Evaluaing Macroeconomic Forecass: A Review of Some Recen Developmens Philip Hans Franses Economeric Insiue Erasmus School of Economics Erasmus Universiy Roerdam Michael McAleer Economeric Insiue Erasmus School of Economics Erasmus Universiy Roerdam and Tinbergen Insiue Roerdam, The Neherlands Rianne Legersee Economeric Insiue Erasmus School of Economics Erasmus Universiy Roerdam and Tinbergen Insiue Roerdam, The Neherlands EI200-9 Revised: March 200 * The auhors wish o hank Les Oxley and Chia-Lin Chang for helpful commens and suggesions. The second auhor wishes o acknowledge he financial suppor of he Ausralian Research Council, Naional Science Council, Taiwan, and he Cener for Inernaional Research on he Japanese Economy (CIRJE), Faculy of Economics, Universiy of Tokyo.
Absrac Macroeconomic forecass are frequenly produced, published, discussed and used. The formal evaluaion of such forecass has a long research hisory. Recenly, a new angle o he evaluaion of forecass has been addressed, and in his review we analyse some recen developmens from ha perspecive. The lieraure on forecas evaluaion predominanly assumes ha macroeconomic forecass are generaed from economeric models. In pracice, however, mos macroeconomic forecass, such as hose from he IMF, World Bank, OECD, Federal Reserve Board, Federal Open Marke Commiee (FOMC) and he ECB, are based on economeric model forecass as well as on human inuiion. This seemingly ineviable combinaion renders mos of hese forecass biased and, as such, heir evaluaion becomes non-sandard. In his review, we consider he evaluaion of wo forecass in which: (i) he wo forecass are generaed from wo disinc economeric models; (ii) one forecas is generaed from an economeric model and he oher is obained as a combinaion of a model, he oher forecas, and inuiion; and (iii) he wo forecass are generaed from wo disinc combinaions of differen models and inuiion. I is shown ha alernaive ools are needed o compare and evaluae he forecass in each of hese hree siuaions. These alernaive echniques are illusraed by comparing he forecass from he Federal Reserve Board and he FOMC on inflaion, unemploymen and real GDP growh. Keywords: Macroeconomic forecass, economeric models, human inuiion, biased forecass, forecas performance, forecas evaluaion, forecas comparison. JEL Classificaions: C22, C5, C52, C53, E27, E37. 2
. Inroducion Macroeconomic forecass are frequenly produced, published, discussed and used. The formal evaluaion of such forecass has a long research hisory. There are many sudies on he design of appropriae evaluaion crieria (see, for example, Chong and Hendry (986), Granger and Newbold (986), Ellio and Timmermann (2008), and various chapers in Clemens and Hendry (2002)). There has also been considerable discussion abou he proper use of daa, as macroeconomic daa are frequenly revised over ime. Thus, he imporan quesion arises as o which vinage of daa is he mos relevan. There is also a considerable lieraure abou alernaive combinaions of forecass. Indeed, i may well be ha combined forecass ouperform he individual forecass (see Timmermann (2006) for a recen survey). The siuaion o be reviewed, a leas in heory, may be presened as follows. The analys has wo (or more) forecass from disinc economeric models, and he issue is o selec he bes model according o some recognized crieria. In pracice, however, i is widely known ha mos macroeconomic forecass are no jus he oucome of an economeric model. For example, he Survey of Professional Forecasers (SPF) delivers he mean of forecass repored by various expers, and i is no likely ha all heir forecass are based on economeric models. Franses e al. (2007) documen ha all forecass from he Neherlands Bureau for