Further Evidence on the Impact of Economic News on Interest Rates. Dominique Guégan 1. Florian Ielpo 2

Transcription

1 Further Evdence on the Impact of Economc News on Interest Rates Domnque Guégan 1 Floran Ielpo 2 Abstract We nvestgate the shape of the term structure reacton of the US swap rates to announcements usng several lnear and non-lnear tme seres models. We document the non-lnearty of the market reacton to macroeconomc news. Frst, we fnd that the ntroducton of non lnear models leads to the fndng of a sgnfcant number of macroeconomc fgures that actually produce an effect over the yeld curve. Second, we notced at least four types of patterns n the term structure reacton of nterest rates across maturtes, ncludng the humpshaped one that s generally consdered. Thrd, we propose a frst nterpretaton and classfcaton of these dfferent shapes. Fourth we fnd that the exstence of outlers n nterest rates leads to an underestmaton of the reacton of nterest rates to announcements, explanng the dfferent results obtaned between hgh-frequency and daly datasets. Keywords: Macroeconomc Announcements, Interest Rates Dynamc, Outlers, Reacton Functon, Prncpal Component Analyss. JEL classfcaton: G14 The authors are thankful to Oscar Bernal, Roberto Reno, Roch Heraud, to the semnar partcpants of the Journée d'econometre : développements récents de l'économétre fnancère (Nanterre, France, 2006) and of the second Italan Congress of Econometrcs and Emprcal Economcs (Rmn, Italy, 2007) for very helpful comments. We also thank two anonymous referees for ther comments and remarks. All errors reman ours. 1 Centre d'econome de la Sorbonne -- CERMSEM, UMR 8174, Mason des Scences Economques, 106 bd de l'hôptal, PARIS. Emal: dguegan@unv-pars1.fr. Tel: Pctet & Ce Asset Management, Route des Acacas 60, CH-1211 Genève 73. E-mal: floran.elpo@ensae.org. 1 Electronc copy avalable at:

2 1 - Introducton Measurng the mpact of news on fnancal markets s essental to document the key features any asset prcng model should wthstand. What s more, due to the tght lnks between economcs and asset prces, questons of ths knd are also essental to macro-economst. For example, when the US GDP fgure s released, the devaton of the realzed fgure from the market consensus leads to a very fast revson of the market's belefs. Ths revson results most of the tme n a change n what s consdered as the far value of asset prces. Ths knd of ratonale s especally true when dealng wth fxed ncome securtes. One of the versons of the expectaton hypothess 3 states that the whole yeld curve can be seen as an expectaton of the upcomng expected short rates. It seems natural to combne the Taylor (1993) rule approach to the short rate modellng wth ths expectaton hypothess. In ths perspectve, t s relatvely easy to understand how, through no arbtrage arguments, t s possble to relate and explan the behavour of the yeld curve, based on a few macroeconomc fgures. Works of ths knd can be found n the recent macrofnance lterature. For example And and Pazzes (2003) propose to descrbe the economy wth a few Vector AutoRegressve (VAR) related macroeconomc factors. They show how these factors under no arbtrage opportuntes are able to prce zero coupon yelds. Ths stream of models am at capturng the dynamc behavour of the level of nterest rates. Unfortunately, these models cannot handle the other way around macroeconomc fgures: when released, these fgures are known to produce movements n nterest rates markets. If several market partcpants bet on the future stance of the yeld curve -- usng Futures or swap rates -- a great number of them also take bets on the daly -- f not ntra-day -- mpact of news on the yeld curve. The ratonale behnd these tradng strateges stems from the fact that the bggest moves n bond markets are actually produced by the dsclosure of economc nformaton. Roughly speakng, most of the macroeconomc announcements are ether released on a weekly, monthly or quarterly bass. Before the announcement, pools of economsts are ntervewed and delver ther forecast 3 On the expectaton hypothess, see the extensve dscusson n Campbell and Shller (1991) and n Jarrow (2002). 2 Electronc copy avalable at:

3 for the upcomng fgure. For Bloomberg users, what s consdered as the market's forecast s the medan of the pooled forecasts. Ths fgure s then used to analyze the actual fgure when released: the market analyss of macroeconomc announcements s often performed by comparson wth the economst forecast. The market reacton to news s then a functon of the spread between the forecast and the dsclosed fgure. The dedcated academc lterature emprcally demonstrated several, now well-known, results: frst, a lot of macroeconomc news produce an mpact on the bond market; second, there exsts a term structure effect of macroeconomc news. The realty s, of course, much more complex: the term structure effect of news on the bond market s expected to be economc cycledependent. The ntuton beyond ths s smply that the macroeconomc fgures and the market's reacton to them s based on the Central Bankers' speech on the upcomng economc threats. When the busness cycle s gong down, actvty and employment fgures are closely montored. On the contrary, when the economy s roarng, the attenton s focused on nflaton and expected nflaton ndcators. Needless to say, the mpact of news on fnancal markets has not only been documented on the bond market sde: the equty market s also known to react to many announcements. There s actually a huge lterature nvestgatng the effect of nformaton dsclosure on ether stock ndexes or ndvdual components of these ndexes. On the reacton of these markets to news, see for example Lardc and Mgnon (2003) and the references presented n ths artcle. Even f the methodologes used for ths stream of lterature are related to what we propose here, bond markets are way more dependent on macroeconomc fgures than stocks. Thus, the news that are nvestgated here strongly dffer from stock-market related news: for example, the consensus forecast regardng the upcomng macro-fgures makes the analyss of the surprses easer. Fnally, there are a lot of news stemmng for example from Central Bankers' speeches, but these are not quanttatve and thus very hard to handle. On ths pont see Brère (2006). Ths s however beyond the scope of ths artcle. Thus, the term structure mpact of news s not always the same: t clearly depends on the type of news that s nvestgated. Brère and Ielpo (2008) provdes elements n ths drecton usng the Euro swap rates: ths dataset s relatvely new and thus small. Wth ths knd of nformaton set, t s dffcult to move one step forward and answer the queston: for a sngle 3 Electronc copy avalable at:

