tht period presumbly led to the conclusion tht interest rtes must be low *The uthors re grteful to Christopher T. Bbb nd H. A. Mrgolis for dvice on the sttisticl problems of this study, to Shigeyuki Fuksw nd Jmes B. Greene for mking vilble the results of their unpublished studies, nd especilly to Keith Crlson, Michel Kern, Thoms Hvrilesky, nd Edwrd Kne for helpful suggestions on erlier drfts of this pper. tm lrving Fisher, The Theory of Interest (New York: Mcmilln, 1930), p Fisher first discussed these reltionships in Apprecition nd Interest (New York: Mcmilln, 1896), pp. 75 nd The term Gibson prdox ws coined by J. M. Keynes in A Tretise on Money, Vol. H (London: Mcmilln, 1930), pp A. H. Gibson hd studied the high correltion between levels of interest rtes nd prices in Englnd throughout the 19th nd erly 20th centuries. The phenomenon ws erlier clled the Ricrdo-Tooke conundrum, fter the leding ntgonists in the Currency School- Bnking School controversy in Englnd in the first hlf of the nineteenth century. For concise exposition of the controversy, see Knut Wicksell, Lectures on Politicl Economy, Vol. II (London: Routledge nd Kegn Pul, 1935), pp in order to stimulte sufficient investment spending for the price level to be high, while empiriclly this hs not been observed. The present study is n exmintion of the second nd third of Fisher s propositions, mking use of modern dt sources nd sttisticl techniques. There is, t present, mjor controversy over (1) the dvntges nd disdvntges of using monetry ggregtes s opposed to using interest rtes s indictors of the effect of monetry policy ctions on the economy, nd (2) the djustments, if ny, which must be mde to n indictor to neutrlize it with respect to chnges tht re not directly the result of policy ctions. 3 Previous studies of the effect of price level chnges on interest rtes, some of which will be reviewed below, hve found the lgs to be so long tht recent price behvior could be ignored in evluting chnges in observed interest rtes. In contrst, results will be presented here bsed on the period which indicte tht the lgs re very short, with most of the effect of price level chnges on both longnd short-term interest rtes occurring within two yers. Interest rtes djusted to remove the pprent influence of price chnges hve sometimes moved contrry to movements in observed rtes. Furthermore, price chnges hve hd greter effect on interest rtes in the 1960 s thn in the 1950 s, nd indeed, price chnges in the ltter period ccount for nerly ll of the movement in interest rtes. Previous Studies of Price Expecttions (Fisher) Effects Tests for Fisher effects hve generlly been bsed on two hypothesized reltionships: (1) rt~ = P ~± rrt n - (2) P = Z w~pt i The first eqution sttes tht the nominl interest rte (rn) previling t time t for prticulr debt instrument is equl to the nnul rte of chnge in prices (P ) expected t time t to occur over the life of the instrument plus its rel rte of interest (it).~ 3 See, for exmple, Leonll Andersen, Michel Kern, nd Emnuel Melichr, The Influence of Economic Activity on the Money Stock, this Review, August 1969, nd Ptric H. Hendershott, The Neutrlized Money Stock (Homewood, Illinois: B. D. Irwin, 1968). t Fisher used rel rte in the sense of virtul or rte. Techniclly, he lso included third term, rrtpt, on the right side of eqution (1). This is the interest tht would he erned on the price diustment to the nominl rte. The term is ordinrily so smll tht it is customrily Pge 19

3 Eqution (2) is n ppliction of the theory of dptive expecttions, error-lerning, oi-, lterntively, extrpoltive forecsting. Fced with uncertinty bout the future, n economic decision-rnking unit is presumed to bse its predictions bout future price movements on weighted verge of current nd pst chnges in prices. Thus, in eqution (2) the rte of price chnge expected t time (F?) for some future period is the weighted sum of ctul pst price chnges (F,~), where the importnce of ech pst chnge is reflected in the weight w 1, nd where is indictes how mny periods in the pst re relevnt in forming expecttions. 5 The pproch is dptive in the sense tht in ech period expecttions re djusted (or forecsting errors re corrected) for ctul price chnges. The pproch is extrpoltive in tht pst chnges re extended (extrpolted) into the future. Substituting eqution (2) into eqution (1) yields the form of the eqution tht is usully estimted: n (3) mt = I sv~pt ~+ rrt The unmesurble price expecttions re not cxplicitly considered, but insted it is ssumed they cn be pproximted by the observble pttern of pst chnges in ctul prices (or in some other vrible tht my be criticl to the formtion of expecttions bout prices). Fisher ssumed tht the weights in eqution (3) declined rithmeticlly s one goes bckwrd in time. His procedure ws first to posit time intervl over which the entire effect of price level chnges would omitted. For the complete derivtion of eqution (1), see Apprecition nd Interest, pp. 8-11, 66 nd 67. Some studies hve lso been concerned with the effect of chnges in the rte of price chnge (i.e., price level ccelertions) on chnges (rther thn levels) in interest rtçs. To see how this my be done, it is necessry to expnd P : dp = t Pt Substituting this term in eqution (1), differentiting, nd mnipulting the result yields: ( d 2 P di dp~ d(mt)= ~y ~+d(rrt) The term withiu the lrge prentheses represents price ccelertion. See, inter die, Alln H. Meltzer, The Approprite Indictors of Monetry Policy, Prt I, Svings nd Residentil Finncing: 1969 Conference Proceedings (Chicgo: U.S. Svings nd Lon Legue, 1969) p For concise survey of the theoreticl literture on dptive expecttions, see Zvi Griliches, Distributed Lgs: A Survey, Econometric, Jnury 1967, pp be reflected in nominl interest rte series, for exmple, ten yers. Ignoring the current period price chnge, he then computed for ech yer the weighted verge of pst price level chnges, using weight of nine for one yer erlier, weight of eight for two yers hck, nd so forth. The xveighted price chnges divided by the sum of the weights (9 + 8 ± ± 0) yielded the weighted verge of pst rtes of price chnge. Fisher then observed which of these weighted verges best correlted with the nominl interest rte. The best fit would be obtined where the correltion ws highest or where further lengthening of the intervl would not dd pprecibly to the con-eltion. 7 A useful sttistic for compring the results of niny distributed lg studies is the men (or verge) lg, tht is, the time tht elpses until hlf of the effect of chnge in the independent vrible is reflected in the dependent vrible. 8 Using nnul nd qurterly dt for the United Sttes, Fisher found very long men lgs for the effect of price chnges on long- nd short.term interest rtes. For exmple, the highest correltion between commercil pper rtes nd rtes of chnge in the wholesle price index from ws obtined when the ltter ws lgged over 120 qurters (30 yers), implying men lg of bout 40 qurters (10 yers). Within the frmework of eqution (3), Fisher clculted the correltion coefficient corresponding to the following regression eqution: (n i) = i~i n(n 1)/2 P~ ~+ rrt +ut where n(n i) /2 is the sum of n terms rnging from zero to (n i). 7 1-Iis procedure ws directly relted to the present-dy prctice of choosing n estimted eqution with the highest R 2 (coefficient of determintion or squre of the correltion rtio). 5 The men lg is simply the weighted-verge lg, where the coefficients [wi s in equtions (2) nd (3)) re used for the weights. When ll of the weights re positive, the formul for the men lg is s follows (Griliches, p. 31): n 1 i Ni ino n 1 vii i=o tht is, weighted sum divided by the sum of the weights. In Fisher s clcultions, the denomintor is unity (his weights necessrily sum to one), so the formul for his men lgs is iu:i\ n ri n(n i)/2 which simplifies to (n i) /3. Fisher estimted his men lgs s n/3. Pge 20

