Anchoring Bias in Consensus Forecasts and its Effect on Market Prices

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1 Finance and Economics Discussion Series Divisions of Research & Saisics and Moneary Affairs Federal Reserve Board, Washingon, D.C. Anchoring Bias in Consensus Forecass and is Effec on Marke Prices Sean D. Campbell and Seven A. Sharpe NOTE: Saff working papers in he Finance and Economics Discussion Series (FEDS) are preliminary maerials circulaed o simulae discussion and criical commen. The analysis and conclusions se forh are hose of he auhors and do no indicae concurrence by oher members of he research saff or he Board of Governors. References in publicaions o he Finance and Economics Discussion Series (oher han acknowledgemen) should be cleared wih he auhor(s) o proec he enaive characer of hese papers.

2 ANCHORING BIAS IN CONSENSUS FORECASTS AND ITS EFFECT ON MARKET PRICES* Sean D. Campbell Seven A. Sharpe February 2007 Previous empirical sudies ha es for he raionaliy of economic and financial forecass generally es for generic properies such as bias or auocorrelaed errors, and provide limied insigh ino he behavior behind inefficien forecass. In his paper we es for a specific behavioral bias -- he anchoring bias described by Tversky and Kahneman (1974). In paricular, we examine wheher exper consensus forecass of monhly economic releases from Money Marke Services surveys from have a endency o be sysemaically biased oward he value of previous monhs daa releases. We find broadbased and significan evidence for he anchoring hypohesis; consensus forecass are biased owards he values of previous monhs daa releases, which in some cases resuls in sizable predicable forecas errors. Then, o invesigae wheher he marke paricipans anicipae he bias, we examine he response of ineres raes o economic news. We find ha bond yields reac only o he residual, or unpredicable, componen of he surprise and no o he expeced piece of he forecas error apparenly induced by anchoring. This suggess marke paricipans anicipae he anchoring bias embedded in exper forecass. *The ideas and opinions expressed are he auhors and should no be inerpreed as reflecing he views of he Board of Governors of he Federal Reserve Sysem nor is saff. This paper has benefied from he commens of Frank Diebold, Peer Hansen, Ken Kavajecz, Frederic Mishkin, Moohiro Yogo as well as seminar paricipans a he Board of Governors and he Universiy of Wisconsin. We would also like o acknowledge insighs provided by Dan Coviz and Dan Sichel during he formaive sages of his paper. Nicholas Ryan provided excellen research assisance. 1

3 I. Inroducion Professional forecass of macroeconomic releases play an imporan role in markes, informing he decisions of boh policymakers and privae economic decision-makers. In ligh of his, and he subsanial effecs ha daa surprises have on asse prices, we migh expec professional forecasers o avoid making sysemaic predicion errors. Previous research has approached his opic by esing ime series of forecass for raionaliy, an approach wih a fairly long and no enirely saisfying hisory. Generally, such sudies focus on esing for a few generic properies such as bias or auocorrelaion in errors, ess ha have yielded mixed resuls which provide limied insigh ino he behavior driving any apparen biases. Such sudies provoke bu do no answer he quesion: Wha are he implicaions of non-raional forecass for marke prices? In paricular, where persisen biases in forecass exis, do he users of hese forecass ake he predicions a face value when making invesmen decisions or dispensing advice? Or do hey see hrough he biases, which would make such anomalies irrelevan for marke prices? As noed by Tversky and Kahneman (1974), psychological sudies of forecas behavior find ha predicions by individuals are prone o sysemaic biases ha induce large and predicable forecas errors. One widely-documened form of sysemaic bias ha influences predicions by non-professionals is anchoring, defined as choosing forecass ha are oo close o some easily observable prior or arbirary poin of deparure. Such behavior resuls in forecass ha underweigh new informaion and can hus give rise o predicable forecas errors. 2