4 fgure, s the shape of the term structure mpact changng, dependng on economc condtons? Followng what s presented n Dufrénot et al. (2004), we show that there exsts a strong dependence on the busness cycle, snce the monetary stance tself -- and thus the yeld curve -- depends on the busness cycle. In ths artcle, we tackle ths ssue usng an Amercan dataset, whose depth s larger than the European one. There has been a flourshng lterature related to the mpact of US news on nterest rates that s surveyed n Flemng and Remolona (1997). Frst, early artcles studed the mpact of a selected number of macroeconomc fgures on selected ponts of the yeld curve. For example, Grossman (1981) and Urch and Watchel (1981) chose to focus on money supply surprses for selected maturtes of the yeld curve. Hardouvels (1988) and Edson (1996) nvestgated the mpact of employment news along wth Consumer Prce Index (CPI) and Producer Prce Index (PPI) n a smlar fashon. Second, whle the former studes used daly datasets, the most recent ones made the most of the newly avalable hgh-frequency data, assumng that the measurement of the nterest rates' reacton to surprses on a narrower wndow of tme was bound to lead to more precse results. The results obtaned ponted toward mportant facts: where studes acheved usng daly data only found a few market mover fgures, these studes (see for nstance Balduzz et al. (2001), Flemng and Remolona (1997) and Flemng and Remolona (2001)) concluded wth the fact that as much as 70 releases actually produce moves wthn the U.S. bond markets. These three artcles can also be regarded as dealng wth nformatonal concerns, snce they nvestgate the actual tme perod necessary for fnancal markets to ncorporate the news n asset prces. Fnally, recent papers focused on the complete term structure response to macroeconomc news. Usng an ntraday dataset, Flemng and Remolona (2001) revealed hump shaped term structure effects. Here, we propose dfferent nested tme seres models to assess the shape of the term structure reacton to macroeconomc announcements. More, we allow ths term mpact to depend on varous state varables: ths way, we ntend to capture the changes n the shapes dependng on the economc or monetary cycles. The man estmaton results unfold as follow. Frst, we fnd that there exst several types of surprses that actually affect the bond market, surprsngly matchng the frst four factors found when performng a prncpal component analyss over the daly changes n swap rates. Second, the rankng of market mover fgures strongly depend upon the market percepton of the economc cycle, measured by publcly avalable ndcators, and upon the 4

5 monetary polcy stance, measured by the Fed's target rate. Fnally, we show that the use of a threshold model when estmatng the market response to macroeconomc news leads to the elmnaton of outlers wthn the dataset, yeldng dfferent - and often more statstcally dfferent from zero - estmates of the market response to selected fgures. The excluson of these outlers brngs about nterest rates' reacton functons that are generally upper than the classcal ones and more concave. The remanng of ths secton s organzed as follow. In Secton 2, we present the methodology to estmate the term structure response to macroeconomc news. In secton 3, we revew the emprcal results obtaned, underlnng the mportance of takng nto account the busness and monetary cycles. In secton 4, we present a detaled analyss regardng selected fgures for whch we present a strong underestmaton problem nduced by the usual lnear model used n the lterature. Secton 5 concludes. 2 - Assessng the shape of the market reacton functon In ths Secton, we detal both the dataset and the tme seres models used to analyze the effect of the announcements on the US swap rate across maturtes. The dataset used along the paper and ts prelmnary treatment s closed to the one used n the man artcles nvestgatng the bond market reacton to macroeconomc news, such as Balduzz et al. (2001) and Flemng and Remolona (2001). The man novelty of ths paper beng the methodology, we present t n a detaled fashon so as to hghlght our contrbutons. 2.1 The dataset Along ths paper we use two types of data. On the one hand, we use the daly changes n the US swap rates from June, 24 th of 1996 untl March, 1 st 2006, for the followng maturtes: 1- to 10-year, 15-year, 20-year and 30-year swap rates. By daly changes, we mean the dfference between two followng daly closng rates. Let r t ( ) be ths change n the closng swap rate r t ( ) for a maturty equal to, on a date t. Then, we have: r ( ) r ( ) r 1( ) (1) t t wth a tme unt equal to one day. One man advantage to use swap rates s that they are generc rates: these rates have a constant tme to maturty t 5

6 over the whole sample and thus do not theoretcally depend on tme. Usng such rates means that we do not have to deal wth the reducton of the tme to maturty. We also had to estmate some mssng rates, whch was done usng the cubc splnes method, lke n Bomfm (2003) 4. The US swap rates dataset has been extracted from the Bloomberg database. The Bloomberg closng swap rates are gathered from dfferent brokers and fnancal nsttutons at the closng of each US bond market tradng day. Durng a tradng day, the moments the ntraday database s updated s rather random and ths randomness extents to the maturtes that are updated. On the contrary, for the closng swap rates, the tme of the update s rather homogeneous. Ths s why we propose to use a daly dataset made of these closng swap rates. From the Bloomberg database, we also extracted the US economc calendar across the dates already mentoned for the swap rates. Ths calendar contans every economc announcement lnked to the US economy whch are supposed to be montored by fnancal market partcpants 5. Several of these fgures are well known by economsts, such as the Non Farm Payroll fgure, whch s the number of jobs created on a one month perod. These fgures are ssued regularly by offce statstcs such as the Bureau of Labour Statstcs. For example, the Non Farm Payroll fgure s ssued every frst Frday of a month and s usually followed by large moves n the bond market. Other fgures are no so well known, and one of the purposes of ths paper s to cast some lght on the effect of these ndcators on the term structure of the US swap rates. 4 Ths s a classc method, dscussed n classcal textbooks, e.g. Martelln et al. (2003). Note that the results obtaned hereafter reman globally unchanged when usng a smple nterpolaton method for mssng observatons. Ths may due to the fact that the number of mssng observatons s below 1% of the whole sample. 5 Ths s however not the only nformaton consdered by the US bond market. However, snce we need an mportant sample length for our estmaton purposes, we dscarded the use of European and Chnese news that would oblge us to use a shorter sample. 6

