CENTRE FOR ECONOMIC PERFORMANCE DISCUSSION PAPER NO November 1993 REAL INTEREST RATES AND INDEX LINKED GILTS D. ROBERTSON AND J.

Transcription

1 CENTRE FOR ECONOMIC PERFORMANCE DISCUSSION PAPER NO. 181 November 1993 REAL INTEREST RATES AND INDEX LINKED GILTS D. ROBERTSON AND J. SYMONS

2 ABSTRACT This paper derives he ex ane pahs of he fuure expeced shor (one period) real ineres raes a quarerly frequency from observaions on he prices of a se of UK index linked bonds. These raes are used o invesigae he impac of moneary policy and he naure of expecaions formaion in he bond marke. This paper was produced as par of he Cenre's Programme on Naional Economic Performance

3 REAL INTEREST RATES AND INDEX LINKED GILTS Donald Roberson and James Symons * Inroducion 1 1. The pah of expeced fuure shor real ineres raes wih perfecly indexed bonds 4 2. Tax and risk issues 9 3. Empirical implemenaion UK ex ane real ineres raes Conclusion 18 Page Endnoes 19 Tables 20 Figures 24 References 27

4 REAL INTEREST RATES AND INDEX LINKED GILTS Donald Roberson and James Symons * Inroducion The ex ane real ineres rae is he cenral variable in mos convenional neoclassical macroeconomics. If one had a ime series of such raes, many conroversies could be resolved. The problem is, of course, ha he ex ane real ineres rae is no usually observed. One observes nominal ineres raes, bu no price expecaions. Price expecaions can be obained from survey daa, abou which economiss are nooriously scepical; or by regression forecass. Woodward (1990) noes ha such forecass "basically amoun o conjecure". Index linked bonds (ha is, coupon and principal paymens rise in line wih a price index) offer a direc measure of he ex ane real ineres rae. A number of counries have issued, and coninue o issue, index linked deb. The Briish marke is by far he larges, wih he mos comprehensive range of mauriies. For governmens, one advanage of index linked bonds occurs when privae secor expecaions of inflaion exceed hose of he governmen, perhaps because markes are wary of governmen inenions. In his case index linked bonds enable funding a lower cos (provided he governmen does indeed deliver lower inflaion), as well as he opporuniy for he governmen o influence expecaions. This argumen led he recenly eleced Briish governmen o inroduce index linked bonds (gils) in For much of he 70s funding had been a negaive ex pos real ineres raes, leading o marke scepicism abou ani-inflaionary resolve. Mrs Thacher's adminisraion had, as i urned ou, a srong commimen o reduced inflaion. More

5 generally, governmens may feel ha caering for a wider range of ases will reduce he cos of financing he defici. The major worry abou index linked bonds, cerainly in he US, is how o ax he indexed componen. In 1985, Francis X. Cavanaugh of he US Treasury argued before he Join Economic Commiee of Congress ha ax privileges would have o be awarded o index linked bonds o make hem aracive, hus raising he cos o he Treasury. However, in principle, given any ax regime, index linked bonds would rade a some price, and a low issue price presumably reflecs he presen value of fuure ax paymens remied o he Treasury. Thus, apar from iming, he Treasury's posiion is unaffeced. This issue is sidesepped in he UK, where capial gains on all gils are ax-exemp. Anoher worry in he US, also expressed by he Bank of England a he firs issue, is ha increased use of index linked conracs could weaken ani-inflaionary resolve. Even so, wihou a deailed model of he coss of inflaion, i is no clear ha his would enail a welfare loss. Beween 1981 and mid-1992 he Briish governmen issued 14 index linked 1 gils, wih mauriies up o abou 30 years, consiuing, by he early 90s, abou a fifh of he marke value of all gils. This paper uses he prices of hese securiies o calculae he expeced pah of shor ex ane real ineres raes a each dae from 1984q1 o 1992q2, up o he 30 year horizon. The paper is organised as follows. Secion 1 uses a presen value formula for bond prices o derive he pah of expeced fuure shor real ineres raes, given observaions on he prices of a se of perfecly indexed bonds. Such observaions enable he calculaion of he expeced average fuure real ineres rae beween he mauriies of he available bonds, i.e. hey give he fuure expeced pah as a sep 2

