The US Term Structure and Central Bank Policy

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1 Regensburger DISKUSSIONSBEITRÄGE zur Wirschafswissenschaf Universiy of Regensburg Working Papers in Business, Economics and Managemen Informaion Sysems The US Term Srucure and Cenral Bank Policy Enzo Weber, Jürgen Wolers ** Ocober 01, 2009 Nr. 436 JEL Classificaion: E43 Keywords: Expecaions Hypohesis, Risk Premium, Policy Reacion Funcion Enzo Weber is Juniorprofessor of Economics a he Deparmen of Economics and Economerics a he Universiy of Regensburg, Regensburg, Germany. Phone: , ** Jürgen Wolers is Professor of Economerics a he Deparmen of Economics a Free Universiy Berlin, Bolzmannsr. 20, Berlin, Germany. Phone: ,

2 The US Term Srucure and Cenral Bank Policy 1 Enzo Weber 2, Jürgen Wolers 3 Absrac The expecaions hypohesis of he erm srucure (EHT) implies coinegraion beween ineres raes of differen mauriies and predics cerain values for adjusmen speed. We esimae reduced-form vecor error correcion models of he US erm srucure. These are derived from a srucural model combining he EHT, auocorrelaed risk premia, ineres rae smoohing and moneary policy feedback, which is able o capure a wide range of empirical oucomes. We explicily es he necessary precondiions for he validiy of he heoreical model. Premia persisence rises wih longer-rae mauriy, while he influence of he according spreads in he cenral bank reacion funcion diminishes. Keywords: Expecaions Hypohesis, Risk Premium, Policy Reacion Funcion JEL classificaion: E43 1 This research was suppored by he Deusche Forschungsgemeinschaf hrough he CRC 649 Economic Risk. 2 Universiä Regensburg, D Regensburg, Germany, phone: +49 (0) , fax: +49 (0) Freie Universiä Berlin, Bolzmannsr. 20, D Berlin, Germany, phone: +49 (0) , fax: +49 (0)

3 1 Inroducion The erm srucure, linking shor- and long-erm ineres raes, carries eviden imporance for ransmission of moneary policy. The expecaions hypohesis (EHT) represens he mos influenial heoreical explanaion for erm srucure relaions. A lo of economeric research has been dedicaed o examining empirical evidence of he EHT. Thereby, he sizeable predicive power of he spread, as implied by he pure EHT version, could regularly no be suppored by he daa (e.g., Campbell and Shiller 1991). Among he numerous approaches dealing wih his puzzle, persisen risk premia and ineres rae smoohing are well esablished. For insance, Tzavalis and Wickens (1995) specify a GARCH-dependen erm premium, while Caporale and Caporale (2008) explain shifs in premia by poliical risk. Mankiw and Miron (1986) argue ha cenral bank behaviour is a he boom of shor-erm raes being close o random walks. McCallum (2005) consrucs a erm srucure model combining auocorrelaed risk premia, ineres rae smoohing and moneary policy feedback. In he following, we analyse he whole range of mauriies from one o 120 monhs, in order o deduce empirical regulariies of he erm-srucure ineracion beween expecaions, risk premia dynamics and moneary policy acions. We provide a solid empirical basis for he heoreical model by explicily esing for coinegraion along he erm srucure and checking he parameer resricions implied by he use of he spread. Furhermore, we invesigae he adjusmen behaviour of boh shor and long raes by deriving and esimaing he vecor error correcion (EC) form of he srucural model. 2 Theoreical Consideraions The EHT saes ha arbirage should equae he reurn of a single n-period invesmen o he expeced reurn of a series of n successive one-period invesmens. In linearised form, he EHT can be wrien as R (n) = 1 n 1 E r +i. (1) n i=0 In (1), R (n) denoes he ineres rae of mauriy n > 1 and r of mauriy one. The operaor E sands for he expecaion given all available informaion a ime. 1