7 Table 1: Lst of the macroeconomc announcements studed n ths paper. These announcements are monthly ones, except for: Weekly Jobless Clams (weekly fgure), Personal Consumpton (quarterly fgure), Capacty Utlzaton Rate (quarterly fgure) and GDP (quarterly fgure). Growth Conjonctural Indcators Real estate Industral New orders ISM manuf Constructon Spendng Wholesale Inventory Phlfed Index Housng Start Industral Producton Conf. Board Consumer Conf. Exstng Home Sales GDP Chcago PMI New Home Sales Trade Balance Non Manuf. ISM Buldng Permts Capacty Utlzaton Rate Consumer Conf. Mchgan NAHB Housng Market Index Durable Good Orders Empre Manufacturng Constructon Spendng Labor Market Consumpton Inflaton Unemployment Rate Household Consumpton Consumer Prce Index Jobless Clams Personal Income Producer Prce Index Non Farm Payroll Consumer Credt Import Prce Index Employment Cost Index Wages Hourly Average Wages Weekly Workng Hours Weekly Jobless Clams Indce Help Wanted Retal Sales Personal Consumpton (Q) 7

8 We dscarded several seres from the Bloomberg database. Table 1 presents the selected fgures used durng the estmaton process. We elmnated these seres for dfferent reasons. Frst, some of the fgures got ther names changed over the studed perod. In ths case, we smply changed the old names nto the newer ones so as to avod havng a sngle fgure known under dfferent names. Ths was the case for the Mchgan Consumer Confdence that was reported under several names n the Bloomberg Calendar. Second, some of these fgures were ll reported and ncluded a lot of mssng values. Fnally, some of these fgures ceased to be released durng the studed perod, such as the M3 aggregate and we chose not to nclude them, to make ths study of nterest both for academcs and practtoners. Most of the announcements studed are monthly (see table 1). The seres were treated by the Bloomberg calendar the way bond market partcpants do. For example, the surprse n the Consumer Prce Index (CPI hereafter) s a surprse n the month-over-month fgure. A month-over-month (m-o-m hereafter) fgure s smply the percentage of growth of the ndex over the month. Wth an ndex denoted I t for the month t, the m-o-m fgure wll It be equal to 1, wth a tme unt equal to one month. The same knd of It 1 transformaton apples for most of the fgures but the sentment survey such as Purchasng Manager Index (PMI) or Mchgan Consumer Confdence. These survey fgures are often presented usng the value of ther ndex. Ths s a rather techncal knowledge many books are devoted to. Anyone nterested n these ways of processng data can get n depth analyss n such books (see e.g. Baumohl (2005)). In our methodology, we used the frst estmates of the macroeconomc news. Most of the macroeconomc fgures released n the US are ntally prelmnary estmates. On the next announcement for the same fgure, a revsed estmate of the precedng fgure s released. Most of the macroeconomc datasets used n emprcal papers are made of the revsed estmates of every macroeconomc fgures. Recently, Orphandes (2001), Bernanke and Bovn (2001) and Kshor and Koeng (2005), among others, took ths data revson problem nto account, hghlghtng the mportance of ths phenomenon on macroeconomc emprcal models. For our purposes, the use of the frst estmate s of tremendous mportance: the frst announcement s the one bond market partcpants had to face wth and eventually reacted to. 8

9 What s more, the Bloomberg calendar also contans the Bloomberg forecasts regardng each of these fgures. Bloomberg forecasts are formed usng the 50% emprcal quantle of the dstrbuton of a survey made of the forecasts of several bank economsts, regardng a precse fgure. The use of the medan as a measure of the expectatons makes the forecast robust to the nfluence of badly ntentoned economsts that would want to shft the forecast n order to make the most of t. What s more, ths forecast s extensvely used by market partcpants. For each fgure that s predcted by Bloomberg's collecton of economsts' forecasts, the medan s regularly updated untl every economst answers the survey, whch can take up to two weeks. We retaned the last medan computed by the Bloomberg servces, so as to match both the practtoners and academc ways of dong thngs. Some of the elmnated seres were dscarded because there was no avalable forecast. 2.2 The econometrc specfcaton In ths secton, we skp to the presentaton of the tme seres models used along the paper. The frst model s the classcal lnear model presented earler. Let S t, denote the surprse at tme t n the fgures ndexed by as follows: S t, R F t, t, (2) S where Error! Objects cannot be created from edtng feld codes. s the market consensus about the upcomng fgures Error! Objects cannot be created from edtng feld codes. for Error! Objects cannot be created from edtng feld codes., the date of release; R, s the real announcement (the frst estmate) at t tme Error! Objects cannot be created from edtng feld codes. of the same fgure Error! Objects cannot be created from edtng feld codes.. To make the surprses comparable, surprses are scaled usng ther hstorcal standard devaton. Ths way of proceedng s very common, see e.g. Edson (1996), Flemng and Remolona (1997, 2001) and Balduzz et al. (2001). We used the Bloomberg forecasts as a measure of the market consensus for a gven fgure at a gven date. Thus Error! Objects cannot be created from edtng feld codes. wll be proxyed by the last forecast n the Bloomberg database for each announcement. 9