4 FEDERAL RESERVE BANK OF ST. LOUIS DECEMBER 1969 In recent yers there hs been considerble revivl of interest in the study of Fisher effects, ostensibly the result of the repjiernce of substntil vribility in interest rtes nd price levels nd methodologicl developments in the estimtion of distributed lgs, Two studies hve ttempted to mesure rel rtes directly nd then to relte the spred between vrious nominl rtes nd the estimted rel rtes to historicl time series for price level chnges, with inconclusive results.0 Most of the published studies hve regressed nominl rtes directly on current nd pst rtes of price chnges (or chnges in nominl rtes on price ccelertions ) J Dt intervls hve rnged from qurters (Gibson) to business cycle phses (Friedmn nd Sch\vrtz). The time spn hs rnged from s erly s 1873 to s lte s Lgged rtes of chnge in vrious price level indexes nd even nominl income (Gibson) hve been tried s indictors of price expecttions. The forms of the distributed lgs esthnted hve generlly been either unconstrined lgs or geometriclly decying lgs. 11 Without exception, the men lgs of interest rtes behind price chnges were found to be very long. For exmple, Friedmn nd Schwrtz found men lgs for short-term rtes of bout ten yers nd for Surj B. Gupt, Expected Rte of Chnge in Prices nd Rtes of Interest (unpublished disserttion, University of Chicgo, 1964), nd Phillip Cgn, Determinnts nd Effects of Chnges in the Stock of Money, (New York: Ntionl Bureu of Economic Reserch, 1965), pp Gupt s work is summrized nd his empiricl work extended in Willim F. Gibson, Effects of Money on Interest Rtes, Stff Economic Studies, No. 43, Bord of Governors of the Federl Reserve System, Mrch 1968, pp nd Preliminry work long similr lines ws reported in Dvid Meiselmn, Bond Yields nd the Price Level: The Gibson Prdox Regined, in Dene Crson (ed), Bnking nd Monetry Studier (Homewood, Illinois: B. D. Invin, 1963), pp lomeiseln,n pp ; Milton Friedmn nd Ann Jcobson Schwrtz, Trends in Money, Income, nd Prices, (unpublished mnuscript, Ntionl Bureu of Ecoconomic Reserch, November 1966), chpter 2, pp ; nd Gibson, pp nd supplementry tbles. In their multiple regression study, Michel J. Hmburger nd Willim L. Silber ( An Empiricl Study of Interest Rte Determintion, Review of Economics nd Sttistics, August 1969, pp ) rejected the rte of chnge in prices s insignificnt. 11 Both forms ~vill be discussed lter. To estimte unconstrined lgs, one merely regresses the current vlue of the dependent vrible on the current nd predetermined number of lgged vlues of the independent vrible there is thus no priori constrint on the time shpe of the coefficients. Geometriclly decying lgs impose geometricl decy on the coefficients, tht is, prt of ech coefficient is constnt decy term less thn one which, when rised to higher powers s the lg recedes into the pst, decys (symptoticlly pproches zero). See Griliches, pp , nd Lwrence B. Klein, The Estimtion of Distributed Lgs, Econometric, October 1958, pp long-term rtes of 25 to 30 yers, which they ttributed to the slow nd grdul djustment of nticiptions of price chnges to the ctul behvior of prices. U A Serch for Fisher Effects This study is bsed upon erlier work but deprts from previous studies in wys tht pper to hve significnt effects on the results, in prticulr: (1) Monthly, insted of exclusively qurterly or nnul, dt re used for short-term nd long-term interest rtes (dependent vribles) nd for price level chnges nd other independent vribles. Further, the interest rte series hve been sesonlly djusted. (2) A vriety of kinds of distributed lgs re estimted, in order to investigte the effect of lg form on the length of the lgs. (3) The monthly dt re ggregted into qurterly nd nnul series to determine the effect of ggregtion over time on the lg estimtes. (4) The study is purposely confined to the period following the Tresury-Federl Reserve Accord of 1951 in order to void hving to contend with the constrint on interest rte movements imposed by the Federl Reserve s pr pegging of Government securities prices. Further, the period is divided into two sub-periods to see whether there hs been ny pprent chnge in the mechnism relting pst price chnges to the formtion of price expecttions nd ny clues to the resons for erlier findings of very long lgs. (5) A model will lso be tested to see wht hppens to the explntory power of pst price level chnges when vribles ssumed to ffect rel rtes of interest re dded to the regressions. (6) Experimentl rel rte series will be generted nd their movements compred with nominl rtes to see whether there hve been times when nominl rte movements might hve been misleding indictors of chnges in rel interest costs. Sesonl Movements in Interest Rtes A number of economists hve observed not only sesonl movements in monthly nd qurterly interest rte series, but lso the influence on the sesonl t2 Friedmn nd Schwrtz, chpter 2, p Gupt, estimting geometriclly distributed lgs for the nominl rte rel rte spred behind price chnges, found men lg of 16 yers for long-tern, rtes. Gibson estimted nnconstrined lgs for reltively short lg intervls (ten qurters nd four yers), so it is not possible to clculte men lgs for the totl effect of price chnges on interest rtes. In Meiselmn s study, the geometric decy coefficients cine out very close to one, implying long men lg (nerly twenty yers, for exmple, with decy coefficient of 0.967, which he found in regressing bond yields on price chnges over the period). Pge 21