6 funcion. These can hen be smoohed in a variey of ways. This echnique uses only he informaion in he prices. I does no assume a specific model of he erm srucure, nor, in paricular, does i make assumpions abou expecaions. Unforunaely he indexaion is no perfec: coupons and principal are adjused 2 in line wih he reail price index lagged eigh monhs. Thus he index linked bond price includes elemens of he nominal erm srucure. Secion 3 describes how o deal wih his wihou making ad hoc assumpions abou expecaions. Essenially we use he observable nominal erm srucure, calculaed from a se of convenional bonds, o discoun he eigh monh lag in indexaion. Woodward (op. ci.) has inroduced his echnique, bu calculaes only yields o mauriy. Our aim, however, is o calculae he full expeced fuure pah of he shor real ineres rae a each dae. Secion 4 uses hese real ineres raes o es some macroeconomic proposiions. So far, Briish Index Linked gils have no been used exensively for his purpose. Barro (1987), in his macroeconomic ex, liss some yields o mauriy as evidence of he relaive sabiliy of he ex ane real ineres rae compared o he nominal rae. Arak and Kreicher (1985) use hem o generae a pah of expeced UK inflaion. Roberson and Symons (1994) sudy he behaviour of real ineres raes and inflaion expecaions, over he period of serling's exi from he ERM. Mos oher discussion has aken place in he finance lieraure. Secion 5 concludes. 3

7 1. The Pah of Expeced Fuure Shor Real Ineres Raes wih Perfecly Indexed Bonds We commence our analysis by assuming he exisence of a riskless bond which pays a coupon c, perfecly indexed o an appropriae price index, wih an indexed mauriy paymen of 100 in m periods' ime. If a single risk-neural zero-ax-paying invesor willingly holds his securiy as well as nominal securiies of all inervening mauriies arbirage implies (1) g =(1/p )[cp /(1+r )+cp /(1+r )(1+r )+..(c+100)p /(1+r )..(1+r )] b m +m-1 where g is he price of he bond r is he nominal ineres rae in period p is he price level in period, b is he base period for indexaion Price levels daed laer han are assumed o be expeced values formed a. If we define he shor real ineres rae D as 1+D =(1+r )/(p /p ) +1 he arbirage condiion akes he form (2) g =(p /p )[c/(1+d )+c/(1+d )(1+D )+...+(c+100)/(1+d )...(1+D )] b +1 +m-1 Wrie (2) more succincly as (3) g =g (D) where D is he vecor of real ineres raes from o mauriy. The published yield o mauriy of his securiy would be he soluion y o (4) g =g (y1) where 1 is a vecor of 1s. We can expand (3) as a Taylor series abou y1: (5) g =g (y1)+( g/ D) (D-y1) 4

8 where he derivaive is evaluaed a y1 and we have negleced higher order erms. Making use of (4) we obain (6) y=(1/( g/ D) 1)(( g/ D) D) The derivaive g/ D can be readily evaluaed from (2). For example, he firs enry is m+1 (7) g/ D =(p /p b)[-c/(1+y)²-c/(1+y)³-...-(c+100)/(1+y) ] 2 The nex enry is obained by deleing c/(1+y) ; and, in general, successive enries are obained in like manner by deleing erms from he lef in (7). Thus (6) expresses he yield on a securiy as a weighed average of fuure shor raes where he weighs decline for more disan raes. I is easy o see ha he weighs decline quie slowly: approximaely a he rae 1/(1+y). Assume here exiss a a family of n indexed-linked securiies, differing by mauriy daes, and perhaps also by coupon value. Then each securiy saisfies a version of (6). We can capure he whole conen of he observed yields in a marix equaion (8) A D =y where y is he vecor of published yields, D is he vecor of shor raes ou o he maximum duraion securiy in he family and A is a marix whose rows consis of posiive declining weighs. There is one row for each bond. For convenience, we assume hese rows are ranked according o mauriy dae, shores o longes. Usually we shall drop he dae subscrips in (8). Equaion (8) gives all he informaion concerning he pah of he ineres rae implici in he curren se of yields (or, equivalenly, he curren se of bond prices). I is clear ha one canno, in pracice, recover D from (8) because here will be many 5