10 Buldng a tme seres model to relate the macroeconomc surprses to the changes n the nterest rates of maturty requres some prelmnary consderatons, and especally for the dataset buldng. Even though there seems to be some regularty n the tme of arrval of these surprses, they are rregularly spaced n tme, preventng the buldng of a sngle global model to relate any surprses to the daly changes n rates. For example, the Non Farm Payroll are scheduled to be released on the frst Frday of each month: even though ths seems to be a regular release pace, t stll leads to data that are rregularly spaced n tme, n so far as the number of days from the frst Frday of a month to the next one s not always the same. What s more, estmatng a global model as asserted before would nvolve the use of 40 exogenous varables whch may threaten the robustness of the results. Moreover, the samplng frequency of the exogenous varables can dffer: our work nvolves both quarterly, monthly and weekly news. Fnally, the endogenous varable (namely r t ( ) ) depends on the maturty of the swap rates. For several maturtes, the model to bult should be a generalzed lnear model (a model that encompasses several dependent varables n the meantme), whch thus requres to be estmated usng the (Quas) Generalzed Least Squares. To solve these dffcultes, we bult one model for each each surprse and each maturty, n a smlar fashon to the \ Seemngly Unrelated Regresson Models. Ths has an obvous consequence over the chosen notatons: the subscrpts must dsplay the dependency on tme, maturty and macroeconomc surprse. Now, let us denote ( ) the daly change n swap rate of maturty r t, on the date t of the release of the fgure ndexes by 1,2,..., I, where I s the total number of surprses. The couple ( t, ) s somewhat a calendar coordnate n the global dataset. The lnear model (model 1 hereafter) assumes for gven (fxed) 1,2,..., I and 1, 2,..., m that: r ) S, (3), t, (,, t, t,,, where and are real-valued parameters. t, s a Gaussan whte nose wth standard devaton,, condtonally upon S t,. In the remanng of the paper, we denote these condtons as condtons (2.2). Ths very smple model s usually augmented wth the other surprses announced on the same day ( t, ) :, 10

11 r j ( ),, St,, St, t,, t, j1 J, (4) j where S t, are the scaled surprses j announced on the same day as surprse. Agan, we assume that,, j s on the real lne. These addtonal surprses are essental to ensure that the estmated, truly solate the effect of the announcement that s analyzed. It s noteworthy to remark that the news tme seres are made of a lot observatons equal to zero, for each nonannouncement day. Because of ths very partcular structure, the correlaton between news tme seres s generally very close to 0. Hence, there s usually no collnearty problem when estmatng equaton (4). What s more, the number of concdent news s not very mportant: see the table presented n Balduzz et al. (2001). In ths secton, we buld a collecton of nested tme seres models to capture the term structure reacton to macroeconomc news. The lnear model defned by equaton (3) s the frst model. For the ease of the presentaton, we wll get rd of the part of the equaton (4) that s dedcated to the announcements released on the same date as the announcement studed (that J j s, S t, ), mantanng t durng the estmaton. What s more, for the sake j1 of smplcty, we do not denote anymore the maturty of each change n the swap rate, skppng from r t, ( ) to r t, (the same treatment also apples to the parameters of the model): we present the models for a gven and fxed. The mmedate consequence of the model 1-lke specfcaton s: r ) S S. (5) t, ( t,,, t, Ths expectaton has an mportant mplcaton: whatever past nformaton and the state of the economy, the condtonal expectaton of the rates' jump s always the same, for a gven surprse,.e., S t,. Ths s not n lne wth what can be observed both by practtoners and academcs. We propose two nested non-lnear models to account for these facts. 11

12 Frst, wth model 1, the market reacton to a gven surprse s bound to be the same for each state of the economy. The rates response to macroeconomc announcements may depend on several factors such as the tmelness of the release - that s the order of release for a one month perod -, the degree of surprse, the condtons of market uncertanty or the sgn of the surprse. On these ponts, see Flemng and Remolona (1997) and Hans (2001). Other artcles ponted toward the fact that the nterest rates response to macroeconomc announcements may also depend on a threshold varable, such as economc leadng ndcators or employment fgures. For example, Prag (1994) shows that the mpact of unemployment surprses on the bond prces may depend on the current level of unemployment. Veredas (2005) shows that the market response to surprses n macroeconomc releases strongly depends upon the momentum of the cycle: n ths framework, bad news have more mpact on bond prces durng expanson perods than recesson ones. Ths may be due to the mportance of bad news durng expanson perods to forecast a change n the busness cycle. Here, we argue that the market response depends on several threshold varables, ncludng ndcators for monetary polcy stance and economc agent sentment regardng future actvty. Thus, we propose to use a threshold tme seres model. Gven the small number of observatons we have at hand 6, we wll consder a two states economy, say recesson/expanson states. Let us defne, an t, observable process that s used as a state varable to capture the condtonal reacton to the surprses n the macroeconomc fgure. Wth ths state varable, we measure the state of the economy as follow: ths process has to cross a threshold value for the economy to go through a change n state, t, say from expanson to recesson. For each 1,2,..., I followng:, model 2 s then the r t, 1, 1 St, 2, 1 St, t,, t, t, t, t, (6) 6 For monthly fgures, we only have one announcement a month, whch makes 120 observatons wth no mssng value n the dataset. For the quarterly fgures, ths makes only 30 observatons. 12

13 as where t, t, 1 t, t, takes value 1 f and 0 f not. t, t, 1 s defned t, t, , and 2, are agan on the real lne. The assumpton 2.2 apples agan. Ths model belongs to the class of the SETAR models (Self- Exctng Autoregressve models) ntroduced by Lm and Tong (1980) and developed n Tong (1990). The partcular choce for ths model s motvated by the ntal purpose of ths artcle. Ths knd of model s desgned to compare two very dfferent perods n the economc cycle, wth a sharp transton between these perods. Ths s a methodologcal choce we made to take nto account the well-known fact that durng sharp economc downturn, fnancal agents' expectatons are gong through a rapd modfcaton. The estmaton of threshold models has been dscussed n Chan (1990), Hansen (1997,2000) and Tong (1990) [chapter 5], and asymptotc estmaton results have been derved n t. Wth these models, the loglkelhood functon s not contnuous n the threshold parameter. Thus, the threshold cannot be estmated usng standard Gradent methods. The estmaton can be performed by grd search. Ths s a standard method n econometrcs, as detaled n Greene (2000), n the chapter dedcated to numercal optmzaton. The model proposed n equaton (6) leads to the followng condtonal expectatons: r t, St,, t, t,, 1, St,. r t, St,, t, t,, 2, St,. (7) (8) Thus, the market reacton clearly dffers, dependng upon the state varable. Once agan, each macroeconomc fgure can be lnked to a proper threshold varable t,, along wth a proper threshold value t,. Now, we need to select varables to proxy ths state varable. Clearly, there s no unque answer: sentment survey (such as PMI ndex or Conference Board ndex) could be a good proxy for ths varable. These sentment survey can be consdered as concdent or leadng ndcators of the stance of the economy and thus reflects the market sentment better than real aggregates such as ndustral ndcators or GDP. Monetary polcy s also known to play an 13