4 We invesigae wheher anchoring influences exper consensus forecass colleced in surveys by Money Marke Services (MMS) beween 1991 and MMS is a widely-used source of forecass in financial markes, which have also been subjeced o ess of forecas efficiency (Aggarwal, e al., 1995; and Schirm, 2003). Our sudy focuses on monhly macroeconomic daa releases ha were previously found o have subsanial effecs on marke ineres raes (Balduzzi, e. al., 2001, Gurkaynak, e al, 2005; Goldman Sachs, 2006). We es a hunch born of years spen monioring daa releases and marke reacions ha recen pas values of he daa release ac as an anchor on exper forecass. For insance, in he case of reail sales, we invesigae wheher he forecas of January sales growh ends o be oo close o he previously-released esimae of December sales growh. We find broad-based and significan evidence ha professional consensus forecass are anchored owards he recen pas values of he series being forecased. The degree and paern of anchoring we measure is remarkably consisen across he various daa releases. Moreover, he influence of he anchor in some cases is quie subsanial. We find ha he ypical forecas is weighed oo heavily owards is recen pas, on he order of 30 percen. These resuls hus indicae ha anchoring on he recen pas is a pervasive feaure of exper consensus forecass of economic daa releases known o move marke ineres raes. These findings imply ha he forecas errors or surprises are a leas parly predicable. Given ha daa surprises measured in his way have significan financial marke effecs, one mus wonder wheher hese effecs represen efficien responses o economic news. If marke paricipans simply ake consensus forecass a face value and rea he enire surprise as news, hen ineres rae reacions o daa releases would display greaer volailiy, relaive o a world wih raional forecass. 3

5 Our second major conribuion hus involves assessing wheher anchoring bias in economic forecass affecs marke ineres raes. Specifically, do ineres raes respond o he predicable, as well as he unpredicable, componen of he surprise? To answer his quesion, we decompose he surprise in each daa release ino a predicable componen induced by anchoring, plus he residual -- he laer being he rue surprise o he economerician. We hen es wheher marke paricipans anicipae he bias by regressing he change in he wo-year (or en-year) U.S. Treasury yield in he minues surrounding he release ono hese wo componens of he forecas error. We find ha he bond marke reacs srongly and in he expeced direcion o he residual, or unpredicable, componen of he surprises. On he oher hand, ineres raes do no appear o respond o he prediced piece of he surprise induced by anchoring. The resuls are similar for almos every release we consider. We hus conclude ha, by and large, he marke looks hrough he anchoring bias embedded in exper forecass, so his behavioral bias does no induce ineres rae predicabiliy or excess volailiy. The remainder of his paper is organized as follows. Secion II lays ou he concepual and empirical framework for he analysis. Secion III describes basic properies of he daa releases and MMS consensus forecass. Secion IV esimaes he proposed model of anchoring bias. Secion V ess wheher he anchoring bias affecs he response of marke ineres raes o daa releases. Secion VI concludes. 4

6 II. Forecas Bias, Anchoring, and Research Design A. Raionaliy ess and anchoring Many psychological and behavioral sudies find ha, in a variey of siuaions, predicions by individuals sysemaically deviae oo lile from seemingly arbirary reference poins, or anchors, which serve as saring poins for hese predicions. As a resul, hose predicions give oo lile weigh o he forecasers own informaion. 1 Tversky and Kahneman (1974) define anchoring o be when people make esimaes by saring from an iniial value ha is adjused o yield he final answer adjusmens are ypically insufficien [and] differen saring poins yield differen esimaes, which are biased owards he iniial values. In his secion, we characerize he relaion beween radiional ess of forecas raionaliy and our proposed model of anchoring. Tesing wheher macroeconomic forecass have he properies of raional expecaions has a fairly long radiion. A variey of earlier sudies (e.g., Mullineaux, 1978; Zarnowiz, 1985) invesigae wheher consensus macroeconomic forecass are consisen wih condiional expecaions. More recenly, Aggarwal, Mohany and Song (1995) and hen Schirm (2003) applied his line of invesigaion o surveys of forecass compiled by MMS. While he more recen sudies brough some new mehodological consideraions o he able, hey have largely followed he basic formulaion of his line of research. In paricular, he ypical analysis involves running regressions wih he acual (realized) values 1 One example where such behavior had acual financial ramificaions is provided by Norhcraf and Neale (1987), who find ha professional real esae agens anchor heir forecas of a home s selling price o he lising price. 5