Economic Policy Analysis (CPB) are he weighed sum of an economeric model forecas (based on a model comprising 2500 equaions) and a human wis, which we will denoe as inuiion. In he same spiri, i is mos likely ha forecass repored by, among ohers, he IMF, World Bank and he OECD are almos cerainly obained in a similar way. In his review, we address he issue of evaluaing macroeconomic forecass when hey are only parly based on economeric models. The main line of hough wih some recen developmens in his area is ha he analys has o disenangle he replicable from he non-replicable componens of hese forecass, whereby he analys can use a publicly available informaion se. The remainder of he forecass, namely he non-replicable 3
componen, would be called inuiion, as i canno be replicaed by he analys. As forecasers can and do incorporae he forecass provided by oher forecasers before presening heir own, he publicly available informaion se would ypically also conain previously published forecass. When formally comparing he forecass, i is necessary o use alernaive economeric ools as he variables of ineres are generaed regressors, which conain esimaion error. As has been well documened, such forecass, which are parly based on models and parly on inuiion, are ypically biased (see Bachelor (2007)). As unbiasedness is a prerequisie for sraighforward combining forecass properly, i is convenien o de-bias he original forecass before conducing a valid comparison of forecass. The ouline of he remainder of he paper is as follows. In Secion 2 we address hree simple cases, which can naurally be exended in various direcions. Consider wo forecass ha migh be generaed from: (i) wo disinc economeric models; (ii) an economeric model and a combinaion of model and inuiion; and (iii) wo disinc combinaions of model and inuiion. I is shown ha, in each siuaion, alernaive ools are needed o compare and evaluae he forecass. In Secion 3 we illusrae he alernaive cases by comparing he forecass from he Federal Reserve Board and he FOMC on inflaion, unemploymen and real GDP growh. I is shown ha each of he hree siuaions can lead o significanly differen evaluaions. 2. Model Specificaions This secion reviews hree differen cases concerning wo macroeconomic forecass, wherein he analys has o evaluae heir relaive qualiy and performance.. 4
2. Forecass from wo economeric models Consider he variable of ineres, forecass, F,, and he availabiliy of wo ses of one-sep-ahead and F 2,, for he sample n, n 2,..., n N. When he forecass are based on linear economeric models, hese models may be given as W,, () W2, 2 2, (2) When OLS is used o esimae he unknown parameers, he unbiased forecass are given as F ˆ (3), W, 2, 2, F W ˆ (4) 2 In pracice, i is quie likely ha only he oucomes analys, bu he informaion ses, W, W, F, F, and 2 are available o he and 2, are no. Le us assume ha he analys can resor o he publicly available informaion se, W. This se can include boh W, and W 2,, bu would generally be unknown. When i is known ha W, W, ness 2, he echniques developed in Clark and McCracken (200) are useful. If he models are non-nesed, one can rely on, for example, he Diebold and Mariano (995) es (see also Wes (996)). An alernaive simple mehod ha migh be used when lile is known abou W, W, and 2 relies on he auxiliary regression: F F (5), 2 2, 5