14 mportant part n the psychology of the bond market. Ths s why we also ntroduced the Fed's target rate, as a measure of the monetary polcy stance. The table 2 presents the dfferent threshold varables that we retaned for the estmaton of the threshold model. Note that to these varables, we add the frst and second factors of a prncpal component analyss performed over all these varables, so as to get a global economc confdence ndex. Ths s a classcal method used to buld ths knd of global economc stance ndex (see e.g. Stock and Watson (2002)). So as to avod any data vntage problem, as presented e.g. n Kshor and Koeng (2005), we used the frst estmates of every of these seres: they were the ones at hand for market partcpants, at the tme of ther reactons to the announcements. In the secton dedcated to the estmaton results, we present the results of the choce of the threshold varable. For each surprse, we retan the threshold value that yelded the hghest log-lkelhood value or the lowest root mean square error. These results show the beneft from estmatng each model for each macroeconomc fgure and each maturtes: the selected threshold varable can clearly dffer dependng both on the rates' maturty and the fgure that s studed. Table 2: Threshold varables used n the estmaton process Indcator as a measure of Mean Std. Devaton PMI Future economc actvty Conf. Board Future economc actvty Mchgan Future economc actvty Fed fund Monetary polcy stance Fed Phladelphe Future economc actvty Factor Factor

15 In the table presentng the results of our estmatons, we refer to these threshold varables usng the followng notatons: PMI s for PMI ndex, CONF s for Conference Board Consumer Confdence, MICH s for Consumer Confdence Mchgan, FED s for the Fed Target Rate, PHI s for the Phlfed Index and FACT1 and FACT2 refer to the frst two factors of a prncpal component analyss performed over all these seres. Fnally, we propose to test for path dependency n the dynamcs of the rates. By ths, we smply mean to specfy a model that would lnk the rates' reacton durng two successve announcements of the same fgure. Note that most of the tme, a month elapsed between two successve announcements. We propose to test whether a part of r t k, s explaned by the rates' reacton at tme ( t k 1, ), that s the bonds over- or under-reacton durng the former announcement for exactly the same fgure. When model 2 provdes consstent estmates of the reacton of the market to announcements, the resduals of ths model can be used as a proxy to measure the rates' over or under reacton to a gven announcement. Thus, a natural measure of the market absolute overreacton at tme ( t k 1, ) s t k 1,. By addng ths term to the model proposed n equaton (6), we obtan model 3: r 1, 1 St, 2, 1 St, t, t,, (9) tk, t, t, t, t, k 1 where such that. Condtons 2.2 stll apply. By r t k, the law of terated expectatons, t, t, t,, St,, t, k k k k k 1 0. Thus, we can rewrte equaton (9) wth a mean revertng error process: k (10) r t ), 1, 1 St, 2, 1 St, ( t, t, t, k, t, t, t, t, k k 1 k The nterpretaton of n equaton (10) arses naturally. Let us dstngush three cases. If 0, ths obvously means that there s no lnear lnk between the past overreacton and the current one. Second, f 0, the bond market tends to be self exctng: when an over/undershoot occurs when releasng a fgure, then there s a hgher probablty that the market wll 15

16 over/undershoot agan on the next release of the same fgure. On the contrary, f 0, the market responses to announcements are mean revertng (toward a mean equal to 0). In the latter case, an over/undershoot s lkely to be followed by a smoother reacton on the date of the next release of the same fgure. Note that from a statstcal pont of vew, f s statstcally dfferent from 0, the estmaton of model 1 s lkely to be based. The condtonal expectaton of r t k, s path dependent: the rates' response wll depend on ther former reacton to the announcement of the same fgures. Thus we have: r t, St,, t, t,, t k,, 1, S 1 t, tk 1, r t St, t, t,, t,, 2, St, t, (11),, k 1 k 1 (12) From ths pont, we now obtan a collecton of nested models that wll help us document further the admssble shapes of the bond market reacton functon to macroeconomc announcements. Ths rather smple approach thus enttles us to buld LR tests, as descrbed n Davdson (1993). Models 1, 2 and 3 are nested, and lkelhood rato tests can be easly performed so as to chose whch s the more nterestng model, regardng the data at hand. These elements wll be studed wthn the next secton, along wth the analyss of the results obtaned wth the models defned by equatons (3), (6) and (9). In the remanng of the paper we refer to the model defned by equaton (3) as model 1, to the one defned by equaton (6) as model 2 and to the model defned by equaton (9) as model 3. These notatons are summarzed n the followng table : Model Equaton # Rates dynamcs Equaton r ( ), 1 (3) t,,, St, t,, Equaton rt, 1, 1 St, 2, 1 St, t,, 2 (6) t, t, t, t, rt, 1, 1 St, 2, 1 St, k t 1, Equaton t, t, t, t, k 3 (9) 16