7 of he daa release, A, as he dependen variable on he forecas available prior o he daa release, F, or A = β F + ε. (1) 1 The hypohesis of raionaliy holds ha β 1 is no significanly differen from uniy and he errors are no auocorrelaed. 2 Broadly speaking, he resuls from such regressions end o be mixed, wih raionaliy being rejeced in a subsanial fracion of he ess. Boh Aggarwal e al. (1995) and Schirm (2003) find ha, when raionaliy is rejeced, i is almos always due o a slope coefficien β 1 greaer han uniy. As an example of a srong rejecion, Schirm (2003) esimaes a slope coefficien of 1.62 in equaion (1) for Durable Goods Orders, which suggess ha he MMS consensus predicions are oo cauious; ha is, errors would be reduced if forecased deviaions (from average growh) were magnified 62 percen. If forecass could be improved by sysemaically magnifying hem, he implicaion would be ha forecasers are oo slow or cauious when incorporaing new informaion. Indeed, in a differen seing, Nordhaus (1987) provides direc evidence of forecas ineria -- ha forecasers hold on o heir prior view oo long. Tha inference is drawn from an analysis of fixed-even forecass of GDP growh, which shows ha forecas revisions end o be highly serially correlaed. 3 Tha seing differs from he more convenional ime series wih rolling-even forecass, including he MMS forecass ha we analyze. If forecasers in he sandard rolling-even seing pu oo lile weigh on new informaion, his raises he quesion: Wha is he prior, or anchor, on which forecasers place 2 These sudies also ypically include a consan in equaion (1). Since we focus only on he condiional (i.e. ime varying) componen of he bias, for sake of simpliciy we omi he consan erm from he noaion here and in laer equaions, bu a consan is included in all he regressions. 3 Nordhaus (1987), for example, finds ha one-sep-ahead professional forecass, for some macroeconomic variables are anchored o he previous monh s wo sep ahead forecas. 6

8 oo much weigh? One plausible scenario is ha forecasers rea he value of he previous monh s daa as he mos salien single piece of informaion ha has come o he fore in he ime beween heir previous-monh and curren-monh forecass. If so, hen he previous monh s realizaion migh be reaed as a saring poin, or anchor, for he curren forecas. 4 More generally, forecasers migh place some weigh on a few lags of he release, paricularly when he forecased series ends o bounce around from monh o monh (i.e., exhibis negaive auocorrelaion). A he exreme, forecasers migh conceivably anchor heir forecas on a long-run average value for he series. To develop his se of ideas more formally, consider he following ransformaion of equaion (1), whereby he forecas is subraced from boh sides. This yields an alernaive version of he basic raionaliy es, where he forecas error or surprise (S) is regressed on he forecas: S A F = β F + ε, (2) Now, he canonical es of raionaliy examines wheher he slope coefficien is significanly differen from zero. As our alernaive hypohesis, we look for evidence in favor of he following model of forecas anchoring: [ ] (1 λ) F = λe A + A, (3) h where E [ A ] represens he forecaser s unbiased predicion of nex monh s release and A h represens he average value of he forecased series over he previous h monhs. If λ < 1, hen we would conclude ha consensus forecass are anchored o he recen pas. Using he 4 Frankel and Froo (1987), for example, find evidence ha professional exchange rae forecass are anchored owards he curren level of he exchange rae. 7