This regression is also a he hear of he combinaion of forecass (see Timmermann, 2006). The regression in (5) can be used o examine wheher each of he forecass adds significanly o he oher forecas. If so, hen one may wan o combine he wo forecass, wih he parameers in (5) being used as weighs. 2.2 One forecas from a model, he oher a combinaion of model and inuiion A second case is he following. Suppose ha he second forecas model, bu also parly based on he firs forecas, F,, and on inuiion, ha is: F 2, is parly based on a F ˆ (6), W, ˆ (7) F 2, W2, 2 F, 2, where denoes he inuiion included in he second forecas. When W 2, ˆ 2 in (7) is 2, he oucome of some economeric model, hen ha par of (7) is unbiased, bu he wo F,, added erms,, may cause bias. Evidence for he presence of bias in macroeconomic forecass is presened in Bachelor (2007), among ohers. I is eviden ha now he regression F F (8), 2 2, canno be used in a sraighforward manner as he forecas F, (2009) and Chang e al. (200) propose he auxiliary regression F, 2 conains. Franses e al. F W F 2,, (9) in order o esimae 6
F, 2 2, Fˆ (0) where ˆ ˆ is obained from (9). F 2, W ˆ F, As ˆ is a generaed regressor, he economeric analysis of (0) is non-sandard. When F 2, he difference beween ˆ and F 2, is viewed as a measuremen error, he covariance F 2, marix of in (0) is no proporional o he ideniy marix, so ha is serially correlaed and heeroskedasic. However, as Franses e al. (2009) demonsrae, OLS esimaion of he parameers in (0) can neverheless be consisen and efficien. Franses e al. (2009) esablish he condiions under which OLS esimaion of he parameers in a more general version of (0) is efficien by appealing o Kruskal s Theorem, which is necessary and sufficien for OLS o be efficien (see Fiebig e al. (992) and McAleer (992) for furher deails). In he conex of OLS esimaion of (0), he necessary and sufficien condiions for OLS o be efficien will be saisfied eiher if he variables used o obain he forecas forecas F, F, are conained in he informaion se of he 2, or are orhogonal o he variables in he informaion se of 2. Of he wo alernaive necessary and sufficien condiions, i is more likely ha he former condiion will hold. I was also shown by Franses e al. (2009) ha, if he incorrec downward biased OLS sandard errors are used, hen he incorrec OLS -raios will be biased upward. Therefore, hey sugges ha he correc OLS covariance marix in (0) should be esimaed consisenly using he Newey-Wes HAC sandard errors. Franses e al. (2009) also discuss he alernaive GMM approach in order o deal wih he generaed regressors issue. F, 2.3 Boh forecass as disinc combinaions of model and inuiion A hird case, which may be he mos likely o occur in pracice, is where boh forecass are disinc combinaions of model and inuiion. To he analys, he naure of his 7
combinaion is unknown. I is also mos likely ha here is no documenaion regarding any such inuiion. Franses e al. (2007) documen ha, a he Neherlands Bureau for Economic Policy Analyis (CPB), deailed records are reained of he size of any changes, bu no of he moivaion for he size of any changes. Hence, one may presume ha he analys has forecass ha migh be generaed as follows: ˆ () F, W,, ˆ (2) F 2, W2, 2 F, 2, where, and 2, are inuiion, and where we again assume ha forecaser 2 has received he oher forecas. If his is no he case, one can impose he resricion 0 in (2). In order o evaluae he relaive meris of hese wo forecass, one would run he regressions: F, W, (3) F 2, W 2 2, (4) Firs, as in case 2, one may consider he auxiliary regression: Fˆ Fˆ (5), 2 2, where ˆ and F ˆ, are obained from (3) and (4), respecively. Again, OLS is F 2, consisen, bu HAC sandard errors are required for valid inferences o be drawn. Second, one may also examine wha he forecass migh add o wha an analys can do using publicly available informaion, and his would be based on he auxiliary regression: W ˆ, 2 2, ˆ (6) 8
