Cross-sectional Variation of Measurement Error and Predictability of Earnings and Stock Returns. Jung Hoon Kim

Transcription

1 Cross-secoal Varao of easureme Error ad redcably of Eargs ad Soc Reurs By Jug Hoo Km A dsserao submed paral sasfaco of he requremes for he degree of Docor of hlosophy Busess Admsrao he Graduae Dvso of he Uversy of Calfora, Bereley Commee charge: rofessor Rchard G. Sloa, Char rofessor arca. Dechow rofessor Sha Lev rofessor Adam Szedl all

2 Cross-secoal Varao of easureme Error ad redcably of Eargs ad Soc Reurs Copyrgh by Jug Hoo Km

3 Absrac Cross-secoal Varao of easureme Error ad redcably of Eargs ad Soc Reurs by Jug Hoo Km Docor of hlosophy Busess Admsrao Uversy of Calfora, Bereley rofessor Rchard G. Sloa, Char I capal mares research, mare expecao of fuure eargs plays a val role. However, almos all proxes evably measure he mare expecao of fuure eargs wh error, whch resuls usasfacory emprcal oucomes pror research e.g., small emprcal values of eargs respose coeffce ad poor qualy esmaes of expeced raes of reur. Usg aalyss cosesus forecass, hs sudy vesgaes how osy measureme of he mare expecao of fuure eargs affecs he predcably of fuure eargs ad soc reurs. Based o he errors--varables approach, hs sudy frs provdes a framewor o capure cross-secoal varao of he measureme error aalyss cosesus forecass. Wh hs framewor place, hs sudy documes ha aalyss cosesus forecass wh more measureme error have less ably o predc fuure eargs ad soc reurs, ad ha corporag formao abou cross-secoal varao of he measureme error ca mprove he predcably of fuure eargs ad soc reurs. These fdgs wll be useful o accoug research ha reles o he mare expecao of fuure eargs ad o pracoers seeg o forecas profably ad soc reurs.

4 Table of Coes Absrac... Table of Coes... Ls of gures... Ls of Tables... v Ls of Appedces...v Acowledgemes... v Chaper. Iroduco.... Relao o pror research odel ad hypoheses developme Effec of measureme error aalyss cosesus forecass o predcably of fuure eargs Improveme of eargs predco ad model specfcao from cosderao of cross-secoal varao of measureme error Esmao of cross-secoal varao of measureme error aalyss cosesus orecass Effec of cross-secoal varao of measureme error o aalyss cosesus forecas s ably o expla soc prce Effec of measureme error aalyss cosesus forecass o predcably of fuure soc reurs Smulao ess Coeffce esmae ad R whe all observaos coa measureme error Coeffce esmae ad R whe half of observaos coa measureme error Coeffce esmae ad R whe sample cosss of mulple groups ad each group has dffere measureme error dsrbuo Summary from smulao ess Sample seleco procedure for emprcal ess Resuls of emprcal ess Aalyss cosesus forecas error regressos Descrpve sascs Effec of cross-secoal varao of measureme error aalyss cosesus forecass o predcably of fuure eargs ad evaluao of measureme error proxy meproxy... 3

5 6.4 Effec of cross-secoal varao of measureme error o aalyss cosesus forecas s ably o expla soc prce Effec of measureme error aalyss cosesus forecass o predcably of fuure soc reurs Ou of sample ess for mproveme predcably of fuure eargs ad soc reurs Robusess checs Effec of eargs perssece Effec of egave aalyss cosesus forecass ad sze Tess wh udeflaed measureme error Tess wh deflaed eargs Cocludg remars...4 Refereces...4 gures...48 Tables...55 Appedces...7

6 Ls of gures gure. Illusrao of sources of error measurg mare expecao of fuure eargs...48 gure. Tmele of predco of oe year ahead acual eargs...49 gure 3. Tmele of predco of oe year fuure soc reurs...5 gure 4. aer of coeffce esmaes ad R s e / x * whe all observaos coa measureme error...5 gure 5. aer of coeffce esmaes ad R s e / x * whe half of observaos are measured wh error ad observaos wh measureme error are defed wh dcaor varable...5 gure 6. aer of coeffce esmaes ad R s e / x * whe sample cosss of four groups wh dscve measureme error dsrbuo ad observaos wh each dscve measureme error dsrbuo are defed wh respecve dcaor varable...53

7 Ls of Tables Table. Coeffce esmaes ad R s whe all observaos coa measureme error...55 Table. Coeffce esmaes ad R s whe half of observaos coa measureme error ad observaos wh measureme error are defed wh dcaor varable...56 Table 3. Coeffce esmaes ad R s whe sample cosss of mulple groups ad each group has dscve measureme error dsrbuo ad observaos wh each dscve measureme error dsrbuo are defed wh respecve dcaor varable...58 Table 4. Aalyss cosesus forecas error regressos ad cosruco of measureme error proxy meproxy...6 Table 5. Descrpve sascs of varables used for predcg fuure eargs ad soc reurs...6 Table 6. Effec of measureme error o predcably of fuure eargs ad evaluao of measureme error proxy meproxy...63 Table 7. Effec of measureme error o explag soc prce wh aalyss cosesus forecas...64 Table 8. Effec of measureme error o predcably of fuure soc reurs...65 Table 9. Ou of sample ess for mproveme predcably of fuure eargs ad soc reurs whe formao abou cross-secoal varao of measureme error s corporaed...66 Table. Effec of eargs perssece...68 Table. Effec of egave aalyss cosesus forecass ad sze...7 v

8 Ls of Appedces Appedx A. Dervao of coeffce ad R whe aalyss cosesus forecas measures mare expecao of fuure eargs wh error...7 Appedx B. Defo of varables for smulao ess...75 Appedx C. Defo of varables used for aalyss cosesus forecas error regresso...76 Appedx D. Defo of varables used for predcg fuure eargs ad soc reurs...77 v