17 3 - Emprcal results In ths Secton, we systematcally analyze the results of the estmatons of the models presented n the prevous secton. Frst, we analyze the results obtaned from the lkelhood rato tests performed over the dfferent nested models, usng the dataset presented earler. From these estmaton results, we propose a lst of the most market mover fgures for each maturty and we show that by usng model 2 the lst of market mover fgures statstcally ncreases. We also notced that model 2 leads to ntercepts that are statstcally equal to 0, unlke model 1. Thrd, we propose to dentfy the shapes of the term structure response wth those of the frst four factors of a prncpal component analyss performed over the daly changes n the swap rates. By dong so, we show that there are several knds of possble shapes for the hump-shaped term structure response to macroeconomc news (see e.g. Flemng and Remolona (2001)). Fourth, we propose a detaled analyss of the term structure response to several announcements, underlyng the fact that the ncluson of a threshold varable reveals that model 1 often underestmates the true reacton functon. We guess that ths can ether be due to the economc cycle dependence of the term structure effect or the exstence of outlers wthn the dataset Bulk effects of the ntroducton of the threshold varable The ntroducton of those threshold varables produced remarkable effects on our estmatons, yeldng results that we beleve are new. We present n tables 7, 8 and 9 the results of the estmaton obtaned from the models presented n the prevous secton. We only present the estmates of the model wth the hgher log-lkelhood functon, along wth the followng LR test. For example, let model 1 be the constraned model, wth log lkelhood denoted ln Lc and model 2 be the unconstraned model, wth a log-lkelhood denoted ln Lu. The null hypothess H 0 assumes that the constrant mposed n model 1 statstcally holds. Thus, under H 0, model 1 s consdered as a better model than the unconstraned model. Tables 7, 8 and 9 report the selected threshold varables along wth the threshold value, that are estmated for each maturty and macroeconomc fgures. We also report the LR test results, testng constraned aganst the unconstraned models. The test statstcs s: 17

18 LR (ln L c ln L ) (13) 2 u wth the prevous notatons. Under the null hypothess that the constrant statstcally holds, ths statstc has a Ch-square dstrbuton, wth a degree of freedom equal to the number of constrants mposed n the constrant model. In our case, we have only one constrant, and the statstcs s 2 dstrbuted as a 1, under the null. We proceed n a smlar fashon to test model 3 vs. model 2. The man result obtaned wth our methodology s that model 2 s globally the preferred model, regardless of the surprse and the maturty. When testng model 2 vs. model 1, the null s rejected at ether a 5% or 10% rsk level most of the tme for every maturty. The few cases when t s not rejected are reported n table 3. Ths s an essental result for our work: model 2 provdes a better explanaton of the rates' behavour than model 1. Even though model 1 s the one that s generally proposed n the lterature, model 2 better encompasses an mportant feature of the rates' dynamc: the economc cycle dependence. Note that we do not report the LR test of model 3 aganst model 2, because the model 3 was almost always rejected at ether a 5% or 10% level when compared to model 2. The fact that the model 3 s always the model favoured n our estmaton results cast some lght on the way fnancal markets process the nformaton dependng on the current economc perod. The dfferent threshold varables are meant to measure the global stance of the economy, ether on the nflaton sde or on the real actvty sde. The statstcally sgnfcant change n the market reacton to these news dependng on these threshold varables ponts toward a dfferent way to process fgures dsclosure condtonally upon the nformaton avalable n the economy. The man explanaton for ths fact s lnked to the market's percepton of monetary polcy. After ts decson meetngs, the Central Bank s known to explan the level of the target rate wth economc consderatons. Durng perods of expanson or recesson, the emphasze s not set on the same fgures. The market readng of the nformaton dsclosure s thus led by the Central Bank speeches: ths concluson s thus n favour of a relatve success n the Fed's communcatons. The ntroducton of the state varables allowed us to pont out more than the usual number of "market movers" fgures: we consder that a market 18

19 mover fgure s an announcement for whch the estmated mpact n models 1 and 3 s statstcally dfferent from zero up to a 5% percent test. Here, almost every announcement that we tested was found to have a sgnfcant nfluence on the yeld curve. Flemng and Remolona (2001) assumed that the use of daly data nstead of ntra day ones were to brng about an underestmaton of the market reacton functon. Here, we fnd that consderng the market responses condtonally upon a threshold varable that has been properly selected puts an end to ths underestmaton. Almost every announcement produces an effect on the yeld curve. In appendces, we propose two comparatve tables to assess ths pont. In table 4, we present the ranked market mover announcements found when estmatng model 1. In table 6, we report the ranked market mover announcements obtaned when estmatng model 2, along wth the selected threshold varable and the threshold value. The man pont about ths table s that the number of market mover fgures sgnfcantly ncreases when usng model 2: the ntroducton of the threshold varable leads to the fndng of a greater number of market mover fgures. The excluson of ths threshold varable seems to brng about an underestmaton of the term structure reacton to several announcements. In subsecton , we detal some of the reasons explanng ths new stylzed fact. One other remarkable fact about our methodology s the followng: when estmatng model 1, most of the ntercepts are statstcally dfferent from zero up to a 5% rsk level, unlke when estmatng model 2. Table 5 reports fgures and maturtes for whch ths ntercept remans statstcally dfferent from zero n model 2. The fact that ths ntercept can be statstcally dfferent from zero nduces the dea of exstng statstcal arbtrages n the bond market. One may thnk of ths constant term as an n the Captal Asset Prcng Model framework, as presented n Goureroux and Jasak (2001) and Campbell et al. (1997). Thus, when compared to model 2, model 1 s msspecfed and leads to msleadng deas. Ths can be vew as a very classc case of estmaton bas due to the model msspecfcaton. Table 3: Announcements and maturtes for whch the null of the LR test s accepted, when testng model 2 vs. model 1. Economc Announcement Swap rates maturtes Household Consumpton 1,6,7,9 and 10 year Employment Cost Index 15,20 and 30 year Empre Manufacturng 4,5,6,7,8,9,10,15,20 and 30 Index year Personal Consumpton 2,3,4,5 and 6 year 19