4 Taken ino consideraion ha ineres raes may be empirically approximaed by inegraed processes of order one (I(1)), Campbell and Shiller (1987) show ha (1) implies coinegraion beween R (n) and r wih he vecor (1, 1). Thereby, long-erm raes will be weakly exogenous, approximaely following random walks (see Pesando 1979). Assuming raional expecaions, E r +1 = r +1 + e +1, wih he expecaion error e, he EC equaion for he shor-erm rae in he wo-period case (n = 2) resuls as r = 2(R (2) 1 r 1 ) e. (2) However, empirical evidence (e.g., Campbell and Shiller 1991) has overwhelmingly shown ha he considerable size of he adjusmen coefficien is no suppored by he daa. One imporan modificaion of he pure EHT is given by auocorrelaed risk premia. Adding a mauriy-dependen AR(1) process 4 wih consan erm, (1) can be rewrien as R (n) = 1 n n 1 E r +i + v (n) wih v (n) = a n + ρ n v (n) 1 + u (n), 0 < ρ n < 1. (3) i=0 The EC equaion (2) now akes he form r = 2(1 ρ 2 )(R (2) 1 r 1 ) + res, (4) where res conains a consan, shor-run dynamics and errors. Besides he mauriy n, he persisence ρ n of he risk premium governs he adjusmen coefficien, which can be rendered arbirarily small. A second explanaion for he failure of he pure EHT is provided by ineres rae smoohing. Mankiw and Miron (1986) argue ha he predicive power of he spread has dramaically declined since he founding of he Federal Reserve Sysem and aribue his fac o he ineres rae sabilisaion policy of he Fed. Approximaely, he shor rae may even follow a random walk, impairing predicabiliy. In sum, he lieraure offers explanaions for random-walk behaviour boh of long and shor raes. Nowihsanding ha resolving his ambiguiy is in he end an empirical ask, we se up a heoreical framework ha encompasses boh hypoheses, in addiion o inermediae soluions. For ha purpose, we recur o McCallum (2005), who proposes a erm srucure model 4 Generalisaions are sraighforward. Noe ha consan premia would no change he adjusmen parameer in (2). 2

5 ha combines he EHT wih a moneary policy rule: The cenral bank conducs ineres rae smoohing, bu may change he shor rae in response o he yield spread. Thereby, he spread may provide an indicaor for moneary policy expansiveness, fuure economic growh or expeced inflaion raes, approximaing forward-looking couner-cyclical policy behaviour; see also Johnson (1988) in his conex. The reacion funcion wih ineres rae smoohing, feedback inensiy λ n and policy shock ε (n) is given by r = r 1 + λ n (R (n) r ) + ε (n). (5) Imporanly, equaion (5) will only be balanced for I(1) ineres raes if long and shor raes are coinegraed wih he vecor (1, 1), as follows from he EHT, oo. According o he Granger represenaion heorem, coinegraion implies an EC model. As soluion of equaions (3) and (5), McCallum (2005) derived for n = 2 he EC equaion for he shor rae. 5 Kugler (1997) generalised his resul for any mauriy, presening according equaions for he shor rae and he spread. We develop he approach one sep furher, deriving he bivariae vecor EC model (VECM): ( ) ( ) ( ) (n) R (1+λn )θ n a n λn ρ n +ρ n 1 = + (R (n) 1 r 1 )+ r λ n θ n a n λ n ρ n ( 1 (1+λn )θ n 1 λ n θ n )( ) (n) ε u (n), (6) where θ n = n/(n λ n n 1 j=1 (n j)ρj n). Evidenly, he spread has predicive power for he shor rae as long as λ n 0 and ρ n 0. In (5) and (6), λ n = 0 would render he shor rae a random walk (up o possible shor-run dynamics), riggering he Mankiw and Miron (1986) resul of no predicabiliy. The same holds for he limiing case ρ n = 0, when he long rae would conain no disinc persisence in he risk premium. The adjusmen of R (n) reduces he spread for small λ n and ρ n (λ n ρ n + ρ n 1 < 0), bu oherwise he long rae even depars furher from equilibrium (λ n ρ n + ρ n 1 > 0). However, sysem sabiliy is ensured for saionary erm premia, as he characerisic equaion has roos 0.5 and ρ n. Long-rae predicabiliy would be los for λ n ρ n + ρ n = 1. Noably, for λ n = 0 and ρ n 1, boh ineres raes would behave like random walks. 5 As already provided in NBER Working Paper 4938 (1994). 3

6 3 Empirical Evidence Our daa se consiss of monhly observaions of cerificae of deposi raes (n = 1, 3, 6) and consan mauriy bond yields (n = 12, 24, 36, 60, 84, 120) obained from he Fed. The sample begins in 1983(1) afer he abolishmen of he non-borrowed reserves argeing policy, and ends in 2008(9). We begin an addiional sub-sample in 1988(1) afer he sar of he Greenspan era and he sock marke crash. In his conex, refer as well o Hsu and Kugler (1997), who argue ha he spread gained imporance as a policy indicaor from 1988 on and esimae he Kugler (1997) model for he hree-period case. We check, wheher he implicaions from EHT are fulfilled, wihin he VECM ( ) (n) R = r ( α1 α 2 ) (R (n) 1 βr 1 c)+ p i=1 ( ) (n) R i Γ i + r i ( ) (n) w 1 w (n) 2, (7) wih adjusmen parameers α, coinegraion coefficien β, errors w and 2 2 parameer marices Γ i in he shor-run dynamics. Moreover, esimaes of ρ n and λ n can be recovered by comparing adjusmen parameers from (6) and (7), see Table (1)-2008(9) 1988(1)-2008(9) n lags ˆβ ˆα1 ˆα 2 ˆρ n ˆλn lags ˆβ ˆα1 ˆα 2 ˆρ n ˆλn 3 1-2, (0.006) (0.04) 24 1, (0.06) 36 1, , (0.10) , (0.12) , (0.13) (0.15) (0.14) , , , , (0.04) , , (0.09) , (0.10) , (0.11) (0.16) (0.14) (0.06) Noes: n: mauriy in monhs, β: coinegraion coefficien, α: adjusmen coefficien, ρ: risk premium AR(1) coefficien, λ: feedback coefficien, sandard errors in parenheses Table 1: VECM resuls Johansen Trace ess uniformly rejec he null hypoheses ha he coinegraion rank is zero a he 1% significance level, excep for he hree longes mauriies in he firs period, where he 5% level applies. LR ess in no case rejec he null hypohesis β = 1. The 4