9 Acowledgemes I ha my dsserao commee, Rchard Sloa Char, arca Dechow, Sha Lev, ad Adam Szedl. I am graeful o rofessor Sloa for showg me he dreco of my dsserao. He was my ellecual lgh he jourey of research. I have leared from hm how o frame research deas ad ssues. Thas o rofessor Dechow s suggesos, hs paper has mproved subsaally. I have leared from her how o orgaze deas ad srucure argumes. rofessor Lev ad rofessor Szedl ecouraged me ad provded me wh sghful commes o my research desg. I am also very graeful o Sul Dua, Km Gulfoyle ad all he faculy members of he Accoug Deparme of he Haas School of Busess a he Uversy of Calfora, Bereley - Xao-Ju Zhag, Qao a, Ncole Johso, aos aaouas, Sueel Udpa ad Vcor Sao. Ths dsserao has also beefed grealy from he suggesos ad advce of Ashq Al, Abhj Barua, Dael Cohe, Wllam Cready, Seve or, Sephe L, Samr arov, Doro Nssm, Seve ema, Clar Whealey ad my colleagues he Haas School of Busess h.d. program. I would also le o express my graude o James Jho Chag, Dohyeo Km ad Igor Vaysma for her ecourageme ad care hroughou he h.d. program. ally, I am ruly graeful o my moher, Aye Ja Lee, ad my lae faher, Chag Ho Km, who provded me wh he excelle educao. They showed me a bg pcure of lfe ad gave me wsdom wheever I became mpae. I also ha my broher, Jug Km. I would especally le o ha my wfe, Joo Hee, for her couous suppors ad cofdece me. Whou her ecourageme, would have bee mpossble o complee hs dsserao. I also ha my daugher, Jae, ad my so, Jaso, who have brough exreme happess o my lfe. v

10 Chaper Iroduco A large body of capal mares research reles o mare expecao of fuure eargs. Sce he mare expecao of fuure eargs cao be observed, proxes are ofe employed. However, hey evably measure he mare expecao of fuure eargs wh error ha vares cross-secoally, whch resuls usasfacory emprcal resuls pror research alhough coclusos mosly go he rgh dreco. Therefore, f cross-secoal varao of he measureme error ca be esmaed alhough he sgs ad magudes of dvdual measureme errors may be uow, beer specfed emprcal es models ca be geeraed. Wh hs oo, usg aalyss cosesus forecass, hs sudy vesgaes he effec of measurg he mare expecao of fuure eargs wh error o he predcably of fuure eargs ad soc reurs. or hs purpose, aalyss cosesus forecass provde he approprae bass because aalyss cosesus forecass devae from he mare expecao of fuure eargs due o several error sources such as saleess, aalyss ably ad aalyss bas. Towards hs ed, based o he errors--varables approach ad characerscs of aalyss cosesus forecass a he me of predco, hs sudy frs provdes a framewor ha capures cross-secoal varao of he measureme error aalyss cosesus forecass. Wh hs framewor place, hs sudy repors ha aalyss cosesus forecass ha measure he mare expecao of fuure eargs wh more error have less ably o predc fuure eargs ad soc reurs. Ths sudy he aalycally documes ha corporag formao abou crosssecoal varao of he measureme error ehaces specfcao of predco models ad smulao resuls cofrm hs. Emprcal es resuls also show ha corporag formao abou cross-secoal varao of he measureme error mproves he predcably of fuure eargs ad soc reurs. The resuls also geerally hold ou of sample ess. Ths sudy corbues o he exa leraure several respecs. rs, ad mos mpora, buldg o pror fdgs, hs sudy shows ha osy measureme of he mare expecao of fuure eargs causes ferece problems emprcal research ad he effec coues o exs for que a log perod. To address he poeal problem caused by measurg he mare expecao of fuure eargs wh error, hs sudy drecly uses formao abou cross-secoal varao of he measureme error whle mos pror sudes use he proxy for he measureme error. Secod, he ma focus of hs sudy s o mprove he predcably of fuure eargs or example, he geeral cosesus s ha emprcal values of eargs respose coeffce are much smaller ha heorecal values. As documeed he revew paper by Kohar, wh he dscou rae of %, eargs respose coeffce should heorecally be bu mos emprcal esmaes rage from o 3 oly. Sce eargs respose coeffce s a coemporaeous mappg of chage eargs o chage frm value, smaller ha expeced eargs respose coeffce would be repored f a proxy measured he mare expecao of fuure eargs wh error. The revew paper by Easo 7 dcaes ha measurg he mare expecao of fuure eargs wh error could cause poor qualy esmaes of expeced raes of reur. Refer o Beaver e al. 98 soc prce, Brow e al. 987 frm sze, Kohar ad Sloa 99 leadg perod soc reurs, Beesh ad Harvey 998 o-lear fuco, achuga sascal mehod ad Barov e al. dsperso of aalyss forecass amog ohers.

11 ad soc reurs, whereas mos pror sudes focus prmarly o eargs respose coeffces. 3 Towards hs ed, s aalycally ad emprcally show ha corporag formao abou cross-secoal varao of he measureme error ca mprove he predcably of eargs ad soc reurs ad ehace he specfcao of predco models. 4 Based o he errors-varables approach, hs paper provdes a framewor ha capures cross-secoal varao of he ex-ae measureme error aalyss cosesus forecass by dsgushg he effec of he ex-ae measureme error from ha of ex-pos eargs ews o he coeffce ad R. Ths framewor ca be easly exeded o oher accoug research ha reles o he mare expecao of fuure eargs. ally, hs sudy repors ha he coeffce ad R from he regresso of he soc prce o he aalyss cosesus forecas decrease as he measureme error aalyss cosesus forecass creases. Ths s drec evdece ha aalyss cosesus forecass wh large measureme error do o well expla he mare expecao of fuure eargs. No may pror sudes drecly exame he relao bewee he soc prce ad measureme error. Ths sudy s orgazed as follows. Chaper summarzes relaed pror research. Chaper 3 develops models ad esable hypoheses. Chaper 4 repors he smulao resuls. Chaper 5 explas he sample seleco process. Emprcal fdgs are dscussed Chaper 6 ad Chaper 7. Chaper 8 cocludes hs sudy. 3 Excepos clude Beaver e al. 98, Das ad Lev 994 ad rael ad Lee 998. Beaver e al. 98 provdes wea evdece ha cludg soc prce o corol for measurg permae eargs chages wh error, may mprove he predcably of fuure eargs over a radom wal wh drf model. Das ad Lev 994 shows ha he predcably of soc reurs ca be mproved by usg a o-lear relao bewee eargs ad soc reurs. However, hey do o ppo why he predcably ca be mproved. rael ad Lee 998 shows ha aalyss forecas error ca be used o predc fuure soc reurs. However, hey do o use he errors--varables approach. 4 To he bes of my owledge, hs s he frs sudy o aalycally docume mproveme of he specfcao of predco models by corporag formao abou cross-secoal varao of he measureme error.