where ˆ, and ˆ2, are he esimaed residuals from (3) and (4), respecively. As W denoes publicly available informaion, he regression in (6) informs wheher he inuiion (which is no observable, bu raher is esimaed) of forecaser and/or of forecaser 2 adds any significan value o he final forecas. For example, if he esimae of is significan, hen one can conclude ha he inuiion of forecaser adds o forecas accuracy when combining i wih he forecas based solely on W. 3. Evaluaing FOMC and Saff Forecass In his secion we evaluae empirically he above hree cases using he daa ha were recenly analyzed in Romer and Romer (2008). In heir sudy, hey compare Saff and FOMC forecass, and heir saring poin is case in Secion 2. In his secion, we examine if a change in assumpions regarding how he forecass were obained, namely cases 2 and 3, can maerially change he conclusions reached in Romer and Romer (2008) regarding he superioriy of Saff versus FOMC forecass. The variables of ineres,, in Romer and Romer (2008) are he inflaion rae, unemploymen rae, and he real growh rae. The daa for he empirical analysis are described in Romer and Romer (2008, pp. 230-23), and are available in an appendix on he AEA websie (hp://www.aeaweb.org/aricles/issues_daases.php). As discussed in Romer and Romer (2008, pp. 230-23), he FOMC prepares forecass in February and July each year. The February forecass for inflaion and he growh rae are for he four quarers ending in he fourh quarer of he curren year, and he unemploymen rae forecas is for he fourh quarer of he curren year. The July forecass are for he same variables for boh he curren and nex year. The sample is from 979 o 200, wih 22 February forecass and 46 July forecass, giving a oal of 68 observaions. [Inser Figures -3 abou here] 9
The acual inflaion rae, unemploymen rae and real growh rae, as well as he corresponding saff and FOMC forecass, are shown in Figures -3, respecively. I is clear ha he saff and FOMC forecass are very similar, bu i is also clear ha hey are no paricularly close o he acual raes hey are forecasing, which raises he quesion as o how much beer hese forecass are relaive o hose ha an analys could make based on publicly available informaion. The similariy in he wo ses of forecass is suppored by he correlaions in Table beween he saff and FOMC forecass, which are obviously very close o each oher. [Inser Table abou here] The similariy in forecas performance is also shown in Table 2, which repors he mean and median squared predicion errors for he saff and FOMC forecass for he hree variables. The saff is clearly beer han he FOMC in forecasing he inflaion rae, he reverse holds in forecasing he real growh rae, and i is oo close o call for he unemploymen rae, wih he saff only slighly beer (worse) han he FOMC in erms of he mean (median) squared predicion error. In erms of forecasing performance, herefore, i would be fair o call he oucome a ie. [Inser Table 2 abou here] Case : Assume ha Saff and FOMC forecass are based purely on economeric models. Romer and Romer (2008) assume ha Case prevails in his siuaion, and hey run he regression: S P (7) 2 In erms of formal ess of he forecasing performance of he saff and he FOMC, he OLS and GMM esimaes of equaion (7) are given in Table 3. When Case 2 would be he real siuaion and Case is assumed, hen OLS is inconsisen and he forecas is no 0
MSE opimal, while GMM is consisen. For he insrumen lis for GMM, we use he one-period lagged values of inflaion, unemploymen rae and real growh rae (excep for he case of real growh, where only he second lag is used for a beer fi). [Inser Table 3 abou here] For each variable, he firs line repors he OLS resuls (which could be inconsisen in case 2), and he second line gives he GMM resuls. The OLS esimaes correspond o hose in Table in Romer and Romer (2008), where i was inferred ha he saff forecass dominaed hose of he FOMC for inflaion and he unemploymen rae, hough no for he