9 implicaion from equaion (2) ha [ ] [ ] rearranging, implies ha where γ = (1 λ) / λ. E A = E S + F and plugging his relaion ino (3) and [ ] γ ( h) E S = F A, (4) Equaion (4) implies ha he surprise, or forecas error, is parly predicable; in paricular, i is posiively relaed o he gap beween he forecas and he average release value over he previous h monhs. This is a sraighforward modificaion of he raionaliy regression (2). Here, a posiive coefficien esimae would imply ha consensus forecass are sysemaically biased oward lagged values of he release (and λ < 1 in equaion (3)). Such a finding could be inerpreed as evidence in favor of he Tversky and Kahneman (1974) adjusmen and anchoring heurisic. B. Marke relevance of economic daa and consensus forecass Along a separae line of research, several sudies have analyzed he news conen of daa releases by measuring he surprise componen of a release as he discrepancy beween is acual value and he consensus forecas from MMS Services. Balduzzi, Elon and Green (2001) as well as Gurkaynak, Sack and Swanson (2005) sudy he impac of macroeconomic news on ineres raes using MMS consensus forecass o gauge surprises. Aggarwal and Schirm (1992) use he deviaion beween macroeconomic releases and consensus MMS forecass o invesigae he reacion of exchange raes o innovaions in he U.S. rade balance. Andersen, Bollerslev, Diebold and Vega (2003) examine he effecs of his and oher macroeconomic news on exchange raes. In each sudy, hese surprises are shown o have large and significan effecs on financial marke prices. 8

10 In ligh of he srengh of financial marke reacions o surprises measured in his way, i would be of boh academic and praciioner ineres o undersand how sysemaic biases in economic forecass migh influence financial marke reacions o news. Do financial marke prices reac o he predicable componen of he surprise, or forecas error, arising from anchoring bias in he same way ha hey reac o he residual componen of he surprise? Or do marke paricipans anicipae he bias, and hus respond only o he residual componen of he surprise? We sudy his quesion by esimaing second-sage even-sudy regressions in which he change in he 2-year or 10-year Treasury yield around he ime of he release is regressed on he wo componens of equaion (4): e ( ) Δ i = δ S + δ S S + v, (5) e 1 2 e where S E( S ) refers o he forecased componen of he surprise idenified from OLS esimaes of equaion (4). If financial markes respond o he forecased componen of he surprise induced by anchoring in he same way ha hey respond o he residual, or unforecased componen, hen we should find δ1 = δ2. Alernaively, if financial markes see hrough he bias in forecass induced by anchoring, hen we would expec haδ 1 = 0. These wo alernaive hypoheses are explored in secion V. III. Daa and Sample Characerisics A. Macroeconomic Releases, Forecass and Surprises Our analysis covers eigh macroeconomic daa releases: Consumer Confidence, Consumer Price Index (CPI), Durable Goods Orders, Indusrial Producion, ISM 9

11 Manufacuring Index, New Homes Sales, and Reail Sales. 5 In wo cases, we also examine he consensus forecass of a key subcomponen of he op-line figure in he release -- CPI ex-food and Energy (Core CPI) and Reail Sales ex-auo. In boh cases, hese daa are released simulaneously wih he op line release and are considered by marke paricipans o conain more value-relevan news han he op line. Table I liss each release, he beginning of our sample period, he iming of he release and he reporing convenion, ha is, wheher he release is repored as a level, a change, or a percen change. While our las observaion is March 2006 in each case, he saring dae varies beween Sepember 1992 and June 1996, deermined by he availabiliy of he forecas daa. For each release, we define he consensus forecas, F, as he mean forecas from he Money Marke Services (MMS ) survey. 6 The surprise is measured as he difference beween he release and he associaed MMS mean forecas. We focus on hese eigh key releases because of heir previously idenified and imporan influence on ineres rae markes. Specifically, Balduzzi, Elon and Green (2001) show ha each of hese releases has saisically significan and economically imporan effecs on bond yields a boh he wo-year and en-year mauriy; specifically, surprises explain 20 o 60 percen of he variabiliy in he movemens of he wo-year and en-year Treasury yields in he momens surrounding each release. In Table II we presen some summary saisics for each release ( A ), is associaed MMS forecas, ( F ), and forecas surprise ( S ). For each variable we repor he sample mean, μ, sandard deviaion, σ, and he sum of he auoregressive coefficiens from a fifh order 5 Previously, he Insiue for Supply Managemen (ISM) index was known as he Naional Associaion of Purchasing Managers (NAPM) index. 6 We also looked a he median MMS forecass bu found resuls o be insensiive o his choice. 10