12 Chaper Relao o ror Research Ths sudy s closely relaed o he pror research ha vesgaes he effec of measurg he mare expecao of fuure eargs wh error. Truema 993 preses a model where researchers erroeously measure he mare expecao of fuure eargs based o aalyss forecass, whch resuls a o-lear relao bewee eargs surprse ad soc reurs. Rya ad Zarow 995 allows for he measureme error eargs o expla varao of eargs respose coeffces ad R s across dffere model specfcaos. The fdgs of Truema 993 ad Rya ad Zarow 995 mply ha correco of osy measureme of he mare expecao of fuure eargs may ehace resuls of he emprcal research ha reles o he mare expecao of fuure eargs. Wh he smlar sgh, examg eargs respose coeffces, some pror research res o mgae he poeal problem caused by measurg he mare expecao of fuure eargs wh error. Ths sream of research cludes Beaver e al. 98 soc prce, Brow e al. 987 frm sze, Kohar ad Sloa 99 leadg perod soc reurs, Beesh ad Harvey 998 o lear fuco, achuga sascal mehod ad Barov e al. dsperso of aalyss forecass amog ohers. Ths sudy s dffere from pror sudes wo respecs. rs, hs sudy drecly uses formao abou cross-secoal varao of he measureme error whle oher sudes use he proxy for he measureme error. Secod, hs sudy focuses o mproveme he predcably of fuure eargs ad soc reurs by corporag formao abou cross-secoal varao of he measureme error, whereas mos pror sudes focus maly o eargs respose coeffces. 5 Ths sudy s also relaed o he pror research ha exames he effec of precso of a sgal abou fuure eargs o he mare reaco. 6 The ma fdg s ha whe a sgal s o precse, he mare respose.e., eargs respose coeffce s decreasg he magude of mprecso.e., o-lear relao bewee eargs surprse ad soc reurs. Ths sream of research cludes Imhoff ad Lobo 993, Subramayam 996, Key e al. ad Burgsahler ad Chu amog ohers. 7 Ths sudy s dffere from pror sudes ha hs sudy employs he errors--varables approach o expla he effec of ex-ae osy measureme of mare expecao o he predcably of fuure eargs ad soc reurs, whereas mos pror sudes rely o he Bayesa model o accou for varous rages of eargs respose coeffces. Some pror research cludg Al e al. 99, Elgers ad Lo 994, rael ad Lee 998, Guay e al. 5, Gode ad oharam 8 ad Hughes e al. 8, proposes mehods o mgae aalyss forecas errors. Ths sudy s smlar o hose pror sudes s mehod for esmag cross-secoal varao of he measureme error aalyss cosesus forecass. However, hs sudy uquely provdes a framewor ha capures cross-secoal varao of he ex-ae measureme error by dsgushg he effec of ex-ae 5 Excepos clude Beaver e al. 98, Das ad Lev 994 ad rael ad Lee 998 as meoed earler. 6 recso refers o he exe ha a sgal capures he mare expecao of fuure eargs. 7 ror sudes cludg Cheg e al. 99, reema ad Tse 99 ad Das ad Lev 994 also docume a olear relao bewee eargs surprse ad soc reurs. They arbue her resuls prmarly o he eargs perssece. 3

13 measureme error from ha of ex-pos eargs ews o he coeffce ad R based o he errors--varables approach. Ths sudy uses he deermas of he aalyss forecas error documeed pror sudes. Abarbaell e al. 995 shows ha varace of he measureme error aalyss cosesus forecass creases he dsperso of aalyss forecass. 8 ror research cludg Abarbaell ad Berard 99, edahall 99 ad Cleme ad Tse 3, repors ha aalyss forecas errors are serally correlaed. Ths sudy addoally defes wo more deermas based o he sgh ha rasory eargs ca cause osy measureme of he mare expecao of fuure eargs. 9 8 Based o he fdg of Abarbaell e al. 995, Barov e al. uses he dsperso of aalyss forecass as a proxy for osy measureme of he mare expecao. ror research cludg Imhoff ad Lobo 99, Key e al. ad Burgshler ad Chu also documes ha he dsperso of aalyss forecass s posvely relaed o he aalyss forecas error. 9 The deermas of he aalyss cosesus forecas error employed he sudy are based o he ex-ae characerscs of aalyss cosesus forecass whle pror sudes ha ry o mgae he aalyss forecas error defy he deermas of he aalyss forecas error based o he frm characerscs. 4

14 Chaper 3 odel ad hypoheses developme Usg aalyss cosesus forecass, hs sudy exames he effec of osy measureme of mare expecao of fuure eargs o he predcably of log-erm fuure eargs ad soc reurs. or hs purpose, aalyss cosesus forecass provde he approprae bass because aalyss cosesus forecass devae from he mare expecao of fuure eargs due o several error sources such as saleess, aalyss ably ad aalyss bas. gure corass he case where all aalyss forecass correcly ad raoally represe he mare expecao of fuure eargs Case agas he case where each aalys s forecas measures he mare expecao of fuure eargs wh error Case. gure dcaes ha he measureme error aalyss cosesus forecass ca occur due o aalyss characerscs eve whe he uderlyg mare expecao of fuure eargs s cera. gure also suggess ha he measureme error aalyss cosesus forecass may vary cross-secoally accordg o he exe ha each error source corbues o he aggregae measureme error. Ths cross-secoal varao of he measureme error should have mplcaos for he predcably of fuure eargs ad soc reurs whe predcos are made based o aalyss cosesus forecass. Based o he errors--varables approach, hs sudy provdes a framewor o esmae cross-secoal varao of he measureme error aalyss cosesus forecass alhough he measureme error self may be uow. Wh hs framewor place, hs sudy he explores he mehod o mprove he predcably of fuure eargs ad soc reurs. 3. Effec of measureme error aalyss cosesus forecass o predcably of fuure eargs gure depcs he mele of predcg acual eargs a me +. rom gure, he predco model ha forecass acual eargs a me + wh he aalyss cosesus forecas a me ca be esablshed as : A ε wh R e ε u wh R EIV EIV A where : Acual eargs a me + A : are expecao a me of acual eargs a me + : Aalyss cosesus forecas a me for acual eargs a me + : Eargs ews durg me + e : easureme error aalyss cosesus forecas a me. Accordg o he errors--varables approach, mples ha f he acual eargs a me + Ths sudy mplcly assumes ha he mare expecao s exogeously gve. I s possble ha aalyss cosesus forecass happe o cocde wh he mare expecao of fuure eargs alhough each aalys s forecas measures he mare expecao of fuure eargs wh error. However, hs s o lely he case for mos of he frms covered by may aalyss. 5