20 It s fnally noteworthy to remark that beyond the regulartes prevously mentoned n the estmaton results, t seems to be dffcult to have a global ratonale for the selecton of the threshold varable. Expected fndngs can be notced, such as the fact that the threshold varable for the "Wage" tme seres s the Fed's target rate -- whch s rather natural snce ths fgure s known to be closely montored by market partcpants to predct the Fed's next gesture. However, for most of the fgures, dfferent threshold varables were selected, regardless of the nature of the fgure tself. Ths should be lnked to the very hgh correlaton between the threshold varables tme seres: for example, PMI seres and the Fed's target rate usually evolve closely. In ths respect, the fact that dfferent threshold varables are found to be lnked to ether real actvty or nflaton fgures s not that surprsng. 20

21 Table 4: Lst of the ranked market mover announcements found when usng model 1. Rank 2 year 5 year 10 year 30 year 1 Non Farm Payroll Non Farm Payroll Non Farm Payroll Non Farm Payroll 2 ISM manuf ISM manuf ISM manuf ISM manuf 3 Employment Cost Index Employment Cost Index Employment Cost Index Employment Cost Index 4 Phlfed Index Phlfed Index Non Manuf. ISM Non Manuf. ISM 5 Durable Good Orders Personal Consumpton Indce Help Wanted Indce Help Wanted 6 NAHB Housng Market Index GDP after 1999 Industral Producton Wholesale Inventory 7 Unemployment Rate Non Manuf. ISM Phlfed Index Phlfed Index 8 Conf. Board Consumer Conf. Retal Sales GDP after 1999 New Home Sales 9 Jobless Clams Industral Producton Retal Sales Retal Sales 10 Industral Producton Conf. Board Consumer Conf. Conf. Board Consumer Conf. Industral Producton 11 Non Manuf. ISM Jobless Clams New Home Sales Jobless Clams 12 New Home Sales New Home Sales Trade Balance Chcago PMI 13 Chcago PMI Durable Good Orders Jobless Clams 14 Chcago PMI Chcago PMI 15 Exstng Home Sales Table 5 : Announcements for whch the ntercept s statstcally dfferent from zero both for model (1) and model (3) Economc Announcement Swap rates maturtes Household Consumpton 3,4,6,7,8,9,10,15,30 Personal Income 2,3,4,6,7,8,9,10,15,30 ISM Manuf. 4,6,7,8,9,10,15,20,30 Exstng Home Sales 8,9,15,20,30 Weekly Jobless Clams 1 Buldng Permts 1 Empre Manufacturng 1 Personal Consumpton 1 Indce Help Wanted 1 NAHB Housng Index 1 Constructon Spendng 1,7,8,9,10,15,20,30 21

22 Table 6 : Lst of the ranked market movers fgures found when estmatng the threshold model for each avalable maturty. R a n k 1 2 year 5 year 10 year Varable Condton Varable Condton Varable Capacty Utlzaton Rate 2 Trade Balance 3 Phlfed Index Exstng Home 4 Sales Industral New 5 orders Consumer Prce 6 Index 7 8 Non Farm Payroll Unemployment Rate FED<3,553 FACT1>97, 784 PMI>60, ISM manuf FED>6,211 1 Retal Sales 0 1 Hourly Average 1 Wages 1 Industral 2 Producton 1 Buldng Permts 3 1 Personal 4 Consumpton 1 Non Manuf. 5 ISM 1 Constructon 6 Spendng 1 Employment 7 Cost Index 1 8 NAHB Housng Market Index 1 Wholesale 9 Inventory 2 Weekly 0 Workng Hours Capacty Utlzaton Rate Phlfed Index Unemployment Rate Consumer Prce Index Non Farm Payroll Hourly Average Wages Buldng Permts GDP after 1999 Industral Producton FACT1< 64,883 PHI<- 10,226 CONF>1 22,779 MICH<1 00,063 MICH>1 02,053 FED>5,3 42 FACT1> 94,128 FACT2>- 109,378 FED>6,211 Employment Cost Index FACT1>97, Wholesale 784 Inventory PHI<- Non Manuf. 14,037 ISM PMI<51,96 Exstng Home 8 Sales MICH>96, Consumer Conf. 011 Mchgan PHI<- 14,037 Personal Income MICH<104,758 ISM manuf FACT1>86, 592 GDP FACT2>- 101,575 PHI<- 10,226 FACT2<- 115,275 NAHB Housng Market Index Conf. Board Consumer Conf. Trade Balance FED<3,553 PMI<41,18 9 PMI>60,64 2 CONF<78, 937 FACT1>97, 784 FACT1>97, 784 PMI<51,96 8 PMI<43,96 8 PHI<- 26,126 PMI<41,18 9 PMI<49,52 6 PHI<- 14,037 CONF<78, 937 PHI<- 14,037 FED>5,342 PHI>11,35 8 PMI<49,52 6 FACT2>- 112,93 Capacty Utlzaton Rate Phlfed Index Unemploym ent Rate ISM manuf Non Farm Payroll Consumer Prce Index Hourly Average Wages Buldng Permts Conf. Board Consumer Conf. Non Manuf. ISM Wholesale Inventory Retal Sales Exstng Home Sales New Home Sales Employment Cost Index Personal Income Trade Balance Weekly Jobless Clams Indce Help Wanted Weekly Workng Condto n FED<3,5 53 PMI<41, 189 PMI>60, 642 FED>6,2 11 FACT1> 97,784 CONF<7 8,937 FACT1> 97,784 PMI<51, 968 PMI<43, 968 PHI<- 10,226 FACT1<64, 883 MICH<100,063 FACT1<61, 227 FACT1>94, 128 MICH>86, 137 FACT1<85, 497 PHI<- 5,616 FED<3,0 53 CONF>9 2,089 22