12 auo-regression, ρ j, a measure of persisence. 7 Releases expressed in levels appear a he op of Table II, followed by he remaining releases. The mean surprise, repored in Table II, is ypically close o zero, suggesing ha he forecass are uncondiionally unbiased. Also, he sandard deviaions of he forecass are in every case smaller han ha of he releases. As one would hope, he sandard deviaion of he surprises is ypically smaller han ha for he underlying release, wih Core CPI being he only excepion. No surprisingly, for daa releases ha are expressed in levels, which have a high degree of persisence, surprises are a lo less variable han he underlying release. The persisence properies of he variables lised in Table II are informaive abou he condiional properies of he MMS forecass. In he case of he level variables, boh he release and he forecas are highly persisen. The remaining releases and forecass show small o moderae degrees of persisence, wih he excepion of Durable Goods Orders and Reail Sales. These releases exhibi a subsanial and saisically significan degree of negaive serial correlaion; for Durable Goods Orders ρ = 2.08, while for Reail Sales ρ j = ,9 However, neiher of he associaed forecass exhibis a significan amoun of negaive serial correlaion, and hus he negaive serial correlaion of he daa shows up in he surprises. Ineresingly, hese are no he only releases where he surprise j 7 Lag lenghs beween wo and welve were considered in he consrucion of ρ j. The resuls repored in Table II are no sensiive o his choice. 8 In each case he modulus of he inverse roos of he esimaed auo-regression are all smaller han one. 9 In he case of Reail Sales he high degree of negaive serial correlaion can be parly explained by he presence of a few ouliers occurring in he wake of 9/11/2001. In Ocober, Reail Sales fell by 2.4%. In November, Reail Sales increased by 7.1% and in December Reail Sales fell by 3.7%. Removing hese periods increases he esimae of ρ o which is saisically significan a all convenional significance j levels. In he case of Durable Goods Orders removing hese hree monhs only increases he poin esimae of ρ j o

13 exhibis significan negaive serial correlaion. The surprise is negaively serially correlaed in every case excep for he ISM release. I is also saisically significan in he case of he CPI, New Home Sales, Reail Sales and Reail Sales ex-auo, suggesing ha he MMS forecass are condiionally biased. The finding ha he serial correlaion in surprises ends o be negaive raher han posiive suggess ha serial correlaion in surprises could be due o he anchoring of forecass on he mos recen lagged value of he release. This can be illusraed by a simple example in which he release is serially uncorrelaed. Suppose forecass were srongly anchored oward he recen pas in paricular, ha he curren forecas is se equal o he lagged acual value, F = A 1. In his simplified seing i is easy o see ha, ( )( ) = ( )( ) = ( [ ]) ( ) E A F A F E A A A A Var A E A, (6) ha is, successive surprises will be negaively correlaed. Finally, before moving on o he main resuls, we noe he unusual empirical properies of he Core CPI and is associaed forecass. As shown in Table II, he Core CPI is by far he leas variable of all releases; ha is, boh he release and he associaed surprise are significanly less volaile han any oher release or surprise. Over our sample period, he MMS forecas of Core CPI is nearly consan, equal o 0.2% (monhly inflaion rae) in 117 ou of 176 monhs. Thus, in he case of he Core CPI, his sample period seems poorly suied o conducing our ess. Sill, we include he Core CPI release in our analysis because Core CPI surprises have subsanial ineres rae effecs, which migh oherwise be spuriously aribued o op line CPI surprises. B. Ineres Rae Reacions o Macroeconomic News Releases 12