9 more enries in D han differen securiies, i.e. here are more unknowns in (8) han equaions. To idenify D some furher assumpions are required. We now consider he procedure we have found mos fruiful. Define he mesh of a family of n securiies of differen mauriies as he decomposiion of he oal duraion of he longes running securiy [, +m ] ino n segmens [,+m ], [+m +1,+m ],..., [+m +1,+m ] n-1 n where m <m <...<m are he periods o mauriy of each securiy. Le D be he mean 1 2 n i of D on he i'h mesh segmen and wrie D =(D,..., D ). If D were consan on mesh 1 n segmens hen (9) D=WD where W is he appropriae m xn marix of 1s and Os. In his case he arbirage n condiion (8) becomes (10) AWD =y I is easy o see ha AW is nxn of full rank so (11) D=W(AW) -1 y If D is no consan over mesh segmens hen one can sill compue he righ hand s s side of (11): call i D. Now D is a sep funcion consan over mesh segmens, and s -1 D = W(AW) y -1 = W(AW) AD -1 = W(AW) A (WD + D-WD ) -1 = WD + W(AW) A(D-WD ) For smooh-changing D and narrow mesh segmens, A(D-WD ) will be approximaely zero (he discrepancy arising because he rows of A are no quie consan over mesh 6

10 segmens). I hus follows ha s (12) D WD s i.e. he values of he seps in D compued according o (11) are approximaely he arihmeic averages of D over he mesh segmens. s The measure D has is aracions as i uses only he arbirage condiion o s produce an esimae of he pah of D. While an esimae of D +i based on D will be he average of values of D around D saisfacory. +i, if he mesh size is small, his may be s One problem wih D is ha i will jump disconinuously a he mesh boundaries. One migh hink one could ge closer esimaes of D if some sor of smoohness were imposed. Smoohness, however defined, is quie a plausible prior for he pah of fuure ineres raes for a leas wo reasons. A good neoclassical reason is ha capial canno jump insananeously - only invesmen - and hence he same applies o is marginal produc. A differen jusificaion of his prior is ha ypically, even if one believes quie srongly ha some even will ake place in he fuure, one is ofen unsure exacly when his will be. This uncerainy ends o smooh he expeced pahs of exogenous variables. We have sudied several procedures o consruc smooh pahs of ineres raes saisfying he arbirage condiion. Consider he soluion o: (13) minimise over D : D DD subjec o AD=y where D is some specified marix. For example, we migh choose D so ha (14) D DD = (D -D )² -1 whereupon he above procedure amouns o choosing he ineres rae pah saisfying he arbirage condiion ha minimises he sum of squared changes. This procedure 7

11 is analogous o he Hodrick-Presco (1980) filer for consrucing he rend of a ime series. A differen, more sandard, mehod of imposing smoohness is o assume he ineres rae pah lies in some specified funcion space: (15) D=H$ where he columns of he marix H are smooh funcions of ime (e.g. polynomials) and $ parameers o be fied. Subsiuing (15) ino (8) we have (16) AH$=y from which $ can be recovered by regression for any number of parameers up o he number of securiies in he family. We sudied he performance of hese mehods by formulaing wo possible synheic pahs for shor erm ineres raes: firs, exponenial decline from a curren high level o a fuure lower level; and second, an ineres rae which increases from a curren low level o a peak in some years ime, and hen declines o some 3 asympoic value. Yields o mauriy were calculaed using hese ineres rae pahs for a family of securiies defined by he coupons and mauriies of he index-linked gils exising in he summer of Using hese yields we aemped o recover he original synheic ineres rae pah. Two classes of funcions were used in (16): n n 2 polynomials in ime { } and he Hermie polynomials { exp(- /2)}. There are abou a dozen index-linked gils in operaion, hus enabling up o welve polynomials o be fied. Once he Hermie polynomials were appropriaely scaled (i.e. unis of ime chosen) hey were much superior o ime polynomials in erms of maximum and minimum error and variance of error. Naurally, he fi improved wih he degree of polynomial used. However, once his mehodology was applied o real daa, an 8