23 Hours Conf. Board Consumer Conf. GDP Productvty Consumer Conf. Mchgan Empre Manufacturng Indce Help Wanted Chcago PMI New Home Sales GDP after 1999 Weekly Jobless Clams Constructon Spendng FED>3,605 FACT1<85, 497 PMI>58,58 9 MICH>92, 105 PMI<55,25 3 FED<3,395 MICH<94, 095 PHI>- 21,658 MICH<108,021 FACT1<81, 692 PHI>1,868 Weekly Workng Hours Indce Help Wanted Retal Sales Personal Consumpton Chcago PMI New Home Sales Wages Weekly Jobless Clams Constructon Spendng CONF>92, 089 FED<3,395 MICH>80, 168 FACT1>71, 872 MICH<94, 095 PMI>41,05 3 FACT1<65, 128 FACT1<81, 692 PHI>1,868 Personal Consumpto n NAHB Housng Market Index Industral Producton Consumer Conf. Mchgan GDP after 1999 Chcago PMI Wages PMI>55, 253 PHI>11,3 58 PMI<56, 474 MICH>9 2,105 MICH>8 4,147 MICH<9 4,095 FACT1< 65,128 23

24 Table 7: Results of the estmaton of the threshold model for the 2-year rate, usng the best performng threshold varable. * s for 10% level and ** s for 5% level Student test confdence. 2 year Intercept >Th <Th LR test Threshold Th. value p-value Household consumpton PMI Personal Income 0,009* FACT ISM manuf 0,011** 0,119** 0,024** FED Industral New orders ,235** PHI Constructon Spendng ,057** MICH Consumer Credt PHI Wholesale Inventory ,044** PHI Retal Sales ,094** FED Industral Producton ,081** PHI Housng Start FACT Phlfed Index ,021** 0,59** PMI Exstng Home Sales ,36** PMI Conf. Board Consumer ,038** 0 Conf. FED GDP ,034** FACT Chcago PMI ,004* 0,014** MICH New Home Sales ,01* PHI Consumer Prce Index ,143** CONF Unemployment Rate ,128** PMI Trade Balance ,077** PHI Jobless Clams PMI Non Farm Payroll ,133** 0,037** FACT Capacty Utlzaton Rate ,013* 9,031** FED Employment Cost Index ,059** FACT Wages FED Productvty ,038* PMI Durable Good Orders FACT Producer Prce Index PHI Hourly Average Wages ,093** FACT Non Manuf. ISM ,067** PHI Weekly Workng Hours ,042** FACT Consumer Conf ,02** Mchgan MICH

25 GDP after ,015* MICH Weekly Jobless Clams ,012* FACT Buldng Permts ,074** PMI Empre Manufacturng ,02** PMI Personal Consumpton ,071* MICH Indce Help Wanted ,024** FED NAHB Housng Market ,052** Index FACT Constructon Spendng ,017** PHI

26 Table 8 : Results of the estmaton of the threshold model for the 5-year rate, usng the best performng threshold varable. * s for 10% level and ** s for 5% level Student test confdence. Household consumpton 5 year Intercept >Th <Th Threshold Th. value LR test pvalue PMI Personal Income ,042** 0 FACT ISM manuf ,049** 0 MICH Industral New orders CONF Constructon Spendng FACT Consumer Credt PHI Wholesale ,061** Inventory PHI Retal Sales ,025** MICH Industral ,071** Producton PHI Housng Start PHI Phlfed Index ,02** 0,587** PMI Exstng Home ,051** Sales MICH Conf. Board ,039** Consumer Conf. PMI GDP ,04** FACT Chcago PMI ,004* 0,014** MICH New Home Sales ,013** PMI Consumer Prce ,142** Index CONF Unemployment ,152** Rate PMI Trade Balance ,036** 0 FACT Jobless Clams PMI Non Farm Payroll ,149** 0,033** FACT Capacty ,013* 7,28** Utlzaton Rate FED Employment Cost ,073** Index FED Wages ,012** FACT Productvty PMI Durable Good Orders PMI

27 Producer Prce Index Hourly Average Wages ,108** PHI FACT Non Manuf. ISM ,063** FACT Weekly Workng ,038** Hours CONF Consumer Conf ,05** Mchgan FACT GDP after ,015* 0,088** PMI Weekly Jobless ,017** Clams FACT Buldng Permts ,103** PMI Empre Manufacturng MICH Personal ,024** Consumpton FACT Indce Help ,033** Wanted FED NAHB Housng ,042** Market Index PHI Constructon ,018** Spendng PHI Table 9 : Results of the estmaton of the threshold model for the 10-year rate, usng the best performng threshold varable. * s for 10% level and ** s for 5% level Student test confdence. Household consumpton 10 year Intercept >Th <Th 0,012** Threshold Th. value LR test pvalue FED Personal Income 0,009* 0,041** FACT ISM manuf 0,018** 0,122** 0,027** FED Industral New orders CONF Constructon Spendng FACT Consumer Credt PHI Wholesale ,059** Inventory PHI Retal Sales 0 0,05** CONF Industral ,027** Producton PMI Housng Start CONF Phlfed Index ,015** 0,568** PMI

28 Exstng Home Sales Conf. Board Consumer Conf ,001* 0,052** ,065** MICH PMI GDP FACT Chcago PMI ,004* 0,012** MICH New Home Sales ,053** MICH Consumer Prce ,118** Index CONF Unemployment ,138** Rate PMI Trade Balance ,043** FACT Jobless Clams PMI Non Farm Payroll ,128** 0,024** FACT Capacty ,238** Utlzaton Rate FED Employment ,058** Cost Index FED Wages ,013** FACT Productvty PHI Durable Good Orders PHI Producer Prce Index PHI Hourly Average ,09** Wages FACT Non Manuf. ISM ,061** FACT Weekly Workng ,034** Hours CONF Consumer Conf ,022** Mchgan MICH GDP after ,02** MICH Weekly Jobless ,042** Clams PHI Buldng Permts ,091** PMI Empre Manufacturng PHI Personal ,033** Consumpton PMI Indce Help ,04** Wanted FED NAHB Housng ,032** Market Index PHI Constructon 0,017** Spendng PHI