14 We measure he reacion of he wo-year and en-year U.S. Treasury yield in he momens surrounding each macroeconomic release using quoe daa from Bloomberg. For each release and mauriy we exrac he quoed yield from a rade occurring boh five minues prior and en minues afer he release. The ineres rae reacion is defined as he difference beween he pos- and pre-release quoe. If no quoe exiss five minues before (en minues afer) he release, we use he las quoe available beween five and hiry minues before he release (he firs quoe available beween en and hiry minues afer he release). 10 In Table III we display he mean, sandard deviaion and he sum of auoregressive coefficiens of he ineres rae reacions. The average ineres rae response is always close o zero, which is consisen wih he near-zero mean of he associaed surprises. The sandard deviaions of he ineres rae reacions provide some informaion abou how much releases affec ineres raes. Consisen wih he findings of Gurkaynak, e. al., (2005) he sandard deviaions of he wo-year and en-year yield change are roughly similar. Also, consisen wih he findings of Balduzzi, Elon and Green (2001) he Non farm Payroll Employmen release produces he larges ineres rae reacions. Looking a he persisence properies of he ineres rae reacions indicaes ha he degree of serial correlaion in he ineres rae responses is ypically small, ranging from -0.3 o 0.3 in mos cases. In he case of Consumer Confidence, ISM, Durable Goods Orders and Indusrial Producion, however, he serial correlaion is saisically significan, which 10 In unusual cases where no quoe exiss 30 minues preceding he release, no yields are recorded, resuling in a missing value for he associaed ineres rae reacion. The number of missing values per ineres rae reacion series is ypically beween 2 and 5. The release associaed wih he mos missing ineres rae reacions is New Home Sales. In his case here are 15 missing values for he wo year reacion and 14 missing values for he en year reacion. 13

15 suggess ha ineres rae reacions migh be parly predicable. In wha follows we examine wheher any of he apparen predicabiliy in hese reacions can be raced o predicabiliy of he associaed surprises. IV. Esimaes of Anchoring Bias As laid ou in equaion (4) of secion II, we es for anchoring bias in MMS consensus forecass by running regressions wih he forecas error as he dependen variable and he difference beween he forecas and he anchor as he independen variable, ( ) S = γ F A + ε. 11 In order o esimae equaion (4) we need o specify he number of h periods (h) used in consrucing he anchor, A h. We focus on wo cases; in he firs A h is simply he lagged value of he release ( h = 1), while in he second i equals he average release value over he prior hree monhs ( h = 3). 12 A posiive value ofγ would consiue evidence ha forecas errors are biased in a predicable way and ha he form of he bias is consisen wih anchoring. In Table IV we presen he wo alernaive esimaes of equaion (4) for each of he macroeconomic releases lised in Table I. The firs wo columns show he coefficien on he forecas-anchor gap, heγ, and he R 2 for he case where he anchor is simply he prior monh s release, h = 1. The hird and fourh columns show he resuls when he anchor is he average value of he release over he prior hree monhs, h = 3. For each macroeconomic 11 Noe ha while equaion (4) does no include a consan erm, we always include a consan erm, γ 0, in is empirical implemenaion. 12 We examined anchors consruced from he lagged value, he average of he prior wo monhs releases and he average of he prior hree monhs releases. We do no repor he resuls from using he prior wo monhs as an anchor because hey are qualiaively similar o he one and hree monh resuls and he performance of he wo monh anchor generally lies in beween ha of he one and hree monh anchor. 14