12 imporan problem emerged. High-order polynomials ended o produce ineres rae pahs wih a large number of inerior maxima and minima. Moreover he ineres rae pah ended o be moving abou subsanially even 30 years ino he fuure. The firs of hese problems affeced also he esimaes calculaed by he smoohing procedure (13) and (14). We found we obained plausible resuls for Hermie 2 2 polynomials up o a maximum degree of wo (i.e. exp(- /2)). This allows, a mos, one inerior maximum and one inerior minimum. In pracice we did no calculae he fied pah from (16). Insead we smoohed s he sep funcion D. Our reasoning was ha i is beer o sick as close as possible o wha one knows o be rue (given arbirage) raher han o leap ino he dark wih economeric esimaes which migh have unpleasan properies given sochasic errors in (8) and (15). 2. Tax and Risk Issues We noe ha (1) is no adjused for axaion. In principle he sream of coupon paymens should be adjused for expeced fuure ax raes. There are wo relaed mehods in he lieraure for dealing wih his. One can nominae a ax rae and calculae he corresponding erm srucure using some mehod o choose he se of ax efficien bonds for ha ax rae (e.g. Schaeffer (1981)), or one can esimae an average ax rae effecive in he marke by some bes fi crierion (e.g. Woodward (op. ci.), Levin and Copeland (1992)). Invariably hese mehods impose a consan ax rae o he mauriy horizon of he securiy; which is plainly quesionable. However here is one large player in he marke for whom a fuure ax rae can be nominaed wih some cerainy: he ax exemp pension funds. There has 9

13 never been any prospec of change in he ax saus of hese insiuions. A he end of 1990 he pension funds had oal asses of billion, roughly 60% of UK GDP. Table 1 shows hey hold nearly half of he oal index linked issue as well as significan holdings of convenional gils of all mauriies, hough skewed o longer daed sock. The cenral conenion of his paper is ha such a large unaxed collecive insiuion, holding a full range of securiies, is sufficien o enforce he arbirage condiion (1). Levin and Copeland (op. ci.) assume he expeced pah of he real ineres rae is consan (bu unknown) a any poin in ime and ha inflaionary expecaions decay exponenially from a curren (unknown) level o some long run level (also unknown). Wih hese assumpions hey are able o solve for he real ineres rae, he pah of inflaionary expecaions and a marginal ax rae effecive in he marke. They find ha his rae declines from an average of abou 15% in he 80s o abou 5% in he 90s. Woodward (op. ci.), esimaing over he 80s, finds an average closer o 25%; an OLS regression of his esimaes on hose of Levin and Copeland gives: (Woodward's ax rae) = (L&C's ax rae) (4.3) (1.8) 2 Esimaion period 84q1-89q1, quarerly daa, R =0.15, -saisics in parenheses Given he srong assumpions required for eiher of hese esimaes, in paricular he consancy of marginal ax raes over he horizon of he se of bonds, he lack of agreemen beween hem suggess ha he issue is no resolved by his sraegy. A beer procedure is o selec, as we do below, securiies ha are especially aracive o ax exemp insiuions, and assume a zero ax rae in (1). Even if he marginal bond owner does pay ax, in he UK his ax is only ever on coupon 10