real growh rae. I is insrucive ha he GMM esimaes indicae ha he saff is beer han he FOMC in forecasing inflaion, bu no in forecasing he unemploymen rae or he growh rae, where he effecs of boh he saff and FOMC forecass are insignifican. Alhough he OLS and GMM esimaes of he coefficiens are markedly differen, i is worh noing ha he sums of he esimaed saff and FOMC marginal effecs are very similar, namely.00 and.3 for inflaion, 0.94 and.0 for he unemploymen rae, and 0.88 and.9 for he growh rae. In his sense, he sum of he pars would seem o be greaer han he whole. Case 2: Le he FOMC forecas be creaed afer he Saff forecas is published, and assume ha he Saff forecas is based on an economeric model. In his case we assume ha (6) and (7) are useful, and are expressed as S ˆ (8) W, P W 2, 2 ˆ S (9) p
This says ha he Saff use an unknown economeric model, while he FOMC has a p model bu also relies on he Saff forecass and unobserved inuiion,. As analyss, we do no observe he informaion ses W, W, and 2, and we do no know p. Hence, we rely on an auxiliary regression, as in (9), in order o calculae Pˆ, which can be expressed as: P W S (20) where, for W, we include one-period lagged values of inflaion, unemploymen rae and real growh rae o be consisen wih he siuaion in case. [Inser Table 4 abou here] The OLS esimaes of equaion (20), where (A) concerns he full model and (B) he case where 0, are given in Table 4. For purposes of esimaing (20) (A), OLS is efficien and he forecas is MSE opimal, bu OLS is inconsisen and he forecas is no MSE opimal for esimaing (20) (B). In he absence of addiional variables oher han he Saff forecass, he inconsisen OLS esimaes for (20) (B) migh seem o sugges ha he effec of he Saff forecas on he FOMC forecas is very close o uniy for all hree variables. However, he inclusion of addiional variable available o he forecasers of he FOMC experise, as approximaed by one-period lagged inflaion, unemploymen and real growh raes, shows ha he effec of he Saff forecas, while remaining significan, is considerably less. The F es of he join significance of wha FOMC adds o he Saff forecass makes i clear i does maer, and significanly so, in obaining he forecas P. In shor, he FOMC uses informaion ha is saisically significan. [Inser Table 5 abou here] 2
The empirical performance of he Saff and FOMC forecass (afer de-biasing) are compared in Table 5. The auxiliary regression is ˆ S 2P (2) where Pˆ is obained from (20). Alhough OLS is efficien and he forecas is MSE opimal for equaion (2), he sandard errors are no proporional o he ideniy marix, so he Newey-Wes HAC sandard errors are calculaed. The Saff is seen o dominae he FOMC for he inflaion rae, bu boh he Saff and FOMC forecass are insignifican for he unemploymen and real growh raes. Alhough he goodness of fi of he OLS esimaes in Tables 3 and 5 are virually idenical, he corresponding coefficien esimaes are markedly differen. However, he sums of he esimaed saff and FOMC marginal effecs in Table 5 are very similar o heir OLS counerpars in Table 3, a.0, 0.95 and 0.98 for inflaion, unemploymen rae and real growh rae, respecively. In summary, in a comparison wih he Saff forecass, he use of FOMC forecass, as in Cases or 2, yield considerably differen empirical resuls. I can be seen clearly ha he FOMC does no forecas well, bu he same can be said abou he Saff! Case 3: Assume ha boh forecass are based on disinc combinaions of model and inuiion. In his siuaion, which seems mos likely o hold in pracice, we assume ha () and (2) hold, which means ha we run he auxiliary regressions: S W, (22) P W S 2, (23) Nex, we firs consider he auxiliary regression: 3