5 FEDERAL RESERVE BANK OF ST. LOUIS DECEMBER 1969 of chnges in Federl Reserve operting strtegy for open mrket purchses nd sles. ~ Since some of the dt used for independent vribles in the regressions were sesonlly djusted, it ws dvisble to sesonlly djust the short-term nd long-term interest rte series, so tht the results could be compred with those genertcd using undjusted series. 4 As expected, stronger sesonls were detected in the short-term thn in the long-term interest rtes. The finding of pronounced sesonls in both for the period nd the virtul elimintion of sesonl movements for the period, probbly the consequence of the Federl Reserve strtegy to ssist the blnce of pyments, confirms the conclusions of erlier studies. The resumption of pronounced sesonls is pprent in the clcultions for the 1966 to mid-1969 period. The explntion my lie in the insertion of proviso cluses in the Federl Open Mrket Committee directives over the lter period nd the implementtion of such directives by the Trding Desk t the Federl Reserve Bnk of New York. 15 Empiricl Results Interest Rtes Regressed on Rtes of Price Chnge Dt for the period were used to test the hypotheses bout the effect of price expecttions on the level of nominl interest rtes. Severl mesures of both prices nd interest rtes were used in the estimtion, nd vrious lengths for the totl lgs were tested. In ddition, severl estimtion techniques were employed. The results were very similr cross the mny combintions of dt, length of the lg distribution, nd estimtion procedures, ll suggesting much shorter time horizon in formtion of price expecttions thn hd previously been found. The interest rtes used in this study re yields on securities issued by the privte sector. ~Short- t3 Leonll C. Andersen, Sesonl Movements in Finncil Vribles Impct of Federl Reserve nd Tresury, Business nd Government Review, University of Missouri, July-August 1965, pp ; A Closer Look t interest- Rte Reltionships, The Morgn Gurnty Survey, April 1961, pp. 3-5; Gibson, pp nd Tbles 3 nd 4; nd Hmburger nd Silber, pp F Dt hve been sesonlly djusted using the X-11 Vrint of the Census Method II Sesonl Adjustment Progrm, U. S. Deprtment of Commerce, Bureu of the Census. Source: Bord of Governors of the Federl Reserve System, Federl Reserve Bulletin. 5 Jn Wrren Duggr, The Proviso Cluse nd Bnk Credit Proxy (unpublished mnuscript, Federl Reserve Bnk of New York, 1969). losince there re mny fctors in ddition to price expecttions tht ffect the level of interest rtes, the dependent vrible used in the regressions should be the one lest term interest rtes (in ) were pproximtely by the yield on four- to six-month commercil pper. The yield to mturity on A-.rted corporte bonds ws used s the mesure of long-term interest rtes (rnl). Price expecttions were pproximted by the rte of chnge of the consumer price index for ll items, p 5 17 Using monthly dt for the period Jnury 1952 to September 1969, the function rut = ~, ip ~+ ip ~ + sp. ± n±ipct_~ 0 ws estimted first by lest squres regression of mt on current nd lgged vlues of price chnges for = 24, 36 nd 48 months. The coefficients of the regressions re presented in Chrt I. These regressions were run with both sesonlly djusted nd nonsesonlly djusted interest rte series, nd in ech cse the results using sesonlly djusted dt trced quite closely those using undjusted dt. The introduction of the sesonl fctor decresed the unexplined vrince (incresed the djusted coefficient of determintion, R 2 ) only slightly. Chrt II presents the coefficients of the regressions: = 0 +,P P ~~ d25p0t_i rn~= 0 + sp t ± 2 P, ± 2 p~:t, The coefficients using sesonlly djusted interest rtes re quite similr to those using undjusted dt. influenced by those other fctors. Yields on privte securities vere selected, insted of rtes on Government debt, becuse they re more free of the direct influences of debtmngement nd monetry ctions. However, Fuksw obtined similr results using yields on Government securities. Greene found tht price expecttions were somewht esier to identify using interest rtes on privte debt. Mortgge costs re included in the consumer price index nd might contribute to some degree of spurious correltion between interest rtes nd price movements. Since mortgge interest rtes tend to move with other nominl rtes, using the consumer price index s the mesure of price movements would tend to result in positive bis in the observed reltionship between interest rtes nd price movements. To test for this effect the consumer price index ws purged of mortgge rte effects. Dt on the mortgge coniponent of the CPI were vilble from the Bureu of Lbor Sttistics only for the period Thus, nominl interest rtes svere regressed on the rte of chnge of the CPI nd the djusted CPI for this period only. The regressions using this djusted P~series were still quite close to those using the index inclusive of mortgge costs, Gibson s procedure of using chnges in ntionl income s proxy for price expecttions ws lso treted, using however, personl income, which is vilble on monthly bsis. The results, summrized in the ppendix, were quite similr to those using the consumer price index. Pge 22

6 Since this close reltionship ws observed in ll of the tests, only the results using undjusted dt will be explicitly considered. The regressions show tht price movements ccounted for bout 50 per cent of the vrince in interest rtes between 1952 nd lte The pttern of coefficients is consistent with the dptive expecttions hypothesis, tht is, they re generlly declining. The presence of smll negtive coefficients in the tils of the distributions could be explined theoreticlly by the eventul domintion of positive extrpoltive effects by negtive regressive effects (see pge 32 below). Although the t-test is suspect in deling with distributed lg regression, 5 the coefficients tend to be smll beyond t-24 months nd generlly insignificnt. Incresing the length of the 5 Multicollinerity (con-eltion between independent vribles) is possible source of difficulty in estimtion of this type of distributed-lg reltionship. In the presence of multicollinerity, the ordinry lest squres regression technique is unble to identify the exct prmeter ssocited with ech independent vrible. See J. Johnston, Econometric Methods (New York: McGrw-Hill, 1963),, pp lg from 24 to 48 months hd httle effect on the distribution of coefficients. The sum of the coefficients incresed s the lg ws extended, however, suggesting tht, lthough gret weight in the formtion of price expecttions comes from quite recent experience, the totl djustment procedure is probbly somewht longer, with only reltively smll weight given to price movements in the distnt pst. In other words, the true distribution probbly hs til of smll declining coefficients. These results suggest much shorter time horizon informtion of price expecttions thn hd been found in the investigtions cited erlier. Due to multicollinerity, direct estimtion of n unconstrined distributed-lg function tends to result in wildly fluctuting coefficients. In order to reduce this fluctution, the reltionships were estimted using the Almon lg technique. This procedure results in much smoother distribution, which is more Shirley Almon, The Distributed Lg Between Cpitl Appropritions nd Expenditures, Econonmetric, Jnury 1965, pp Pge 23

7 consistent with the dptive-expecttions hypothesis, tht is, expecttions re continuous function of pst price movements. The Almon lg estimtes re presented in Chrt The distribution of the Almon coefficients follows the lest squres estimte quite closely. For lgs from 24 to 48 months, most of the effect on interest rtes come from price movements over the previous yer. The tils of coefficients beyond these points sum to nerly zero. The regression using 48 lgs suggests tht, if the nnul rte of chnge of the consumer price index incresed by one per cent in given month (for 20 The regressions presented here were generted using sixth-degree polynomil. Other degree polynomils were tested nd gve similr distributions. The sixth-degree ws chosen becuse it best pproximted the unconstrined estimtes, in tht it minimized the sum of the squres of the difference between the unconstrined nd Almon estimtes. The only constrint on the selection of the degree of the polynomil is tht it must be less thn or equl to the number of lgged coefficients. The sixth-degree polynomil ws the mximum which could be used in the progrm vilble to the uthors. exmple, from 3per cent nnul rte of increse to 4 per cent nnul rte) nd prices continued to rise t tht rte, the yields on four- to six-month commercil pper would rise 72 bsis points (for exmple, from 4 per cent to 4.72 per cent) during the first yer, if ll other fctors ffecting interest rtes were unchnged. After 48 months, short-term interest rtes would hve risen by 69 bsis points n the long run, the nominl rte of interest does not rise by the full mount of the chnge in price expecttions. An increse in price expecttions will increse the difference between the nominl nd \Vicksellin mrket rtes. However, the chnge in price expecttions will tend to lower the mrket rte. Assuming n equilibrium position with expected price chnges equl to zero, then mm=rmt. If price expecttions increse by one per cent per yer, fter 4 yers the nominl interest rte will rise by 69 bsis points, thus (1) (2) Since rut = rrnm, (3) mt+48 rmm±48= 1.00 mm+4s mm = 0.69 equtions (I) nd (2) reduce to rmt t 4s urn = 0.31 bsis points fol- Thus the mrket interest rte flls by 31 lowing the increse in price expecttions. This result is consistent with findings of other investigtors; for exmple, see Keith M. Crbon nd Denis S. Krnosky, The Influence Pge 24

8 /74.7.7/4/4447,~ j_ -~/,4 4 /1 4 / Short-Term Interest Rte /7 ( } /7 1, / ~ /, LL jt ~.. ~ 27~-~ 2 ~, ~ 24 Lgs :fe:~ 7/./ 444 /7,) \\\ \ ~ 241.6gm ólgm.775 4/ Constnt \\~\ -.7 t \ 4, \~\. r-4~.- --~ \ \~~~ /,~, \~j)ic:2} 36 Lgs ~L < 1 4 /7/7, /.7 /7/ ~1?:) s 1~,.7/7+ ~: I, : c len ts. Long-Term Interest Rte ( ~i/ /7 7/~//7.7/7. 1 / \ \ \ 24 Lgs Constnt 24logs.457 3,403 3 ólogs Lc~s ~L ~i ~ ~ /7 4,7.7, ~ / ~ 7, : ~< 4 t ~/4 /. ~3c2Z., 4M,~Si, / ~ t t 7 1Y4W 4i,~*,,, J y~ ~77 \ /7/44/4 /11.,\,7,2,:/ ~,~,, ///~7 / y1 ~ 2 7,,, 4/7/ 7 ~ ~Ø~tr$t. 4, /7 / 7.7 4// /7.7 /4.4,\,//7,,/ ///,.,/ /.7 /74/ /7 / /7 4,7/.7 / /4/7 /4 /7/ 7/ 7 /77,4 7/ /7/77 / / 4/4.74 / / of Fiscl nd Monetry Actions on Aggregte Demnd: A Quntittive Apprisl, Federl Reserve Bnk of St. Louis, Working Pper No. 4, Mrch In the ggregte demnd model developed there, n increse in expected prices ceteris pribus genertes Government budget surplus Fisher hypothesized tht the time horizon in forming price expecttions ws relted to the term to which rcsult in decrese in th tock Of we sith nd reduces the r l inter st rte The net result is n increse in nominl rtes I thn the incr ye in expect d prices. Pge 25