14 paymens. For long daed socks, where he coupon componen of he price is large in he presen value formula, Table 1 shows ha he ax exemp insiuions hold a large par of he sock. So axaion is no an issue here. A he shor end of he marke, he low coupon values mean ha he (axable) coupon sream only comprises a small par of he price. Here, he major par of he reurn is he (ax free) principal repaymen. So ax effecs are likely o be minor here as well. We calculae ha for a 2% bond wih a en year horizon and a marginal ax rae of 10%, he assumpion of a zero ax rae would give an error of a mos abou a fifh of one percen in he real ineres rae calculaion if he real ineres rae is wo per cen. The presence of risk however would break he arbirage condiion. There are hree possible sources of risk for holders of a gil: he risk of defaul, he risk of changes in inflaion, and he risk of changes in he spo ineres rae. The UK has never defauled and one can safely assume his risk away. We wish o argue ha he remaining wo caegories are small compared o he real ineres rae. Levin and Copeland (op. ci.) are also able o calculae an inflaion risk parameer a each period. They find ha he risk premium is a mos abou en percen (and usually considerably less) of he real ineres rae. To he exen ha heir assumpions are some sor of approximaion o realiy, he consisency of heir esimaes of he risk premium indicaes ha i is probably a small effec. Woodward (op. ci.) argues similarly, by differen mehods. 3. Empirical Implemenaion Briish index-linked gils are no perfecly indexed o he price level. Coupons 11

15 and he principal repaymen are adjused by he reail price index (RPI) eigh monhs before he paymen; and he base price iself is he RPI eigh monhs before he issue of he bond. Thus, leing refer o monhs, (17) g =(1/p )[c p /(1+r )+c p /(1+r )(1+r )+...c p /(1+r )...(1+r ) b c p /(1+r )...(1+r ) c p /(1+r )...(1+r )] m +m-8 +m-1 where c is he monhly unadjused paymen, zero if here is no paymen in monh +i +i, and including he principal a mauriy. As before prices daed laer han are assumed known only in expecaion. In (17) he firs eigh erms are known a. 4 Call his componen O and he remainder F (O and F sanding for observed and forecas). Then (18) g =O (r)+f (r,d) where (19) F =(p /p )[c /(1+D )(1+r )..(1+r ) +... b c /(1+D )..(1+D )(1+r )...(1+r )] +m +m-9 +m-8 +m-1 Equaion (18) makes clear ha he price of index-linked gils is he sum of he price O of a hypoheical pure nominal bond, and he price F of a bond ha depends on boh he nominal and he real erm srucure. Published yields are he soluion y o (20) g =O (r 1)+F (r 1,y1) where r =(1+y)(1+B)-1 and B is some assumed inflaion rae, eiher 5 or 10 per cen in he Financial Times. Assume he nominal erm srucure is known and expand F from (19) as before around he vecor y1. One obains whence g=o+f(r,y1)+( F/ D) (D-y1) 12

16 (21) y+(1/( F/ D) 1)(g -O -F (r,y1))=( F/ D) 1)( F/ D) D) Comparing (21) wih (6) one can see ha here is an exra erm on he lef. In pracice his erm is always quie small. Thus we have reesablished (8) provided a small correcion is made o y. Given a family of index-linked bonds we have herefore (22) A D = y where now he rows of A are F/ D for each bond. * This analysis is predicaed on knowing he nominal erm srucure since F/ D depends on r. We amend he mehods discussed above. The arbirage condiion for nominal bonds leads o an analogue of (8). N A r=y N N where A is a readily-calculable weighing marix, r is he vecor of shor-erm N nominal ineres raes and y is a vecor of published yields. We compue he s nominal erm srucure r ha is consan on mesh segmens (for he chosen family s of nominal bonds) according o (11). Where r sops shor of he mauriy of he longes daed index-linked, we carry i forward a is compued average over he final s wo years of is duraion; we hen smooh r ono a consan and he firs hree Hermie polynomials. In order o work a quarerly frequency, nominal yields were colleced on he las working day of each quarer for he family of nominal gils recorded in Table 2. This family was seleced where possible o be congruen in mauriy srucure o he index-linked family (lised in Table 3), and, imporanly, o have higher coupons han coniguous nominal gils. Our reasoning here was ha such gils would be especially aracive o zero ax payers, as discussed above. Thus hey approximae he 13