ˆ ˆ S 2P (24) where Ŝ and Pˆ are obained from (22) and (23), respecively. [Inser Table 6 abou here] In Table 6, we repor he OLS esimaes of he parameers in (24), wih he HAC sandard errors. The evidence from his able demonsraes clearly ha he Saff forecass ouperform he FOMC forecass for all hree variables, as he saff forecass are significan whereas he FOMC forecass are no. The final siuaion ha is of ineres is o see wheher he Saff and FOMC forecass conain any unobservable inuiion ha migh significanly add o wha an analys could achieve using publicly available informaion. We consider W ˆ, 2 2, ˆ (25) and repor he esimaes in Table 7, where i is found ha he Saff inuiion is significan for all hree variables, whereas he FOMC inuiion is no. [Inser Table 7 abou here] These resuls are consisen wih he findings in Table 6, namely ha he inuiion conained in he FOMC forecass does no add significanly, whereas he inuiion conained in he Saff forecass does add significanly, in forecasing acual values of all hree variables. 4
4. Conclusion The purpose of he paper was o review he evaluaion of macroeconomic forecass using alernaive combinaions of economeric model and inuiion, which is he non-replicable componen of forecass. In he empirical illusraion, which was concerned wih a comparison of he forecass provided by he Federal Reserve Board s Saff and he Federal Open Marke Commiee (FOMC), i could safely be concluded ha he FOMC did no add significanly o he forecass of inflaion, unemploymen rae and he real growh rae, in comparison wih he Saff. Moreover, when we regress he inflaion rae, unemploymen rae and he real growh rae on one-period lags of hese hree variables, we obained mean squared predicion errors of 0.64, 0.25, and.3, respecively, while he median squared predicion errors are 0.03, 0.07 and 0.23. Hence, he analys wih simple forecasing ools could ouperform boh he Saff and he FOMC. Table 7 suggesed ha he analys could benefi from he inuiion conained in he Saff forecass, bu no from he inuiion in he FOMC forecass. This review concerned he siuaion ha seems o prevail in pracice. I is rarely found ha macroeconomic forecass are based on model oucomes only. When evaluaing hese forecass, one can hen no rely enirely on sandard ools, as he added inuiion may render he final forecass biased. We evaluaed some recen developmens in his area, bu i can safely be said ha here are furher developmens o come. 5
Table Correlaions beween Saff Forecass and FOMC Forecass Variable Correlaion Inflaion 0.99 Unemploymen 0.99 Real growh 0.97 Noe: The sample is from 979 o 200, wih 22 February forecass and 46 July forecass, giving a oal of 68 observaions. 6
Table 2 A Comparison of Saff Forecass and FOMC Forecass Squared Predicion Errors Mean Median Variable Saff FOMC Saff FOMC Inflaion 0.7 0.89 0.9 0.28 Unemploymen 0.54 0.57 0.6 0.5 Real growh 2.0.99.22.04 Noe: The sample is from 979 o 200, wih 22 February forecass and 46 July forecass, giving a oal of 68 observaions. 7
Table 3 (Case ) A Comparison of Saff and FOMC Forecass in Predicing Acual Values (Sandard errors are in parenheses) Esimaion mehod Inercep Saff (S ) FOMC (P ) R 2 Inflaion OLS -0.20.0 ** -0.0 0.86 (0.22) (0.39) (0.37) GMM -0.26 4.77 ** -3.64 0.64 (0.34) (2.32) (2.26) Unemploymen OLS 0.26 0.97 * -0.03 0.79 (0.4) (0.38) (0.40) GMM -0.37 3.4-2.40 0.64 (0.76) (2.78) (2.87) Real growh OLS 0.43 0.25 0.63 0.44 (0.36) (0.49) (0.52) GMM -0.22.70-0.5 0.3 (0.83) (3.6) (3.42) Noes: The regression model is S P 2, which is equaion () in Romer and Romer (2008)), and equaion (7) in he paper. The OLS esimaes correspond o hose in Table of Romer and Romer (2008). The insrumen lis uses he one-period lagged values of inflaion, unemploymen rae and real growh (excep for he case of real growh, where only lag 2 is used). * and ** denoe significance a he 5% and % levels, respecively. 8