16 release, he resuls from he model wih he highes 2 R are shown in bold. Finally, he resuls for he hree releases ha are repored as levels appear a he op of Table IV. The resuls for he remaining releases follow. Broadly speaking, he resuls indicae a fairly consisen paern of bias in macroeconomic forecass. The esimaed coefficien on he gap beween he consensus forecas and he previous monh s release (1-monh anchoring), is posiive for every release; and, in six of en cases i is significan a he 1% level. Togeher wih he resuls from he 3- monh anchoring model, we find ha he dominan model (in bold) has a significanly posiive coefficien for 8 of 10 releases. Aside from he Core CPI, which earlier was shown o be a poor candidae for his analysis, he coefficien in he dominan (bold) model is no significan only in he case of he ISM Manufacuring Index. The R 2 of he dominan models (again excluding he Core CPI) ranges from 1.3 o 25 percen, wih an average value of around 11 percen. The paern of resuls is also sensible in ligh of he ime series properies of he releases. The op hree daa releases, each of which is expressed in levels, were shown in Table III o display a high degree of persisence. In all hree of hese cases, we find ha he model wih he one-monh lag as he anchor clearly dominaes he model based on he hreemonh anchor. Alhough anchoring iself may or may no be raional, he forecasers seem sophisicaed enough o rea furher lags of hese hree releases as largely redundan. In he case of Consumer Confidence and New Home Sales, looking a he poin esimaes of γ suggess he anchoring bias is no only saisically significan bu ha is influence also can be sizable. In he case of Consumer Confidence, he poin esimae of 0.71 suggess ha, o minimize he mean squared error, he average forecas would have o 15

17 be shifed by 71 percen furher from he lagged release value (in he direcion indicaed by he sign of he gap). In erms of he framework laid ou i equaions (3) and (4), forecasers are placing roughly 40 percen of he weigh on he previous monh s release and only 60 percen on he expeced value. λ γ ( γ) (1 ) = \ 1+ = 0.71\ The R 2 saisics of 11.5 percen for Consumer confidence and 4.9 percen for New How Sales are also noable. Given he imporance of hese releases for bond markes and he relaively large variance of surprises, an R 2 of even 5 percen represens a subsanial amoun of predicabiliy wih poenially noiceable implicaions for ineres rae responses o hese releases. The remaining releases in he able are expressed in erms of changes or percen changes. Among hese, he evidence in favor of one-monh versus hree-monh anchoring is mixed. In hree of he six cases (again leaving aside he Core CPI), he one-monh anchoring model yields he bes fi. Even so, we find robus evidence of anchoring behavior for Durable Goods Orders, Indusrial Producion, Reail Sales and Reail Sales ex-auo. In each of hese cases he null hypohesis of no anchoring is rejeced a all convenional significance levels regardless of wheher a one or hree monh anchor is employed. For he CPI and Non-farm Payroll Employmen, anchoring is significan in he case of he hree monh anchor bu no he one monh anchor. The magniude of anchoring in he MMS forecass of he change variables is generally somewha less han ha of he level variables, hough i appears o be economically meaningful in mos cases. The magniude for Reail Sales falls close o middle of he pack; he coefficien of 0.25 in he one-lag model for Reail Sales implies forecasers place roughly 20 percen ( 0.25 /1.25 = 0.20 ) of he weigh on ha anchor. In addiion, he forecas errors for Reail Sales appear o be unusually predicable: he R 2 16

18 suggess ha he forecas-anchor gap explains 25 percen of he variance in surprises. Among he oher change variables, he variables. 2 R covers a range comparable o ha of he level The resuls in Table IV indicae ha he gap beween he curren forecas and he anchor predics fuure surprises in almos every release we consider. In hose ess, he alernaive hypohesis is ha forecas errors are unpredicable, ha is, orhogonal o all known informaion. A more demanding es of our model would involve esing i agains a more general model, for insance, a model where he forecas error migh be relaed o he curren forecas for some unspecified reason. To implemen his, we es wheher he coefficien on he hypohesized anchor is opposie in sign and equal in magniude o he coefficien on he curren forecas. In Table V we show esimaes of he following unresriced anchoring model, S = γ F + γ A + ε. (7) f A h For hese regressions, we choose he anchor from he bes-fiing model in Table IV. The firs column in Table V denoes he choice of anchor. The nex wo columns display he poin esimaes of γ f and γ A. The final wo columns display he Wald es ha γ f = γ A 2 and he model R. A quick perusal of he poin esimaes reveals a paern of coefficiens on forecass and anchors ha is remarkably consisen wih our model of anchoring bias. In paricular, in every case aside from he Core CPI, he esimae forγ f is posiive while ha for γ A is negaive. In mos cases, boh he curren forecas and he anchor are saisically imporan for predicing fuure surprises. Wha is more, he difference in he coefficiens magniudes 17