9 FEDERAL RESERVE BANK OF ST. LOUIS DECEMBER 1969 mturity of the instrument. Potentil buyers nd sellers of long-term debt would be interested in how prices move over n extended period nd would tend to look further into the pst thn would those people who were deling in short-term instruments. Prticipnts in the mrket for short-term securities re less likely to be concerned with long-term price movements nd might need less informtion in forming their expecttions. The results in the present study re consistent with this ide. The long-term interest rte is reltively less responsive to chnges in price expecttions. Twelve months fter the one per cent increse in prices, long-term rtes would be 59 bsis points higher thn they were onginlly, s opposed to 72 bsis points for short-term rtes. The effect on long-term rtes would be totl increse of 56 bsis points fter 48 months. Why Such Long Lgs In Erlier Studies? Three Hypotheses The present study hs found men lgs for the effect of price level chnges on 130th long-term nd short-term interest rtes of less thn yer. In contrst, erlier studies yielded men lgs of nywhere from scven to thirty yers It is importnt to try to explin this discrepncy nd to defend the results presented here. The uthors hve explored three hypotheses tht might reconcile the differences: (1) The true lgs of interest rtes behind price chnges re short, so tht bises rise in ggregting the interest rte nd price chnge series over longer observtion periods, which led to systemtic overestimtes of the length of the lgs. 22 (2) The forms of the lgs estimted in other studies, in contrst to the snore flexible clss of lgs estimted in this study, re bised towrd yielding longer verge lgs. (3) Institutionl chnges hve occurred over time in finncil nd rel mrkets, with the result tht price level chnges hve come to hve prompter 22 Criliches, pp ; Yir Mundlk, Aggregtion Over Time in Distributed Lg Models, Interntionl Economic Review, My 1961, pp ; nd \Villim H. Bryn, Bnk Adjustments to Monetry Policy: Alterntive Estimtes of the Lg, Americn Economic Review, September 1967, pp Griliches summrizes the issue s follows: ggregtion over time (e.g., from qurterly to nnul dt) will in generl result in misspecifiction of the model. It will iso.. -cuse us to overestimte the implicd verge lgs. Pge 26

10 nd lrger effects on interest rtes. 2 To put it differently, there hs been considerble thinning of the molsses (long-lg) world, prticulrly in the pst decde. Aggregtion of Dt To test the first hypothesis, the monthly dt for ll of the interest rte series nd the rte of chnge in the consumer price index were ggregted to qurterly nd nnul verges of monthly dt for the period. Almon distributed lgs over 16 qurters with sixth-degree polynominls were estimted for the qurterly series. The results (see Chrt IV) \vere virtully identicl to the originl monthly regressions with 48 month lgs nd the sme degree polynomils he post-wr increse in the de,gree of finncil ninrket perfection nd its consequent effect on interest rte flexibility is the subject of Jmes S. Duesenberry s essy, The Effect of Policy Instruments on Thrift Institutions, in Svings nd Residentil Finncing: 1969 Conference Proceedings, pp Fuksw hs m unconstrined lgs extending bck six qurters with qurterly dt from IV/1951-lV/1968 for l resury bill nd bond rtes regressed on the rte of chnge in the GNP defltor. His results re similr to those reported here. The qurterly regressions suggest tht if the nnul rte of chnge of prices increses by one per cent in ny qurter nd remins t the higher level the shortterm rte would rise by 84 bsis points fter 4 yers. The long-term rte would rise by 66 bsis points over the sme period. Using the results of the monthly estimtes, n increse by one per cent in the nnul rte of chnge in prices, would yield n increse of 69 bsis points in short-term rtes nd 56 bsis points in long-term rtes fter four yers. There were too few observtions, given the length of the lgs nd the degree of the polynomils, to fit Almon lgs to the nnul observtions, so only unconstrined lgs were estimted, rnging from one to five yers (see Chrt V). For the undjusted commercil pper rte, the R 2 ws highest (0.709) with only the current rte of chnge in prices in the regression; in ll cses, only the coefficient for the current price chnges ws significnt. As might be expected, the R 2 for the undjusted corporte A yield ws highest (0.552) when the current nd one yer lgged price chnge term were included, lthough in every Pge 27

11 cse only the coefficient on the current term ws significnt. The regressions using nnul dt gve somewht lrger totl effects. If the rte of chnge of prices rises by one per cent per yer, short-term rtes would be 137 bsis points higher fter four yers. Long-term rtes would rise by 134 bsis points. The discrepncy between this nd erlier studies pprently cnnot be explined on grounds of n ggregtion bis in the ltter, nd the first hypothesis cnnot be ccepted. The reson probbly lies in the fct tht the djustment of interest rtes to price level chnges is not so rpid tht ggregtion of monthly into qurterly nd nnul dt leds to systemtic overestimtes of the underlying lgs. Estimtion Procedure The second hypothesis pertins to the nture of the lg distributions estimted in other studies. Since severl of the studies hve estimted geometriclly decying (Koyck) lgs, the monthly dt used in the erlier prt of the present study were used to estimte such lgs. The following regression ws run for ech of the yield series, using for P, both the simple monthly rte of chnge nd compounded nnul rtes of chnge: 25 mt =?crnt..i + OPt + constnt The decy coefficient X, presumbly somewhere between zero nd one, indictes the rte t which the weight of the pst rtes of price chnge declines bckwrd in time (tht is, X = 1 mens tht the lgged terms never decy t ll, while X = 0 mens tht only the current price chnge term hs ny effect). All of the initil regressions yielded decy coefficients slightly greter thn one, which, tken t fce vlue suggests tht the lgged terms do not decy. rn = rn P S t 4 rl = rut pc A dnger in such estimtes of the decy coefficients nd the J3 prmeter is tht they re inconsistent, nd the estimte of X is probbly bised upwrd. 2 Following procedures outilned by Griliches nd by Goldberger, the decy coefficients \vere re-estimted, which reduced them by only very smll mount: = m = rn~~ p~.020 S s Decy coefficients greter thn one re clerly inconsistent with the dptive expecttions hypothesis. It \vould not be unresonble to expect decy coefficients only slightly less thn one to result from tests using different smple periods or dt definitions thn were used here. The monthly dt were divided into two subperiods, nd , nd seprte estimtes of the decy coefficients obtined. For the erlier period, the coefficients dropped below one, rnging (undjusted for consistency) from for commercil pper rtes to for corporte A yields. These results imply long men lgs for both interest rtes, with longer lgs for the long-term rtes. The coefficients on the current rte of price chnge in the comn3ercil pper rte regressions strngely becme negtive for the period. 27 For , the decy coefficients were nerly the sme s for the entire period, tht is, slightly greter thn one, for which it is difficult to find ny theoreticl rtionliztion. To see wht would hppen to the decy coefficients, the monthly dt were ggregted into qurterly dt nd the decy coefficients re-estimted for the period nd for the subperiods mentioned bove. All of the decy coefficients for the entire period declined, which would be expected if monthly decy process were to be converted into n equivlent fl 2 = qurterly process, but the decy coefficients for short-.980 term rtes fell to below one (0.968 for commercil pper rtes, with men lg of 20 qurters or five H 2 =.994 yers). For lone, ll the coefficients were less thn one, but the decy process ws gin negtive for short-term rtes. For the results were ll plusible, nd the decy coefficients were 25 This is the convenient form in which such lgs re usully estimted. This eqution my be expnded into the following: = X PP 5 + Xb5Pe.i + X 2 tip,_ X CPP 5 r + constnt or, more simply, 7,. rut = OX X~P _ + constnt. i: o See Criliches, p. 41, nd Arthur S. Coldberger, Econometric Theory (New York: John Wiley nd Sons, 1964), pp , nd Kenneth F. Wllis, Some Recent Developments in Applied Econometrics: Dynmic Models nd Shnultneous Eqution Systems, Journl of Economic Literture, September 1969, pp This implies tht the lgged price chnge effects re opposite in sign from those hypothesized; they could he interpreted s evidence for Srgent s regressive effects of price chnges on short-term rtes (see p. 32 below). Pge 28