15 are predced wh he aalyss cosesus forecas a me as a proxy for he mare expecao, he coeffce EIV ad R R EIV are aeuaed as because aalyss cosesus forecass measure he mare expecao wh error e : p lm ˆ p lm R EIV EIV R e e. The formal dervao of s provded Appedx A. also dcaes ha f he measureme error aalyss cosesus forecass vares cross-secoally, he aalyss cosesus forecass ha measure he mare expecao wh more error raslae less o fuure eargs ad, ur, have less ably o predc fuure eargs. Smlar uo apples o he predco of log-erm fuure eargs.e., fve year ahead mea acual eargs. 3 Hypohess : Coeffces ad R decrease as measureme error aalyss cosesus forecass creases whe aalyss cosesus forecass are used o predc fuure eargs. rom, should be oed ha eargs ews durg me + s he measureme error o he depede varable ha s o correlaed wh he ex-ae measureme error aalyss cosesus forecass sce was o acpaed a he me of predco. 4 Hece, aeuao he coeffce s purely arbuable o he measureme error aalyss cosesus forecass, bu R s decreasg boh varace of he measureme error aalyss cosesus forecass ad varace of eargs ews durg me +. These properes of he coeffce ad R repored are used o cosruc he proxy for he ex-ae measureme error aalyss cosesus forecass meproxy, whch s used o es he hypoheses. 3. Improveme of eargs predco ad model specfcao from cosderao of cross-secoal varao of measureme error I he prevous sub-seco, was show ha he predcve ably of aalyss cosesus forecass vares cross-secoally accordg o he exe of he measureme error hem. Ths sub-seco vesgaes he effec of gorg cross-secoal varao of he measureme error o he predcably of fuure eargs ad provdes he mehod o mprove he predcably of fuure eargs. Towards hs ed, he coeffce ad R are derved for he case where wo groups of aalyss cosesus forecass are aggregaed o predc fuure eargs whe each group s subjec o he dffere degree of measureme error. or hs aalyss, s assumed ha boh ad are vecor wh + observaos respecvely. The frs observaos of A If aalyss cosesus forecass were raoal, hey would be he same as he mare expecao of fuure eargs. However, sce he observed aalyss cosesus forecass coa measureme error, hey become osy measureme of he mare expecao of fuure eargs. 3 or he predco of log-erm eargs, aalyss cosesus forecass are used as a proxy for he mare expecao of log-erm eargs. 4 If here were o eargs ews durg me +, he depede varable should be equal o he mare expecao a me. Whe eargs ews comes ou, acual eargs a me + becomes dffere from he mare expecao a me. Therefore, eargs ews adds error o he depede varable. 6

16 measure he mare expecao wh a cera degree of error e ad he remag observaos measure he mare expecao wh a dffere degree of error e as 3 5 : A ε wh R A e ε where : Acual eargs a me + A OOLED z wh R e : easureme error aalyss cosesus forecas a me e e for frs observaos ad for e e remag observaos : Eargs ews durg me +. : are expecao a me of acual eargs a me + : Aalyss cosesus forecas made a me for acual eargs a me + e for frs observaos ad e for remag observaos OOLED 3 Wh he sadard assumpos, he probably lm of he coeffce R OOLED uder hs seg ca be derved as 4: ˆ OOLED ad R plm ˆ plm R OOLED OOLED R e e e e 4. The formal dervao s provded Appedx A. 6 4 shows ha aggregao whou cosderg cross-secoal varao of he measureme error obscures he predcve ably of each group sce he coeffce ad R are decreasg he weghed average of measureme error varace of each group wh he wegh deermed based o he umber of observaos of each group. I should also be oed ha he coeffce ad R are more based oward hose of he group wh large measureme error. 7 Therefore, he predcve ably of he group wh small measureme error would be especally mpared f observaos were aggregaed whou cosderg cross-secoal varao of he measureme error. The resuls of 4 mply ha beer eargs predcos ad model specfcaos ca be geeraed f formao abou cross-secoal varao of he measureme error ca be corporaed. Applyg hs oo, hs sudy vesgaes how he coeffce ad R chage f formao abou cross-secoal varao of he measureme error s corporaed as 5 where he coeffces are allowed o vary usg a dcaor accordg o he cross-secoal varao of he measureme error: A 5 e ε γ γ γ D γ D x wh R 3 EV A ε wh R 5 To udersad he effec of cross-secoal varao of he measureme error aalyss cosesus forecass, s assumed ha eargs ews durg me + has he same dsrbuo for boh groups. 6 These resuls ca be readly exeded o ay umber of groups. 7 Das ad Lev 994 ad Burgsahler ad Chu oe he smlar uo. 7

17 where A : Acual eargs a me + : are expecao a me of acual eargs a me + : Aalyss cosesus forecas made a me for acual eargs a me + e for frs observaos ad e for remag observaos e : easureme error aalyss cosesus forecas a me for frs observaos ad for e e e e remag observaos D : whe e ad oherwse : Eargs ews durg me +. The, he coeffce ad R for 5 ca be expressed as 6: plm γˆ plm γˆ 3 plm R EV R e e e e e 6. The formal dervao s provded Appedx A. 8 Comparg 4 ad 6 reveals ha R creases whe formao abou cross-secoal varao of he measureme error s corporaed. 9 Ths s formally show 7 ad urepored smulao resuls cofrm hs fdg: plm R plm R 7. EV OOLED e e e e e e R Hypohess : redcably of fuure eargs ad R of eargs predco model are mproved f formao abou cross-secoal varao of measureme error s corporaed. 3.3 Esmao of cross-secoal varao of measureme error aalyss cosesus forecass To emprcally es Hypohess ad Hypohess, cross-secoal varao of he measureme error eeds o be esmaed sce he mare expecao of fuure eargs ad measureme error aalyss cosesus forecass cao be observed. Towards hs ed, he aalyss cosesus forecas error s employed, whch s defed as he absolue dfferece bewee acual eargs a me + ad he frs avalable aalyss mea cosesus forecas afer he acual eargs a me s aouced, scaled by he soc prce a he ed of he hrd 8 These resuls ca also be easly exeded o ay umber of groups. 9 Ths argume s cosse wh Sheffr 996. As Sheffr 996 pus, f ay formao ha s correlaed wh he forecas errors ha s avalable a he me of forecasg, would be possble o mprove he forecas by corporag hs correlao o forecasg. 8