17 appropriae discoun facor for he nominal componen of index linked gils held by zero ax payers. This hen allows calculaion of a gross nominal erm srucure. Noe ha he longes daed nominal gil maures in 2017, seven years before he longes daed index linked, so ha we shall use he procedure oulined above o exend he nominal erm srucure o he full horizon. Given he nominal erm srucure we may now compue he rows of A, F/ D, in (22). To conver he exising family of index-linked gils ino a form suiable for analysis a quarerly frequency we replace hem by a synheic family whose coupon drops occur on he las day of he appropriae quarer. For example, if an indexlinked pays on February 17 and Augus 17 we calculae by he presen value formula he price of an index-linked of he same yield (as published in he Financial Times, aking he 5 per cen inflaion varian) and quarers o mauriy, bu paying a he end of March and Sepember; and replace he original gil price by his new hypoheical gil price as g in (21). Finally, o conver (19) ino quarerly form, we assume nominal and real ineres raes are consan wihin quarers so ha, for example, he 1/3 2/3 erm (1+D )(1+r +1)... (1+r +8 ) is replaced by (1+D ) (1+r +2 )(1+r +3 ). Noe ha in he second expression indexes quarers (and r refers o a quarerly ineres rae) whereas indexes monhs in he firs expression. above To summarize, o obain he erm srucure of real ineres raes: (a) We evaluae he nominal erm srucure according o he mehod described (b) This enables F/ D o be calculaed from (19) and evaluaed a he published yields. (c) Thus A in (22) is known; and y* can be compued from (21). 14

18 s (d) Formula (11) hen gives D, which can be smoohed if desired. 4. UK ex ane real ineres raes The resuls of applying his procedure over he period 84q1 o 92q2 are displayed in Figures 1-4. Figure 1 displays he surface of he underlying sep funcions for he nominal erm srucure and Figure 2 he resul of smoohing his surface ono he Hermie polynomials. Similarly Figures 3 and 4 graph he surfaces of he underlying sep funcion and he corresponding smoohed surface for he real erm srucure. A differen perspecive on he behaviour of he real ineres rae is obained by graphing secions hrough he surfaces. Figure 5 graphs, and Table 4 liss, he average expeced real ineres rae over he nex eigh quarers, and he esimae of he real ineres rae in 2024, quarerly from 84q1 o 92q2, aken from he smoohed surface. Wha is immediaely sriking is he volailiy of he shor real ineres rae and he sabiliy of he long real ineres rae. The long real ineres rae is approximaely consan a abou 2.7% from 1984 o 1989, hen rises sharply o abou 4.2%. The rise coincides wih he emergence of a genuine possibiliy of marke economies in Easern Europe. The associaed capial requiremens will raise he demand for world savings and hence imply an increase in he world real ineres rae. If his is he correc explanaion for he rise in he long rae in Figure 5, i is ineresing ha he markes ake he view ha equipping he former communis saes will ake more han 30 years. The behaviour of he shor real ineres rae is more problemaical from a neo-classical perspecive. If we assume he major insrumen of moneary policy rae in he UK in his period o be he reasury bill rae, and ha changes in his rae correspond o 15

19 moneary shocks, we can invesigae he correlaions beween moneary policy and he real ineres rae. Defining he shor real ineres rae as he average expeced rae over he nex wo years, he medium rae as he average expeced rae beween horizons of four and five years, and he long rae as ha expeced a he horizon of he longes daed index linked bond (i.e. 2024), we obain he following OLS esimaes from 84q1 o 92q2 (-saisics in parenheses): 2 (shor RIR) = (shor RIR) )TBR R =0.49 (2.5) (5.5) (2.1) (medium RIR) = (medium RIR) )TBR 2 R =0.34 (1.8) (3.7) (0.8) 2 (long RIR) = (long RIR) )TBR R =0.85 (0.3) (13.1) (0.1) where )TBR is he one quarer change in he UK reasury bill rae. There is lile evidence of residual misspecificaion in hese regressions. The level of he reasury bill was insignifican in all regressions. These regressions sugges ha moneary policy, as capured by movemens in he reasury bill rae, does have an imporan effec on he shor real ineres rae, bu only on he shor rae. The impac effec of a 1 percenage poin reducion in he reasury bill rae is a 0.17 percenage poin reducion in he expeced shor real ineres rae. Afer one year, his reducion implies a fall of abou 0.03 percenage poins in he expeced shor real ineres rae. To obain a more persisen fall in he shor real ineres rae will require coninual cus in he reasury bill rae. Thus from early 1986 o mid 1988, he reasury bill rae fell from 12.5% o 7.3% in a sequence of downward and upward movemens around a downwards rend, accompanied by he 16