Table 4 (Case 2) Auxiliary regressions o de-bias he FOMC forecass (Sandard errors are in parenheses) Inflaion Unemploymen Real growh Variables (A) (B) (A) (B) (A) (B) Inercep -0.8 0.0-0.00 0.9-0.22 0.28 (0.6) (0.07) (0.3) (0.2) (0.20) (0.08) Saff Forecas, S 0.9 **.03 ** 0.77 ** 0.96 ** 0.86 ** 0.93 ** (0.06) (0.02) (0.06) (0.02) (0.04) (0.03) P - 0.38 ** 0.32 ** 0.33 ** (0.2) (0.2) (0.2) S - -0.26 * -0.4-0.9 (0.3) (0.2) (0.) Inflaion - -0.03-0.00 0.02 (0.04) (0.02) (0.03) Unemploymen - 0.04 0.04 0.03 (0.03) (0.05) (0.03) Real growh - 0.0 0.0 0.02 (0.02) (0.02) (0.03) R 2 0.99 0.98 0.98 0.98 0.96 0.94 F es 4.86 ** 5.79 ** 5.87 ** Noes: The regression equaion correlaes P and S hrough P W S which is equaion (20) in he paper. * and ** denoe significance a he 5% and % levels, respecively. 9
Table 5 (Case 2) A Comparison of Saff and FOMC Forecass in Predicing Acual Values: Saff forecass are based on an economeric model, and FOMC forecass are based on Saff forecass, oher variables and inuiion (Sandard errors are in parenheses) Esimaion mehod Inercep Saff (S ) FOMC (P ) R 2 Inflaion OLS -0.20.89 ** -0.88 0.85 (HAC) (0.25) (0.55) (0.56) Unemploymen OLS 0.22 0.80 0.5 0.79 (HAC) (0.67) (0.7) (0.7) Real growh OLS 0.0-0.28.26 0.45 (HAC) (0.48) (.07) (.06) Noes: The regression model is a ˆ 0 S P, which is equaion (2) in he paper. The Newey-Wes HAC sandard errors are given in parenheses. ** denoes significance a he 5% level. 20
Table 6 A Comparison of Saff and FOMC Forecass in Predicing Acual Values: Saff forecass are based on an economeric model and inuiion, and FOMC forecass are based on Saff forecass, oher variables and inuiion (HAC sandard errors are in parenheses) Esimaion mehod Inercep Saff (S ) FOMC (P ) R 2 Inflaion OLS -0.34 0.58 * 0.43 0.85 (HAC) (0.29) (0.27) (0.23) Unemploymen OLS -0.3 0.80 ** 0.20 0.82 (HAC) (0.67) (0.20) (0.4) Real growh OLS -0.95.6 ** 0.30 0.62 (HAC) (0.56) (0.8) (0.2) Noes: The regression model is ˆ ˆ S 2P, which is equaion (24) in he paper. The Newey-Wes HAC sandard errors are given in parenhese. *,** denoes significance a he % and 5% level, respecively.. 2
Table 7 A Comparison of Saff and FOMC Forecass in Predicing Acual Values: Inuiion is added o lagged variables (chosen by he analys) (parameer esimaes for lagged inflaion, lagged unemploymen and lagged growh are no repored) (HAC sandard errors are in parenheses) Inuiion of Esimaion mehod Saff (S ) FOMC (P ) R 2 Inflaion OLS 0.58 * 0.25 0.87 (HAC) (0.24) (0.48) Unemploymen OLS 0.32 ** -0.9 0.90 (HAC) (0.0) (0.40) Real growh OLS 0.29 * 0.45 0.65 (HAC) (0.5) (0.62) Noes: The regression model is ˆ, W ˆ, 2 2, which is equaion (25) in he paper. The Newey-Wes HAC sandard errors are given in parenheses. *,** denoes significance a he % and 5% level, respecively 22
2 0 8 6 4 2 0 5 0 5 20 25 30 35 40 45 50 55 60 65 INFLATION S_INFLATION P_INFLATION Figure Inflaion rae, Saff forecass (S_inflaion) and FOMC forecass (P_inflaion) The sample is from 979 o 200, wih 22 February forecass and 46 July forecass (979 is observaion and 200 is observaion 68). 23
0 9 8 7 6 5 4 3 5 0 5 20 25 30 35 40 45 50 55 60 65 UNEMP S_UNEMP P_UNEMP Figure 2 Unemploymen rae, Saff forecass (S_unemp) and FOMC forecass (P_unemp) The sample is from 979 o 200, wih 22 February forecass and 46 July forecass (979 is observaion and 200 is observaion 68). 24
8 6 4 2 0-2 -4-6 5 0 5 20 25 30 35 40 45 50 55 60 65 GROWTH S_GROWTH P_GROWTH Figure 3 Growh rae, Saff forecass (S_growh) and FOMC forecass (P_growh) The sample is from 979 o 200, wih 22 February forecass and 46 July forecass (979 is observaion and 200 is observaion 68). 25
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