18 moh afer fscal year ed of me as 8. The secod equaly 8 s derved from he relao amog he acual eargs a me +, aalyss cosesus forecas a me ad mare expecao a me as depced gure : Aalyss' cosesus forecas error A 8 where A : Acual eargs a me + : are expecao a me of acual eargs a me + : Aalyss cosesus forecas a me for acual eargs a me + : Soc prce a me : Eargs ews durg me + e : easureme error aalyss cosesus forecas a me. The reaso for choosg 8 as a sarg po s ha he cross-secoal varao of he measureme error ca be reasoably esmaed f dvdual measureme errors ca be defed as show 9: Var e E e E e E e e e 9, where e : easureme error aalyss cosesus forecas a me. Sce he fuure eargs cao be observed a he me of predco, 8 cao be drecly used. Isead, a proxy s cosruced based o he characerscs of aalyss cosesus forecass a he me of predco.e., ex-ae deermas of he aalyss cosesus forecas error. The followg varables are used as he deermas. Sadard devao of aalyss cosesus forecas a me e e sd : I pror research cludg Abarbaell e al. 995 ad Barov e al., he sadard devao of he aalyss forecass.e., dsperso s used as a proxy for he measureme error aalyss forecass. abs A Aalyss cosesus forecas error a me - : ror research cludg Abarbaell ad Berard 99, edahall 99 ad Cleme ad Tse 3 repors ha aalyss cosesus forecas errors are serally correlaed. 3 Absolue dfferece bewee acual eargs a me ad aalyss cosesus forecas a me for acual eargs a me + abs A : Ths deerma dcaes eher ha aalyss do o reflec ew formao embedded acual eargs a me or ha a large Ths s, spr, smlar o he measure used Elgers ad Lo 994. Elger ad Lo 994 uses he sged aalyss forecas error as a proxy for he mare s eargs expecao error. Imhoff ad Lobo 99, Key e al. ad Burgshler ad Chu also docume ha he dsperso of aalyss forecass s posvely relaed o he aalyss forecas error. 9

19 proporo of eargs s herely rasory. 4 Absolue dfferece bewee aalyss cosesus forecas a me for acual eargs a me + ad a me + abs : Ths deerma maly capures he measureme error from rasory eargs. Boh forecass are requred o be made he same moh. The measureme error proxy meproxy a me s he cosruced by mulplyg each deerma a me by he respecve coeffce from he regresso based o he daa bewee he sample sarg year.e., 99 ad me - : abs A sd abs A abs A abs α α α α α ε 3 4 where A : Acual eargs a me + A : Acual eargs a me : Aalyss cosesus forecas made a me for acual eargs a me + : Aalyss cosesus forecas made a me - for acual eargs a me : Aalyss cosesus forecas made a me for acual eargs a me + : Soc prce a me : Soc prce a me -. rom 8, s oed ha aalyss cosesus forecas errors capure boh he measureme error aalyss cosesus forecass a me ad eargs ews durg me Therefore, wheher he measureme error proxy meproxy prmarly capures he ex-ae measureme error aalyss cosesus forecass s a emprcal queso. rom, s oed ha f he measureme error proxy meproxy successfully capures he measureme error aalyss cosesus forecass a me, he coeffces ad R s from he predco model where acual eargs a me + are predced wh he aalyss cosesus forecas a me, are expeced o decrease as he meproxy creases. 5 To emprcally operaoalze hs uo ad es he hypoheses, qule ras are formed o he meproxy for each year. The, for each ra, fuure eargs are predced wh he aalyss cosesus forecas a me o vesgae chages he coeffces ad R s across he qule ras. 6 I spr, hs approach s smlar o Al e al. 99, Guay e al. 5, Gode ad oharam 8 ad Hughes e al 8. Ths sudy uses o proxy cross-secoal varao of he measureme error wh he assumpo ha he measureme error self s o observed, whereas pror sudes use o correc measureme error wh he assumpo ha represes a leas a poro of he measureme error. 3 I should be oed ha f here were o eargs ews durg me +, 3 would be exacly equal o he measureme error aalyss cosesus forecass a me. 4 ror sudes cludg Barro 998, Barro ad Suere 998, Barro e al. 9 ad Yeug 9 show ha he dsperso of aalyss forecass also capures he ex-ae uceray abou he frm s fuure eargs.e., frm value. However, hs sudy does o explcly model he ex-ae uceray wh he assumpo ha he uceray s mosly resolved by eargs ews durg me + ad mosly affecs R s as show. 5 If he measureme error proxy meproxy oly capured eargs ews durg me +, o oceable chages he coeffces would be expeced as he meproxy chages. Isead, R s would decrease as he meproxy creases. 6 As meoed, he meproxy also capures a poro of eargs ews durg me +. Therefore, R s are expeced o decrease a a faser rae ha he coeffces. Smlar uo apples o he predco of log-erm eargs.e., fve year ahead mea acual eargs.

20 Hypohess : If measureme error proxy meproxy capures ex-ae measureme error aalyss cosesus forecass, coeffces ad R decrease as meproxy creases whe aalyss cosesus forecass are used o predc fuure eargs. 3.4 Effec of cross-secoal varao of measureme error o aalyss cosesus forecas s ably o expla soc prce Sce he es of Hypohess ca be raher mechacal 7, o drecly es wheher he measureme error proxy meproxy successfully capures he measureme error aalyss cosesus forecass, s mpora o exame how he relao bewee he aalyss cosesus forecas ad soc prce chages as he measureme error aalyss cosesus forecass crosssecoally vares. 8 Towards hs ed, a smple eargs capalzao-based valuao model s employed 9 : e r r where : Soc prce a me : are expecao a me of acual eargs a me + : Aalyss cosesus forecas a me for acual eargs a me + e : easureme error aalyss cosesus forecas a me r: are mpled expeced rae of reur a me. mples ha he measureme error aalyss cosesus forecass causes he coeffce o be smaller ha /r ad he coeffce ad R decrease as he measureme error creases whe he soc prce a me s regressed o he aalyss cosesus forecas a me. Hypohess 3: Coeffce ad R decrease as measureme error proxy meproxy creases whe curre soc prce s regressed o aalyss cosesus forecas. Hypohess 3 mples ha aalyss cosesus forecass ha coa larger measureme error expla less of he curre mare value of he frm ad he mare expecao of fuure eargs. 3.5 Effec of measureme error aalyss cosesus forecass o predcably of fuure soc reurs Hypohess ad Hypohess 3 also sugges ha he measureme error aalyss cosesus forecass may well affec he eargs-based predcably of fuure soc reurs. To exame hs uo, he effec of measurg he mare expecao of fuure eargs wh error o he predcably of fuure soc reurs s examed. The predco of fuure soc 7 The es of Hypohess based o he meproxy ca be mechacal because he meproxy s cosruced based o he dfferece bewee he aalyss cosesus forecas ad fuure eargs. 8 Ths argume s based o he sgh ha soc prce s formed based o he mare expecao of fuure eargs. 9 I hs valuao model, s assumed ha eargs all fuure perods wll be pad ou or, aleravely, revesed eargs wll ear r. Refer o Kohar ad Zmmerma 995.