20 long fall in shor real ineres raes eviden in Figure 5. The moneary squeeze ran hese evens in reverse. Levin and Copeland (op. ci.) deec similar movemens wih heir version of he real ineres rae. The esimaes imply ha only 20% of he effecs of a moneary shock remain afer four quarers. This seems o imply ha, a leas via his channel, he classical dichoomy is approximaed wihin one year. The calculaed pahs of expeced ineres raes also offer he opporuniy o sudy expecaions formaion and, in paricular, a direc es of he raionaliy of expecaions. By he law of ieraed expecaions we have E(D *S )=E(E(D *S )*S ) H H +1 where H> is a (fixed) horizon dae and S he informaion se available a. This implies ha revisions o he mahemaical expecaion are orhogonal o -daed informaion. If he marke expecaion coincides wih he mahemaical expecaion hen our calculaed expeced raes should possess his propery. We ake as he informaion se curren and lagged growh raes of GDP, he GDP deflaor and he reail price index, and curren and lagged absolue changes in he reasury bill rae. For he four horizons: 1995q1, 2001q1, 2005q1 and 2010q1, regressions of he change in he expecaion of he real ineres rae a hese horizons upon curren and firs lagged values of he informaion se beween 1984q1 and 1992q2 gave F-saisics ha were insignifican in all four regressions a he 10% level. Univariae regressions of he change in he expecaion on he curren and firs lagged values of each of he variables in he informaion se, hiry-wo regressions in all, yielded only wo significan -raios a he 5% level (2001q1 on he lagged change in he reasury bill rae, =-2.3; and 2005q1 on he lagged change in he reasury bill rae, 17

21 =-2.0). These resuls are consisen wih he raional expecaions hypohesis. Whils hey may be consisen wih oher expecaion formaion mechanisms, noe ha he absence of significan correlaions implies here are no forecasable arbirage gains in his marke, a weak form of efficiency. In Roberson and Symons (op. ci.) we applied he above echniques o daily daa covering he period of serling's exi from he ERM. We found ha his moneary acion brough abou an immediae fall in he ex ane shor real ineres rae, leaving more disan raes unchanged. Inflaion expecaions, which are hen readily calculaed (wih cerain assumpions abou risk premia) were found o decline in he shor run bu o increase in he long run. Thus useful insighs can be obained from he sudy of hese securiies. 5. Conclusion This paper has described a mehod o obain esimaes of he ex ane pah of fuure real ineres raes from Briish Governmen index linked deb. The erm srucure of expeced fuure real ineres raes a quarerly frequency was obained for he period 84q1 o 92q2. These are he implied real one period reurns a fuure daes available in he marke. Wih he assumpion of free capial markes and purchasing power pariy, hey are hen esimaes of he world real ineres rae. They allow a consideraion of he impac of moneary policy, and an assessmen of he expecaions formaion mechanism in he marke. 18