12 ll lower thn corresponding coefficients for The effect of price level chnges on commercil pper rtes for the ltter period decyed with X of (men lg of bout three qurters), while the decy fctor ws (men lg of seven qurters) for corporte A yields. 28 The preceding experiments with simple geometriclly declining lg structures suggest tht such lgs, requiring n exponentil decy, my not be the most pproprite ones to impose on the interest rte nd price level dt for the period of this study in the ttempt to cpture the true underlying lg distribution. In every cse the verge lgs obtined with this procedure were considerbly longer thn with either unconstrined or Almon lgs, which provides some explntion for the differences between this nd previous studies. 2 Institutionl Chnges The third hypothesis sserts tht price level chnges hve come to hve lrger nd prompter effects on interest rtes becuse of institutionl chnges in the economy. As preliminry test of this hypothesis, the period ws gin divided into two subperiods, nd , nd vrious Ahnon lg structures estimted seprtely for ech. 5 Tble I contins the sum of the lg coefficients for J.2 to 48 lgs nd second- to sixth-degree polynomils. As ws the cse with the entire period, there ws little difference in the totl price expecttions effect between different degree polynomils. The length of the lg distribution ws crucil, however. The totl effect on short-term interest rtes tended to decline s the lg ws extended beyond 24 months, nd this ws quite pronounced in the period. The effect on long-term rtes, however, incresed s the lg ws extended up to 36 months. Beyond 36 months, the sum of the coefficients remined lmost constnt. None of the coefficients beyond 48 months were significnt. These results suggest tht the time horizon in forming price expecttions increses s the term to mturity of the security increses. The totl price expecttions effect is much lrger in the period thn in the erlier period. In the ltter period the totl effect on short-term rtes is bout 90 per cent of the nnul rte of chnge in prices. The effect on long-term rtes is bout 80 per cent of the rte of price chnge. In the period the sum of the coefficients rnge between 5 nd 35 per cent of the price chnge for lg of 36 months. Chrt VI contins the lg coefficients for short-term rtes (second-degree polynomil nd 24 lgs for , nd sixth-degree with 36 lgs for ) for the reltionship between the commercil pper rte nd the rte of chnge in the consumer price 28 jmes B. Creene, using qurterly dt for , obtined decy coefficient of for the commercil pper rte regressed on the rte of chnge in the consumer price index, which implies men lg of bout 2½qurters; for the corporte A yield his decy coefficient ws implying men lg of bout seven qurters. 29 Experflnent.s were lso conducted for the whole period nd the subperiods with simple second-order lgs (in the regressions the dependent vrible ws lgged one nd two periods). The results were not pprecibly different from those for the first-order lgs. 30 The Chow test ws conducted to see whether there ws fundmentl shift in behvior ptterns within the period. For both commercil pper rtes nd corporte A yields the F sttistics were significnt t the one per cent level, which indictes substntil difference in the oticiptions fonning mechnism in the two subperiods. For n explntion of the test, see Cregory C. Chow. Tests of Equlity between Sets of Coefficients in Two Liner Regressions, Econometrie, July 1960, pp , Tuble I SUM OF THE REGRESSION COEFFICIENTS~ (monthly db) Short term nterest rtes Ler.gtl, of log Degrneof Polyr,orvil / ! Long-term nierest rtcs Length of Log Deqr~o of -.. Poiyroiniol ? / u 5.~j, ~ :,,-ri,,t,..j,,~..n,i_ u i_h.,.,,. I he 5~j. II,,:! I Pge 29

13 index. The sum of the coefficients for the erlier period ws.344 nd the men lg, 1 to 2 months. For the ltter period, the sum ws.952, nd the men lg 4 to 5 months. While it is true tht the smller effect in the erlier period ws exhusted more quickly (the men lg ws shorter), the pek in totl effect for the erlier period ws reched fter eleven months, while the sme level of effect ws ttined in the ltter period in only 2 to jumps from to 0.901, rte of chnge in prices cent of the vrition in 3 months. Further, the R 2 so for the ltter period the ccounts for over 90 per commercil pper rtes. 31 The highcst B 2 (0.938) for the commercil pper rte ws obtined for using sixth-degree polynomils nd 48 month lgs. Pge 30