7 presence of coinegraion ogeher wih he parameer resricion ensure saionariy of he spreads. Imporanly, his provides he necessary condiion for he validiy of he srucural specificaion (3), (5). Adjusmen of he one-period rae is faser han ha of he longer-erm raes (ˆα 2 > ˆα 1 ), bu reduces wih increasing mauriy. The long rae adjusmen coefficiens are wrong - direced for mauriies unil wo (hree) years and become slighly negaive hereafer. While ˆα 2 is significan in all esimaed VECMs, his holds for ˆα 1 only unil he mauriy of six (welve) monhs. In our model, his reduced-form oucome resuls from underlying srucural processes, namely risk premia persisence and policy feedback. The former is of subsanial srengh even for relaively shor mauriies and rises o nearly 1 for he en-year bond. Inuiion is sraighforward: When one monh passes, he fracion ρ of he risk premium survives unil he nex period. This fracion will be he higher he less a single period couns for he whole premium (for example only 1/120 for he en-year bond) and he less news from his period coun for he overall oulook unil mauriy. In conras, he impacs λ of he respecive spreads in he cenral bank reacion funcion sar a abou one for he hree-monh rae and approach zero for long mauriies. Again, his paern is in line wih a priori expecaions, as moneary policy is likely o concenrae is forward-looking behaviour on near-fuure oulooks. In his sense, he spreads agains relaively shor raes provide immediaely relevan informaion. Risk premia persisence says abou he same in boh esimaion periods. This is no surprising, because he sample pariion was largely guided by crieria conneced o moneary policy. Indeed, he feedback coefficiens are uniformly higher from 1988 on, confirming he presumpion of increased significance of he spread for cenral bank decisions. Furhermore, as far as he spread incorporaes inflaion expecaions, he resul can generally be inerpreed in he sense of higher inflaion sensiiviy ofen supposed o characerise he Greenspan era. 4 Conclusion We adop a srucural framework of McCallum (2005) and Kugler (1997) in order o model simulaneously bond marke arbirage and cenral bank behaviour. We derive he vecor EC form from he srucural equaions, es wheher essenial precondiions are fulfilled and esimae he VECM for a wide range of he US erm srucure. We find ha persisence of risk premia is he higher he larger he difference in mauriy 5

8 beween he considered ineres raes. This resul probably reflecs he fac ha he weigh of news from a single period, relaive o he incumben premium, is naurally lower for long-horizon risk assessmens. Following he sylised policy rule, he Fed reacs srongly o spreads agains money-marke raes, bu much less agains long-erm bond raes. Since i is common sense ha cenral banks align operaive policy o prospecs of he near fuure, again he poenial of he model o grasp real-world phenomena is underlined. References [1] Campbell, J.Y. and R.J. Shiller, 1987, Coinegraion and Tess of Presen Value Models, Journal of Poliical Economy, 95, [2] Campbell, J.Y. and R.J. Shiller, 1991, Yield spreads and ineres rae movemens: a bird s eye view, Review of Economic Sudies, 58, [3] Caporale, B. and T. Caporale, 2008, Poliical risk and he expecaions hypohesis, Economics Leers, 100, [4] Hsu, C. and P. Kugler, 1997, The revival of he expecaions hypohesis of he US erm srucure of ineres raes, Economics Leers, 55, [5] Johnson, M.H., 1988, Curren Perspecives on Moneary Policy, Cao Journal, 8, [6] Kugler, P., 1997, Cenral Bank Policy Reacion and he Expecaions Hypohesis of he Term Srucure, Inernaional Journal of Finance and Economics, 2, [7] McCallum, B.T., 2005, Moneary Policy and he Term Srucure of Ineres Raes, Federal Reserve Bank of Richmond Economic Quarerly, 91, [8] Mankiw, N.G. and J.A. Miron, 1986, The changing behavior of he erm srucure of ineres raes, Quarerly Journal of Economics, 101, [9] Pesando, J.E., 1979, On he Random Walk Characerisics of Shor- and Long-Term Ineres Raes in an Efficien Marke, Journal of Money, Credi, and Banking, 11, [10] Tzavalis, E. and M.R. Wickens, 1995, The persisence in volailiy of he US erm premium , Economics Leers, 49,

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