19 is ofen remarkably small. For insance, for Consumer Confidence, γ f = 0.76 and γ = A The Wald ess repored in he fourh column of Table V show ha only in he aberran case of Core CPI is he null hypohesis ha γ f = γ rejeced a all convenional A significance levels. Elsewhere, he Wald saisic provides scan evidence agains he null hypohesis. The possible excepions are Indusrial Producion and Non-farm Payroll Employmen, where he null hypohesis can be rejeced a he 10%, bu no he 5%, level. Even here, he discrepancies beween γ f and γ A are relaively small. Finally, comparing he fi of he unresriced and resriced (Table IV, bold) models reveals only a small deerioraion in fi when we impose heγ f = γ resricion (in he original specificaion); A he decline in R 2 is ypically on he order of a percenage poin. Our model of anchoring bias assumes ha forecasers always il heir forecas oward he value of he previous monh s (or few monhs ) release by a similar proporion. On he oher hand, i is plausible ha he exen o which forecasers rea a lagged release as reasonable saring poin for curren-monh forecass could depend on wheher ha lagged release is viewed as represenaive or normal. For insance, when lagged realizaions are far ou of line wih recen rends or broader hisorical experience, hey may have less influence on curren forecass. Of course, he opposie migh be rue; ha is, i migh be ha mos of he anchoring occurs on he heels of ouliers or rend-breaking observaions, while very lile anchoring occurs in normal imes. In principle such consideraions would sugges ha a more complex specificaion han our simple anchoring model migh be informaive, bu here is no clear a priori case for any paricular alernaive. Thus, raher han posulae a more complicaed anchoring model, 18

20 we simply re-esimae equaion (4) on a sub-sample of observaions ha excludes ouliers. Specifically, we exclude observaions in which he change in he release from monh 2 o 1 is larger han 1.5 sandard deviaions of he hisorical monhly change in he release. The resuls are conained in Table VI. As wih he model resricion ess in Table V, we repor resuls only for he besfiing model (1-monh or 3-monh anchoring) based on he Table IV regressions. The second and hird columns repor he esimaes ofγ and he R 2 saisics from he full sample, while he final wo columns repor he same for he sample ha excludes he ouliers. Broadly speaking, he oulier exclusion does no subsanially aler he picure. The esimaes of γ are all sill posiive; in mos cases, he esimaed degree of anchoring appears o increase somewha. The mos noable change is in he case of he ISM Manufacuring Index release, where he coefficien doubles o 0.44 and becomes saisically significan, while he 2 R rises o 5%. The Nonfarm Payrolls release is he only case showing a noable decline in he coefficien esimae when ouliers are excluded, from 0.25 o 0.17, reducing is significance. The broad picure ha emerges from Tables IV, V and VI is one in which anchoring plays a saisically and economically meaningful role in deermining MMS forecass of key macroeconomic releases. In some cases he esimaes imply ha he anchor receives as much as a 40 percen weighing (Consumer Confidence) in he curren forecas and he anchoring variable can accoun for up o 25 percen (Reail Sales) of he variance in fuure surprises. The paern in he resuls is remarkably uniform. Accordingly, anchoring appears o be an imporan and robus feaure of he MMS forecas daa. These findings hus raise 19

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