14 These results re thus consistent with the hypothesis of the effect of institutionl chnges.~ Similr results were obtined for the corporte A yield (Chrt VI), nd the jump in R 2 for the ltter period is even more pronounced, from to The coefficients of the long-term rte were generted using second-degree polynomil nd 48 lgs for nd sixth-degree xvith 36 lgs for All of the coefficients estimted for the period re significnt t the one per cent level, A men lg of 16 months is implied by this result, mening more thn hlf of the djustments in interest rtes to price chnges in the period were ttined in less thn yer nd hlf. A summry of the regi-essions ppers in the ppendix. \Vht fctors might cuse shift in the frmework for trnsmitting pst price level chnges, vi price expecttions, to nominl interest rtes? A listing of plusible explntions might include the following: (1) According to Friedmn nd Schwrtz, the period used in forming nticiptions should depend on the chrcteristics of price behvior, prticulrly the vribilit in the behvior of the generl level of prices. 33 Thos, one could rgue tht prices hve been more vrible, t lest in n upwrd direction, in the 1950 s nd 1960 s thn over long, erlier historicl periods. Further, the greter publicity given to price level movements, s well s the more rpid processing of dt, could convey greter wreness of recent price level behvior nd ffect price level expecttions nd interest rtes more substntilly thn 011cc ws the cse. (2) Nominl rtes my hve come to reflect pst price level chnges more fully both becuse of decrese in money illusion nd becuse of decresed effects of price chnges on rel welth over time. 31 The former could be explined by the incresed importnce of lrge institutionl investors in mrkets such s tht for corporte bonds. For the ltter to be contributory fctor, rel welth would hve to be ffected reltively less thn before by price chnges (becuse ssets not 32 Fuksw hs estimted unconstrined lgs xvith qurterly dt for five subperiods from nd hs obtined similr results. 33 Friedmn nd Schwrtz, p Money illusion mens tht behvior is bsed on nd directed towrd ominl mgitudes rther thn rel mgnitudes, for exmple, investment outly in money terms would be relted to money income rid nominl interest rtes. If rel welth influences the decisions of svers, the sving function would not shift upwrd by the expected rte of increse in prices becuse of expected decreses in the rel vlue of ssets fixed in nominl terms (for exmple, money), which dmpen the effect (If price expecttions on nominl rtes (see Robert Mundell, Infltion nd Rel Interest, Journl of Politicl Economy, June 1963, pp ). fixed in nominl tenns nlv hve become reltively more importnt), thus reducing the drg on upwrd shifts ill tile sving function by the mount of expected price level chnges. (3) Interest rtes re more flexible thn in mny pst periods. According to Duesenbeny, Restrictive monetry policy hs in the pst operted to lrge extent through [nonprice} rtionmg Mrket forces nd public policy hve been working towrd perfecting cpitl mrkets, nd thereby reducing the effectiveness (If rtioning... [nd resulting in] world requiring wide swings in interest rtes for stbiliztion purposes Thus, (Inc would expect to find lrger coefficients linking price chnges to interest rtes thn hi the pst. (4) The frme of reference for forniing expecttions my well hve chnged, prticulrly in the 1960 s. The reltive bsence of cycles in prices except for the very distnt pst deprives individuls of succession of comprble reference points from which to extrpolte into the future nd forces the use of hevier xveights On tile more recent pst. Price Expecttions In An Expnded Model A recent study by Thoms J. Srgent~ differs from erlier studies of the effect of price expecttions on interest rtes in two importnt respects. Besides relting pst price chnges to nominl interest rtes, he sought lso to decompose the rel rte into components representing the equilibrium rel rte nd the devition of current rel mrket rtes from the equilibrium rte. In ddition, the shpes of the distributed lgs he estimted were more generl, tht is, cpble of fitting the dt into greter vriety of geometricl configurtions. Srgent devised useful identity: 3~ () (b) (c) mt = ret + (mint ret) ± (mt lint) Rel rte (rmt = rr Fisher effect (Pt) 1 where re 1 is the rte of interest t which rel sving nd investment would be in long-run equilibrium nd rm~is the current mrket level of the rel rte, tht is, rut, is the sme s n, in eqution (1) bove. Movements in the nominl rte my then be ttributed to chnges in the equilibrium rte (), to devition between the equilibrium rte nd the rel mrket rte (b), nd to Fisher effect (c) Duesenberry, pp. 136 nd 140. Thoills J. Srgent, Commodity Price Expecttions nd the Interest Rte, Qurterly Journl of Economics, Februry 1969, pp Smgent, p It is n identity, since it simplifies to rut = nit. Pge 31

15 FEDERAL RESERVE BANK OF ST LOUIS DECEMBER 1969 Erlier studies (including tht which we hve reported bove) regrded either (b) or (+b) s residul nd regressed nominl interest rtes on pst price chnges only, but Srgent ttempted to estimte ech of the components of the level of nomthl rtes. The reltionships mong the components of the nominl rte nd how he sought to identify them sttisticlly re shown in Figure I. Assume tht rel investment (lip) nd rel sving (S/P) re funclions of rel income nd rel mrket rtes of interest nd tht rel income is given (so shifts hi the sving nd investment schedules do not hve to be ccounted for). The equilibrium rel interest rte (re) is the rte t which rel sving nd investment would be in equilibrium. The mrket rte (rm) below the equilibrium rte indictes tht some porlion (AB) of current investment is being finnced from sources other thn intended sving, for exmple, by newly creted money from the bnking system or through the drwing down of previously ccumulted money blnces. This is sometimes clled the Wicksell effect on interest rtes. 38 Assuming svers nd investors form the sme price expecttions nd tht neither re subject to money illusion (n importnt Fisherin concepto), both functions would be shifted upwrd by the expected rte of chnge in prices, P, = rn~ rut 1. Since the equilibrium rte cnnot be directly observed, Srgent used reduced fonn proxy for it. He solved his rel sving nd investment functions simultneously, so tht the one mrket rte consistent with equilibrium (equlity of intended svings nd investment) is function of the other determinnts of rel sving nd investment, nmely rel income nd (from n investment ccelertor) the chnge in rel 38 Knut Wicksell, Lectures on Politicl Economy, pp , nd Interest nd Prices (London: Mcmilln, 1936). Wicksell ssumed tht svers nd investors expected current prices to continue into the future, so he did not need to ccount for price expecttions effects on interest rtes. As Srgent points out, views similr to Wicksell s were lso held by Henry Thornton in 1802 nd by Keynes in A Tretise on Money. Emphsis on the equilibrium rte-mrket rte reltionship s the proper one in using interest rtes s monetry policy indictors nd reiection of price expecttions effects on empiricl grounds chrcterizes recent work of Ptnic H. Hendershott nd Ceomge Horwieb (see, for exmple, The Approprite Indictors of Monetry Policy, Prt II, in Svings nd Residentil Finncing: 1969 Conference Proceedings, pp ). Wht is here clled the Wicksell effect my lso be interpreted s the liquidity effect or impct effect of chnges in the money stock; similrly, the rel GNP vribles reflect the income effect or feedbck effect on interest rtes ssocited with chnges in the money stock (see references to works by Friedmn nd Schwrtz, Gibson, nd Meltzer cited bove). 39 See footnote 34 bove. Jnterest Rtes Figure Illustrtion of Srgent s Identity l/pi (rm,y,y,...) Rel Sving nd Investment income. This solution ws then used to mesure component () in the equlions he estimted. Similrly, hving no independent observtions for the mrket rte, he used nother proxy, the current rte of chnge in the rel (deflted) money stock, for the,devition of the mrket rte from equilibrium. 40 Finlly, Srgent estimted geometriclly distributed lgs on pst price chnges s proxy for price expecttions. Using nnul dt for (two of the regressions were lso run for ) nd tking for nominl rtes Durnd s one-yer nd ten-yer bsic yields, he obtined estimtes implying very long men lgs (twenty yers or more for short- nd long-term rtes). In severl of his regressions he estimted two sets of decy coefficients. Both were positive for the longterm rte; for the short-term rte one ws negtive nd more quickly decying, which Srgent rtionlized s indictive of regressive effect of price chnges on short-term rtes (s opposed to the positive extrpoltive effect ), tht is, price chnges temporrily generte expecttions of chnges in the opposite direction (tht is, tht they will move bck to norml level). The sum of the regressive nd 10 1n Figure I the gp between the equilibrium nd mrkc4 interest rtes will widen s the portion of rel investment not finnced by current rel svings (AB) increses. The rte of chnge in the rel money stock, on the other hnd, should he positively correlted with the mgnitude of AB. As proxy for (tm-re) the rte of money chnge should hve negtive coefficient (tht is, be positively relted to n (re-rim) gp). The entire reduced form for rel rtes should lso cpture the effects of other cpitl mrket disturbnces, for exmple, Covemment surpluses or deficits nd the wys they re finnced (bnking system versus nonbnk public). Pge 32