21 reurs s based o eargs yeld a me defed as he aalyss cosesus forecas a me scaled by he soc prce a me. 3 gure 3 depcs he mele of predcg oe year fuure soc reurs. The relao follows from ad he oo ha oe year fuure soc reurs s he sum of curre expeced reurs ad uexpeced reurs from he chages he mare expecao of fuure eargs due o he eargs ews durg + 3 : e Re r where Re : Oe year fuure soc reurs : Soc prce a me : are expecao a me of acual eargs a me + : Aalyss cosesus forecas a me for acual eargs a me + e : easureme error aalyss cosesus forecas a me : Eargs ews durg me + r: are mpled expeced rae of reur a me. dcaes ha whe fuure soc reurs are predced wh eargs yeld based o he aalyss cosesus forecas, he measureme error aalyss cosesus forecass mpars he predcably of fuure soc reurs. Ths s uvely appealg sce aalyss cosesus forecass ha measure he mare expecao wh more error should be less assocaed wh he mare reaco. Therefore, mproveme he model specfcao ad predcably of fuure soc reurs s expeced f formao abou cross-secoal varao of he measureme error s corporaed. 3 Smlar uo apples o he predco of log-erm fuure soc reurs.e., fve year fuure soc reurs. Hypohess 4: Coeffce ad R decrease as measureme error proxy meproxy creases whe eargs yeld.e., aalyss cosesus forecas scaled by curre soc prce s used o predc fuure soc reurs. redcably of fuure soc reurs ad R of soc reurs predco model are mproved f formao abou cross-secoal varao of measureme error s corporaed. 3 As ama 99 dcaes, he predcably of eargs yeld or dvded yeld may be arbuable o msprcg or o prce beg hgh relave o eargs or dvdeds due o low expeced reurs. 3 Reurs ews may be a addoal possble source of measureme error Re sce he curre model oly capures he ews relaed o eargs. 3 The predcably of soc reurs hs sudy does o mea o bea he mare. The assumpo s ha he equlbrum fuure soc reurs are gve based o he mare expecao of fuure eargs ad we ca approach more closely he equlbrum fuure soc reurs by corporag formao abou cross-secoal varao of measureme error.

22 Chaper 4 Smulao ess I hs chaper, before emprcal ess wh acual facal daa are coduced, smulao ess are mplemeed o vesgae wheher he aalycal sghs developed Chaper 3 are vald ad o exame effecs of he measureme error prese a osy observed predcor o he degree of he bas he coeffce esmae ad R, ad how o mprove he predco model specfcaos ad forecasg based o a osy observed predcor. Smulao ess provde a approprae es bed for valdag he aalycal sghs sce hey are based o radomly geeraed deal umbers. or he smulao ess, he oal of 4, observaos s used, whch cosss of 4 groups of, radomly geeraed observaos. rs, a rue predcor x * s radomly geeraed from he ormal dsrbuo wh mea of ad sadard devao of. The, a depede varable y s defed as he sum of mes rue predcor x * ad he dsurbace ε ha has a ormal dsrbuo wh zero mea ad sadard devao of Nex, a osy observed predcor x s assumed o measure he rue predcor x * wh error. I s defed as he sum of he rue predcor x * ad he measureme error e or u ha has a ormal dsrbuo wh zero mea ad a cera varace. The deals abou each varable are descrbed Appedx B. 4. Coeffce esmae ad R whe all observaos coa measureme error Table repors he resuls of he coeffce esmaes ad R s whe all observaos coa he measureme error based o he followg smple predco model 3. y EIV x w 3 where y: Idepede varable x: Nosy observed predcor ael A repors he coeffce esmaes ad R s based o he smulao ess. As predced Hypohess, he coeffce esmaes ad R s decrease as he measureme error varace creases. The coeffce esmae ad R decrease o.998 ad 7.3% whe he measureme error varace s 9 from 5.3 ad 36.9% whe he measureme error varace s. To exame wheher he decrease he coeffce esmae ad R based o he smulao s cosse wh wha he aalycal sghs developed Chaper 3, he coeffce esmae ad R are compued based o for each measureme error varace. Almos decal o he resuls from he smulao ess, he resuls from he heorecal predcos.e., compuao based o show ha he coeffce esmae ad R decreases o. ad 7.35% whe he measureme error varace s 9 from 5. ad 36.77% whe he measureme error varace s. gure 4 depcs he paer of he coeffce esmaes ad R s as he relave measureme error varace o he varace of he rue predcor creases. Boh he coeffce esmaes gure 4A ad R s gure 4B show he decreasg red as he relave 33 Resuls rema he same regardless of he dsrbuo of he depede varable y. 3

23 measureme error varace o he varace of he rue predcor creases. I should be oed ha here s a covex relao bewee he degree of he bas ad he relave measureme error varace o he varace of he rue predcor. Ths mples ha eve small amou of measureme error ca much bas he coeffce esmaes ad R s bu he margal effec of creasg measureme error varace o he bas s decreasg. 4. Coeffce esmae ad R whe half of observaos coa measureme error Table repors he resuls of he coeffce esmaes ad R s whe he half of he observaos coas he measureme error ad he oher half does o coa he measureme error. ael A repors he coeffce esmaes ad R s based o he smulao ess. Cosse wh he resuls repored Table, he coeffce esmaes ad R s decrease as he measureme error varace creases. I should be oed ha he bas he coeffce esmaes ad R s s smaller ha whe all observaos of he osy observed predcor are measured wh error as repored Table. To exame wheher he bas he coeffce esmae ad R based o he smulao s cosse wh wha he heory predcs, he heorecal bas he coeffce esmae ad R s compued based o 4 wh zero varace for he half of he observaos ad respecve varace for he oher half of he observaos. As repored ael B, for all cases, he coeffce esmae ad R from he smulao es are very close o wha he heory predcs.e., compuao based o 4. Nex, s examed how he smple defcao of he observaos ha coa he measureme error mproves he predco model specfcaos alhough he perfec measureme error dsrbuo s sll uow. The dcaor varable s used o defy he observaos wh he measureme error he predco model as 4. y γ γx γd γ3 xd υ 4 where y: Idepede varable x: Nosy observed predcor D : whe x coas measureme error ad oherwse As show 7, R s should crease whe he dcaor varable s used sce boh he heorecal predcos ad smulao ess assume ha he varace of he rue predcor s. As repored ael A ad B.e. secod colum for each case, boh smulao es resuls ad heorecal predcos are very close ad show ha R creases for all cases. The dfferece R bewee whe he dcaor varable s used ad whe he dcaor varable s o used s cosse wh wha he heory predcs based o 7. gure 5 also shows ha he mproveme he predco model specfcaos gure 5B ad predcve ably of he osy observed predcor gure 5A. The mproveme becomes more prome as he measureme error varace becomes larger. I cocluso, he resuls repored Table ad gure 5 mply ha smple defcao of he measureme error mproves he specfcao of he predco models. 4.3 Coeffce esmae ad R whe sample cosss of mulple groups ad each group has dffere measureme error dsrbuo 4