22 Endnoes * Cenre for Economic Performance and Cenre for Economic Forecasing, London Business School; and Cenre for Economic Performance and Deparmen of Economics, Universiy College London; respecively. The Cenre for Economic Performance is financed by he Economic and Social Research Council. 1. A furher hree were issued in Sepember We believe his is o permi he calculaion of accrued ineres before he sixmonhly coupon drops, allowing for a wo monh lag in he publicaion of he reail price index. The Bank of England publishes bond prices ne of accrued ineres (he so called "clean price") so ha prices do no jump a he coupon drop. I is a piy ha his minor convenience has been allowed o conaminae he macroeconomic signals implici in he bond prices. Even he publicaion lag is escapable, as all paymens could be rolled over a shor nominal raes unil all informaion has appeared. I does seem, however, ha imperfec indexaion is widespread: see Boole (1991), Appendix The economic inerpreaion of hese pahs could be, firsly, igh curren moneary policy; and, secondly, fuure increased invesmen demand such as migh follow a growh ake-off in Easern Europe. We fel ha, as a minimum requiremen, an esimaion procedure should be able o cope wih hese pahs. 4. Even hough he RPI is published wih a lag of one monh, we assume agens in he marke know he curren price level. 19

23 Table 1 Marke & Pension Fund Holdings of Gil Edged Sock, end 1990 Marke Value (%) Pension Fund %ge of Pension Fund % of marke billion Holdings Gil porfolio (%) billion Shors 31.2 (27.1) 1.2 (4.3) 3.8 (0-5years) Mediums 52.0 (45.2) 12.7 (45.3) 24.4 (5-15years) Longs 8.3 (7.2) 4.3 (15.4) 51.8 (>15years) Index Linked 23.5 (20.5) 9.8 (35.0) 41.7 Toal Sock (100.0) 28.0 (100.0) Sources: Pension Fund Holdings: CSO Financial Saisics, February Marke Holding of Gils: Bank of England Quarerly Bullein, Feb. 1992, p56. 20

24 Table 2 Nominal Gils used o evaluae Term Srucures Bond Mauriy Dae quarers o mauriy from 84q1 14% h Oc % nd Jan % nd Mar % nd Sep % h Apr 41 14% nd Jan 48 15% h Oc 55 13% h Jul 66 10% h Sep % h Sep % h Jul 94 9% h Oc 99 9% h Aug % h Aug

25 Table 3 Index Linked Gils used o evaluae Term Srucures Bond Mauriy Dae quarers o mauriy from 84q1 2% h Mar 16 2% h Jan 24 2% rd Mar 32 2% h May 41 2% h Sep % h Sep % h May 77 2% h Jul % h May % rd Aug % h Aug % h Jul % h Apr % h Jul

26 Table 4 Shor and Long Expeced Real Ineres Raes 84q1-92q2 Shor Long 84q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Noe: (i) "shor" is he average expeced rae over he following eigh quarers. (ii)"long" is he expeced rae in (iii) These daa are graphed in Figure 5. 23

27 Figure 1 Figure 2 24

28 Figure 3 Figure 4 25

29 Figure 5 Noe (i) "shor" is he average expeced rae over he following eigh quarers. (ii) "long" is he expeced rae in

30 References Arak, M. and Kreicher, L. (1985) "The Real Rae of Ineres: inferences from he new UK indexed gils", Inernaional Economic Review, Vol.26,No.2. Barro, R. (1987) Macroeconomics, 2nd ed. John Wiley & Sons, New York. Boole, R. (1991) Index Linked Gils 2nd ed. Woodhead Faulkner, Cambridge, England. Hodrick, R. and Presco, E. (1980) "Pos-war U.S. Business Cycles. An EmpiricalInvesigaion", Carnegie-Mellon Universiy, manuscrip. Levin, E. and Copeland, L. (1992) "Reading he message from he UK indexed bond marke: real ineres raes, expeced inflaion and he risk premium" mimeo Universiy of Sirling. Roberson, D. and Symons, J. (1994) "Five weeks in he life of he pound: ineres raes expecaions and serling's exi from he ERM" forhcoming Oxford Bullein of Economics and Saisics. Schaeffer, S. (1981) "Measuring a ax-specific erm srucure of ineres raes in he marke for Briish Governmen securiies" Economic Journal, vol.91, pp Woodward, G. (1990) "The Real Thing: A Dynamic Profile of he Term Srucure of Real Ineres Raes and Inflaion Expecaions in he Unied Kingdom, " Journal of Business, vol.63, no.3, pp