16 I FEDERAL RESERVE BANK OF ST. LOUIS extrpoltive weights did not rech pek until eight yers nd declined even more slowly therefter (since the negtive component deced more rpidly), so the men lg would not be much different from his other results. The uthors hve subjected Srgent s bsic pproch to further test, with the following modifictions: 1) Both rel sving nd investment re ssumed to depend on both rel CNP nd rel mrket rtes of interest, Thus, there is no priori expecttions s to the sign of the coefficient for the rel CNP tenn in the regressions. A negtive coefficient would presumbly indicte tht shifts in the sving function in response to chnge in rel GNP outweighed shifts in investment, so tht nominl nd rel rtes would tend to fll s rel CNP rose. 4 A positive coefficient would suggest just the opposite, while coefficient ner zero might indicte roughly offsetting effects of sving nd investment shifts. (2) Qurterly nd monthly insted of nnul dt re used, nd s before, the emphsis is completely on the entire post-ccord period nd the subperiod. The regressions with monthly dt necessrily use proxies for rel GNP (personl income deflted by the consumer price index nd, lterntively, the index of industril production) nd the CNP price defltor (consumer price index), (3) The interest rte series nd distributed lg forms re different; further, regressions were ron with nd without constnt term (Srgent did not suppress the constnt term in ny of his regressions The equtions estimted re of the following form: n. - nit = ~ + 2 ± P~ ± js,y + ji AY* + 3 AM t I where P is the nnul rte of chnge in the GNP defltor (or monthly proxy), 1~nd AY re the level nd rte of chnge in rel GNP (or monthly proxy), nd AM is the verge chnge in the rel money stock (nominl money stock deflted by the GNP defltor or its monthly proxy). Nominl rtes (rn) re gin the four- to six-month commericl pper rte (rn ) nd the corporte A yield (rn ~), using qurterly verges of monthly dt in the qurterly regressions. Only results for the subperiod will be reported here, in Chrt VII, nd in the ppendix. The explntory power of price level chnges ws chnged little when the equtions were more fully 41 Srgent obtined negtive coefficients in ll of his regressions. In his theoreticl model he ssumed tht only sving ws functionlly relted to the level of rel GNP. DECEMBER 1969 specified, nd the djusted R s rose by smll mounts. For exmple in the equtions for the long-term rte with second-degree Almon polynomils, totl lgs of 16 qurters (best sttisticl fit), nd constnt term, the sum of the coefficients on current nd lgged rtes of price chnge ctully rose from 0.80 to 0.86, nd the R 2 ws unchnged t when the current rel GNP nd rel chnge in the money supply were dded to the regression; further, the men lg for the effect of price chnges on nominl rtes incresed from 3.2 qurters to 5.5 qurters. In other words, recent price chnges lone tend to overstte the necessry djustment of nominl rtes to ccount for the Fisher effect. As would be expected, the coefficients on current nd lgged rtes of price chnge were redistributed towrd the pst in the expnded equtions, since the current nd lst qurters price levels implicitly enter into the other independent vribles. 4 Suppressing the constnt term in the eqution (tht is, forcing % to zero) forces redistribution of its effects over the other coefficients. In the cse of the long-tenn rte, the constnt ws not significnt, nd suppressing it enhnced slightly the explntory power of rel CNP nd the chnge in the rel money supply, lowered the sum of the price chnge coefficients (to 0.80) nd the ccelertion coefficient (p ), left the R 2 virtully unchnged, nd lengthened the men lg (by three qurters with totl lgs of 16 qurters). In the cse of the short-term rte, the men lg rose from zero to nerly one qurter. Otherwise, the effects on the coefficients were exctly opposite to wht hppened when the constnt ws suppressed in the eqution for the long-term rte. Since the expnded equtions contin vribles not ll mesured in the sme units, bet coefficients were computed in order to ssess the reltive contribution of ech independent vrible to the determintion of nominl interest rtes. In the eqution for the long-term rte with vrious lg lengths the bet coefficient for price level chnges is nerly three times s lrge s for rel GNP, which rnks second in importnce. 4m The eqution ws lso estimted for vrious lengths of totl lgs without the current rte of price level chnge (ll of Srgent s regressions were of this form) to try to reduce multicollinerity. With totl lgs of 16 qurters, the sum of the coefficients on the lgged price chnges i-i-i rose slightly, P~nd 1~,remined bout the sme, /3~ declined in bsolute vlue by bout 10 per cent, nd the R2 nd Durbin-Wtson sttistics rose slightly. Pge 33

17 FEDERAL RESERVE BANK OF ST. LOUIS DECEMBER 1969 A? tr -~~A ~ new sin ~ /4A A,. AAW4 n<~e~a~~ / AN A A A çaan 2 L~ ~AA¼A /A\ A_ N A ~ >~ ~ n~-~c coefficients were smller thn in the qurterly regressions, suggesting tht the response of the equilibrium rel rte of interest to rel income growth my occur over substntilly longer period thn the current month. 44 >~ei~t I Fl- FF11 ii Ni U Thus, the findings reported in this section pper to support the specifiction of vribles in Srgent s model. The use of qurterly nd monthly dt over post-ccord period nd the estimtion of Almon lgs provide better sttisticl results thn in his study. The importnce of price level chnges in explining nominl interest rtes is diluted very little by the expnded equtions, nd the men lgs re not sufficiently lengthened to lter the conclusions of the erlier sections of the present study. V r~ C AN Srgent s expnded model ws lso tested with monthly dt, using lterntively, personl income deflted by the consumer price index nd the index of industril production s proxies for the rel GNP ( series derived from the regression using the ltter ppers in Chrt VII s rel rte 3). The results closely prlleled those for the equtions using qurterly dt, For exmple, in the eqution for the longterm rte with totl lg of 48 months, the index of industril production s the rel GNP proxy, nd constnt term (which ws significnt in the monthly regressions), the sum of the price chnge coefficients fell from 0.87 to 0.82, the men lg rose slightly from 15.6 to 16.4 months, nd the R went from to Ø 971~ The chnge in industril production nd the chnge in the rel money supply hd the correct signs but were not significnt; one month is probbly too short period to cpture the full Wicksell (liquidity) effect. The level of industril production turned out to be quite significnt, but the m flesults using pcrsonl income deflted by the consumer price index ~verevirtully identicl to those using the index of industril production s the proxy for rel CNP. Pge ~ ~ ~ - ~n. ~ 4flT4t,\~flMt~?R / A A A AN~AN ~ A, ~~ - A~A AAAAA~,~\N / -- A A <A A, AN -A A A <,A, -~ A N ~<~A-A<NT~ /\ /AN NAN~± ~<Nc,,/A -AN C,, A/A A t Experimentl Time Series For The Rel Rte of Interest The Federl Reserve Bnk of St. Louis begn clculting nd publishing n experimentl monthly series for the expected rel rte of return on Corbonds in 1966.~~The procedure em- porte A ployed ws to subtrct from the ctul A yield simple verge of rtes of chnge in the implicit GNP price defltor for the previous twelve months (qurterly price defltor dt were interpolted to obtin n estimted monthly index). Such procedure necessrily implies tht the men lg is hlf s long (six months) s the totl lg nd tht the cot4it should lso be noted tht there is nother possible source of mis-specifiction in ll of the expnded equtions, nmely, the interreltionship between chnges in the nominl money stock nd both price levels nd rtes of chnge. In other words, the monetry uthorities would be expected to respond to deprtures from stble prices. One wy round this problem is to mke the policy vrible endogenous in simultneously estimted model contining rection function for the Federl Reserve (see Michel W. Kern nd Christopher T. Bbb, An Explntion of Federl Reserve Actions ( ), this Review, July 1969, pp. 7-20; nd Rymond C. Torto, An Edogenous Tretment of the Federl Reserve System in Mcro-Econometric Model, unpublished disserttion, Boston College, ~ 5 Strong Totl Demnd, Rising Interest Rtes, nd Continued Avilbility of Credit, this Review, August 1966, pp. 3 nd 4.