24 Ths subseco exames he bas he coeffce esmae ad R whe he sample cosss of four groups ad each group has a dffere measureme error dsrbuo. The resuls are documeed Table 3. I s oed ha he resuls of he smulao ess repored ael 3A ad he heorecal predcos.e., compuao based o 4 repored ael 3B are very close. Hece he focus of he dscusso les how he predco model specfcao s mproved as he degree of he defcao of he observaos wh he measureme error creases. I Table 3, he secod colums are he coeffce esmaes ad R s whe all observaos are pooled regressed. The hrd colums repor he coeffce esmaes ad R s whe he observaos wh large measureme error.e. measureme error wh varace of 4 or 9 are defed wh he dcaor varable as 5 wh he assumpo ha he observaos wh small measureme error ca be roughly dsgushed from hose wh large measureme error. y τ τ x τ D τ xd χ 5 s 3 s where y: Idepede varable x: Nosy observed predcor D s : whe observaos coa measureme error wh varace of 4 ad 9 ad oherwse The fourh colums repor he coeffce esmaes ad R s whe he observaos wh he measureme error are defed wh he dcaor varable as 6 wh he assumpo ha each measureme error dsrbuo cao be separaely defed alhough all observaos wh he measureme error ca be defed. y γ γ x γ D γ xd υ 6 3 where y: Idepede varable x: Nosy observed predcor D : whe x coas measureme error ad oherwse The las colums docume he coeffce esmaes ad R s whe he observaos wh each dffere measureme error dsrbuo are separaely defed wh he respecve dcaor varable as 7 wh he assumpo ha he exac dsrbuo of each measureme error s sll uow. y γ γ x γ D γ xd γ D γ xd γ D γ xd ν where y: Idepede varable x: Nosy observed predcor D : whe x coas measureme error wh varace of ad oherwse D : whe x coas measureme error wh varace of ad oherwse D 3 : whe x coas measureme error wh varace of 9 ad oherwse The hrd colums docume he crease R whe he observaos wh large measureme error are separaely defed. R s crease from 6% o 9%. As repored he fourh colums, he smple defcao of he observaos wh measureme error also helps o mprove he model specfcaos. R s creases o aroud 8% from 6% he secod colums. The separae defcao of he dffere measureme error dsrbuo furher 5

25 mproves he model specfcaos. R s he las colums are aroud 33%, whch s aroud 5% crease from he hrd colums. The same cocluso ca be draw from gure 6. I should be oed ha for he aalyss gure 6, he sample cosss of four groups wh equal umber of observaos. The frs group of observaos coas o measureme error. The secod group of observaos coas he measureme error wh zero mea ad varace of e. The hrd group of observaos coas he measureme error wh zero mea ad varace of 4e. The las group of observaos coas he measureme error wh zero mea ad varace of 9e. gure 6 preses he paer of he coeffce esmaes ad R s as he relave measureme error varace of he secod group e o he varace of he rue predcor vares from o 9. I all cases, he separae defcao of he observaos wh measureme error mproves he specfcaos of predco models. The mproveme s more prome for he case of separae defcao of all observaos wh measureme error ad separae defcao of each measureme error dsrbuo. Whe oly he observaos wh large measureme error are separaely defed, o he cera po.e. e s aroud, he mproveme R s creasg ad eve larger ha R from he predco model wh he dcaor varable ha separaely defes all he observaos wh he measureme error. The, he mproveme R sars o decay ad become smaller ha R from he predco model ha separaely defes all he observaos wh he measureme error. Ths s because here s a effec of separag he observao wh he small measureme error from he observaos wh he large measureme error becomes ambguous as he smalles measureme error varace e becomes larger. 34 However, R s sll greaer ha he predco model whou he dcaor varable. I cocluso, he resuls repored Table 3 ad gure 6 sugges ha f he observaos wh measureme error ca be separaely defed eve f he exac measureme error dsrbuo s sll uow ay way, beer specfed predco models ca be geeraed. oreover, he predcve ably of he osy observed predcor s also mproved sce he observaos wh he dffere degree of he measureme error are allowed o have dffere predcve ably. 4.4 Summary from smulao ess Ths sudy exames he effec of he measureme error embedded he osy observed predcor o coeffce esmaes ad R s based o he smulao ess. The bas he coeffce esmaes ad R s depeds o he weghed average of he measureme error varace of each group wh he wegh deermed based o he umber of observaos of each group f he sample cosss of he several groups. These resuls mply ha poolg he observaos wh he dffere degree of he measureme error obscures he erpreao of he coeffce esmae ad R. Therefore, separae defcao of he dffere measureme error dsrbuo subsaally mproves he predco model specfcaos wh respec o R s ad he predcve ably of he osy observed predcor. Eve approxmae defcao of he observaos wh measureme error duces he mproveme. 34 The covex relao bewee he degree of he bas ad he relave measureme error varace o he varace of he rue predcor also corbues o he resuls gure 6B. Afer a cera po, he margal effec of creasg he measureme error varace s o creasg as much. 6