18 efficients re constrined to sum to one. 4 Shortly fterwrd the lg for verging price chnges ws extended to 24 months (men lg of 12 months), nd the resulting proxy for the rel rte hs been reported periodiclly ever since. As testimonil to the intuition of the series cretor, the distributed lg results in the present study yield estimtes of the mgnitude of effect nd the men lg which re remrkbly close to the originl rel rte series. Chrt VII contins the nominl corporte A yield from 1960 to October 1969 nd vrious estimted monthly rel rte series. Rel rte 1 is the originl series, tht is, the nominl rte minus the verge of rtes of price chnge over the preceding two yers. Rel rte 2 is obtined from the regression using monthly dt for , totl lgs of 48 months, nd second-degree polynomils.. Rel rte 3 is derived from the regression reported in the preceding section, which seeks to explin the contribution of rel rtes, s well s price expecttions to nominl rtes of interest; rel rtes here re ssumed to be relted to the level of nd chnges in the index of industril production nd chnges in the deflted money stock. Detiled nlysis of the movements in these series will require seprte study. 4~ Only few observtions will be mde here. The pttern of movement in ll three rel rte series is remrkbly similr. The old rel rte 1, however, ppers to hve overstted the price expecttions component of the nominl rte over most of the period. Wht is of prticulr interest re the occsions when chnges in nominl rtes gve pprently flse signls bout the nture of chnges in rel rtes nd the extent of greement bout directions of movement mong the three rel rte series. All three rel rtes indicted tht credit conditions were progressively tighter during the first hlf of 1961, when the nominl rte ws virtully unchnged. The nominl rte ws resonbly good proxy for rel rtes 2 nd 3 during 1962 but not for rel rte 1, which rose for most of the yer (the consequence of hevier implicit weights thn the other two series on price chnges two yers 40 Mthemticlly, pe = P, ~,where is the length i=1 of the totl lg, nd there re exctly coefficients, ech of which equls 1/n (hence, the sum is ~1/n = 1). Moving verges with equl weights re discussed by Griliehes, p ~Avriety of other monthly nd qurterly rel rte series hve been computed, including short term rel rtes. erlier nd lighter weights on the pst yer). The grdul upwrd creep in prices from cused rel rte 1 to creep smoothly downwrd, generlly opposite in direction to the nominl rte. With the different pttern of weights, movements in the rel rtes 2 nd 3 were more pronounced, indicting tht underlying price level chnges were not entirely smooth over the intervl. Rel rtes 1 nd 2 fell nd rel rte 3 oscillted round constnt level during the first hlf of 1966, while the nominl rte rose. From lte 1966 until erly 1967, ll rtes moved down in step. From , the originl rel rte 1 tended to drift downwrd nd oscillte somewht mbiguously, lthough the three rel rte series fell before nominl rtes declined in the summer of Rel rtes 2 nd 3 moved upwrd wi-th the nominl rte from lte 1968 until erly For severl months therefter, nominl rtes did not rise by enough to offset the effects of rpid infltion, with the consequence tht the monthly rel r-tes ctully fell from bout Februry until lte in the summer. Such movenient in rel rtes could be used to explin, in prt, the strength of the 1969 surge in investment spending. Conclusions Citing the findings by Gibson nd Srgent of long lgs in the forming of price expecttions, Hendershott nd Horwich recently rgued: Their experience contrdicts the monetry voices in government, industry nd the cdemy tht proclim, hi it do not demonstrte, tht price level expecttions, rther thn rel forces, re lrgely responsible for interest rte move mets in this decde. ls In contrst, the present study hs shown tht, unlike the erlier historicl periods on which most of the previous studies hve been bsed, price level chnges since 1952 hve evidently come to hve promp-t nd substntil effect on price expecttions nd nominl interest rtes. tn ddition, the totl effect of 1 rice expecttions on interest rtes nd the speed t which they re formed pper to hve incresed gretly since This conclusion is invrint to the form or the term of the flexible clsses of distributed 48 Hendershott nd Horwich, Approprite Indictor, p. 44. Criticizing the erlier St. Louis rel rte, they continue, The Fisherin zel of tht institution would shock no one more thn In ing Fisher, who himself stressed the fntsticlly long lgs in the formtion of price level expecttions nd their impct on interest rtes in this country. Pge 35

19 FEDERAL RESERVE BANK OF ST. LOUIS DECEMBER 1969 lgs estimted. Most significnt is the finding tht price level chnges, rther thn rel rtes, ccount for nerly ll the vrition in nominl interest rtes since Furthermore, the ddition of vribles to the regressions to ccount explicitly for the rel rte components of nominl rtes does not pprecibly lter these findings. The cuses of price level chnges over the period of the study hve not been investigted. The primry concern hs been to determine the extent to which nominl rte movements my be ttributed to expecttions bout future rtes of chnge in prices, so tht nominl rtes my consequently be djusted to yield informtion bout movements in underlying rel rtes. 4 The filure to mke such n djustment nd the sole use of chnges in nominl rtes s indictors of monetry ese or tightness my on occsion give misleding informtion bout the direc- 10 An interesting ttempt to neutrlize interest rtes with respect to the impct of movements towrd or wy from full employment ws reported in Dennis H. Strlef nd Jmes A. Stephenson, A Suggested Solution to the Monetry Policy Indictor Problem: The Monetry Full Employment Interest Hte, Journl of Finnce, September 1969, pp Unfortuntely, the uthors did not incorporte price level chnges into their nlysis, which is serious deficiency in their work. tion nd the extent of movements in rel rtes. The importnce of the Fisher effect to the controversy over pproprite monetry policy indictors hs been succinctly stted by Dvid Fnd: As we get closer to world of high employment, nd especilly if interest rtes nd prices re both rising, the money stock my be better (less misleding) indictor or trget vrible thn [nominl] interest rtes. Prdoxiclly, the current tendency to emphsize interest rtes nd to ignore chnges in the money stock would seem more relevnt to society where interest rtes nd prices re flling while the money stock is constnt, or using t lower rte thn output. 5 According to economic theory, chnges in rel rtes should then reflect both shifts in the equilibrium reltionship between rel sving nd investment nd current cpitl mrket disequihbrium. Further, it is such rel rte series tht should be employed in studies of the term structure of interest rtes nd of the effects of interntionl interest rte differentils on short nd long term cpitl flows DvidFnd, Keynesin Monetry Theories, Stbiliztion Policy, nd the Recent Infltion, Journl of Money, Credit nd Bnking, August 1969, p This rticle is vilble s Reprint No 49 The Appendix to this rticle begins on the next pge. Pge 36

20 APPENDIX Nominl income As Proxy for Prices ny devitions due to short-run chnges in finncil Gibson suggested tht movements in nominl income mrkets. The series 2 ws generted from the following reltionship: might serve s mesure of price behvior. His resoning ws tht the CPI might be unble to ccurtely mesure short-term price movements since it is selective index of prices. Nominl income, on the other hnd, contins n implicit generl price index. (1) mt = o + ip t +,P, ~ Pc~ 9 4~ Regressions using current nd lgged monthly rtes of chnge of nominl personl income (PY) were run nd the ptterns of coefficients re similr to those resulting from the runs using the CPI. To djust for the difference in mgnitude between the income nd price index series, bet coefficients were computed in Tble 1 below. Tble I SUM OF THE BETA COEFFICIENTS ( ) Short-term rtes Lng term rte 24 lgs lgs lgr / The expecttionl effects of prices on interest rtes, s indicted by movements in nominl income, re lrger thn those suggested by movements in the CPI. In ddition, use of nominl income results in somewht longer lgs, hut lmost ll of the effect still occurs within two yers. The Rel Rte of Interest Series The rel interest rtes (series 2 nd 3) presented in Chrt VII re ctully the Wicksellin mrket rte (rmt) or the long-run equilibrium interest rte plus Tble ii REGRESSION COEFFICIENTS mr. ~ j ~.,I. N Iinucry September 1969~. t.viuc I i t VOIJe / / ) Il i )8/ IS % ) ~oristr t Arthur S. Goldberger, Econometric Theory (New York: John Wiley & Sons, 1964), pp It: Pge 37