26 Chaper 5 Sample seleco procedure for emprcal ess or he emprcal ess, he I/B/E/S Summary Hsory ad CRS daabases are maly used. Bewee 99 ad 7, all frm years whose aalyss mea cosesus forecas s avalable he I/B/E/S daabase are frs defed. or ease of porfolo cosruco, oly December edg frm years are seleced. 35 Sce he predco of log-erm fuure eargs ad soc reurs s he ma focus of hs paper, oly he frs aalyss cosesus forecass made afer he pror year eargs are aouced are seleced. I erms of oher daa avalably, s requred ha acual eargs, mmedae pror year s acual eargs, aalyss cosesus forecas for he mmedae pror year ad ex year, soc prce a he ed of he hrd moh afer pror fscal year ed, sadard devao of aalyss cosesus forecass be avalable he I/B/E/S ad oal asses a pror fscal year ed be avalable from Compusa. To compue he sadard devao of aalyss cosesus forecass.e., dsperso, he umber of forecas esmaes s requred o be greaer ha.e., or greaer. 36 Oe year fuure soc reurs s compued wh mohly raw soc reurs ad accumulaed for mohs begg he fourh moh afer he pror fscal year ed. ve year fuure soc reurs s compued he same maer for 6 mohs. or he frms ha are delsed durg he accumulao perod, -3% delsg reurs are assged o NYSE ad AEX frms ad -55% delsg reurs are assged o NASDAQ frms accordg o Shumway 997 ad Shumway ad Warher 999. Sce he emprcal ess are coduced based o per share facal formao, all releva varables are adjused o per share bass afer corollg for soc spls ad soc dvdeds. To accou for oulers, all varables excep for soc reurs are wsorzed a % level for boh exremes, ad observaos whose soc prce s less ha $5 are elmaed. 37 The sample seleco procedure provdes,74 frm year observaos bewee 99 ad 7 6,684 frm year observaos bewee 99 ad 4 for he es of predcg fve year mea acual eargs ad fve year fuure soc reurs. The varable defos are descrbed Appedx C ad D. 35 Resuls do o chage eve whe fscal edg moh s o resrced. 36 Tess are also coduced wh he samples whose umber of forecas esmaes s greaer ha 3 ad 5 respecvely ad he resuls are qualavely smlar. 37 Gve ha he small socs.e., soc prce less ha $5 ed o coa more measureme error, he resuls become eve sroger whe he small socs are cluded. 7

27 Chaper 6 Resuls of emprcal ess 6. Aalyss cosesus forecas error regressos Table 4, ael A repors he resuls of aual ama-acbeh regressos of he aalyss cosesus forecas error o he ex-ae deermas.e., characerscs of aalyss cosesus forecass bewee 99 ad 6. The resuls show ha all deermas are sgfcaly posvely relaed o he aalyss cosesus forecas error. As show, aalyss cosesus forecas errors capure boh ex-ae measureme error aalyss cosesus forecass ad ex-pos eargs ews. To corol for he effec of ex-pos eargs ews, he aual ama- acbeh regressos repored Table 4, ael A are repeaed wh he coemporaeous soc reurs cluded. The urepored resuls sll show ha all deermas are sgfcaly posvely relaed o he aalyss cosesus forecas error eve afer corollg for he ex-pos eargs ews ad he coeffces are almos decal o hose repored Table 4, ael A. 38 Ths dcaes ha he proxy for he measureme error aalyss cosesus forecass ca be successfully cosruced wh he defed deermas. The measureme error proxy meproxy s cosruced by mulplyg each deerma a me by he wegh for he respecve deerma.e. respecve coeffce derved from he aalyss cosesus forecas error regresso repored Table 4, ael A based o he daa bewee 99 ad me ael B repors he earso correlao bewee he measureme error proxy meproxy ad aalyss cosesus forecas error. The hgh correlao.63 mples ha he measureme error proxy meproxy s successfully cosruced wh reasoable precso. 6. Descrpve sascs Descrpve sascs for he varables used predcg fuure eargs ad soc reurs are repored Table 5. The measureme error proxy meproxy has mea of.5 ad meda of.4, suggesg ha s slghly rgh sewed. Cosse wh he opmsm aalyss forecass documeed pror research, he mea ad meda of aalyss cosesus forecass are greaer ha hose of boh oe year ahead acual eargs ad fve year ahead mea acual eargs. 6.3 Effec of cross-secoal varao of measureme error aalyss cosesus forecass o predcably of fuure eargs ad evaluao of measureme error proxy meproxy 38 I should be oed ha he measureme error proxy meproxy sll capures he formao relaed o he eargs ews due o he ex-ae uceray abou frm s fuure eargs.e., frm value ha s resolved by eargs ews. 39 or example, o cosruc he meproxy for year, each deerma of year s mulpled by he respecve coeffce from he aalyss cosesus forecas error regresso usg he daa bewee year 99 ad year

28 Table 6, ael A preses he resuls of he regressos for predcg oe year ahead acual eargs for 99 ~ 7 ad fve year ahead mea acual eargs for 99 ~ 4 wh aalyss cosesus forecass. Cosse wh he mplcaos of he errors--varables approach, boh coeffces ad R s are smaller ha oe for all predco models, whch mples ha aalyss cosesus forecass measure he mare expecao of fuure eargs wh error. I should be oed ha he coeffces of he regresso models for predcg fve year ahead mea acual eargs are geerally smaller ha hose of he regresso models for predcg oe year ahead acual eargs. Ths dcaes ha aalyss cosesus forecass measure he mare expecao of log-erm eargs wh more error. To vesgae wheher he measureme error proxy meproxy acually capures he ex-ae measureme error aalyss cosesus forecass, qule ras are formed o he measureme error proxy meproxy for each caledar year where ra s he porfolo wh he smalles meproxy ad ra 5 s he porfolo wh he larges meproxy. The, for each ra, acual eargs a me + s predced wh he aalyss cosesus forecas a me o vesgae chages he coeffces ad R s across he qule ras. Cosse wh Hypohess, he coeffces ad R s repored Table 6, ael A show a decreasg paer as he meproxy becomes larger. Ths resul cofrms ha he measureme error proxy meproxy successfully capures he measureme error aalyss cosesus forecass a me. Cosse wh Hypohess, hs also mples ha he measureme error vares crosssecoally ad aalyss cosesus forecass ha measure he mare expecao wh more error have less ably o predc fuure eargs. I should be oed ha R s are geerally decreasg a a faser rae ha he coeffces wh some excepos. 4 Ths suggess ha he measureme error proxy meproxy also capures he effec of ex-pos eargs ews. To exame wheher he specfcao of eargs predco models s mproved whe formao abou cross-secoal varao of he measureme error s corporaed, he eraco erm bewee he aalyss cosesus forecas a me ad a dcaor for each ra s cluded model ad 4 of Table 6, ael B. R s model ad 4 are compared wh R s model ad 3 respecvely. Cosse wh Hypohess, whe formao abou cross-secoal varao of he measureme error s corporaed as model ad 4, he adjused R s are greaer. Ths mples ha he sum of all squared predco errors.e., he squared dfferece bewee fuure eargs ad he predced value from each model s smaller for he predco model wh formao abou cross-secoal varao of he measureme error. 4 The sgfcaly egave coeffces o he eraco erms cofrm he resuls repored Table 6, ael A Effec of cross-secoal varao of measureme error o aalyss cosesus forecas s ably o expla soc prce Table 7 preses he resuls of he regresso of he soc prce a me o he aalyss cosesus forecas a me. Cosse wh Hypohess 3, he resuls Table 7, ael A show 4 or example, for he oe year ahead acual eargs predco model, he coeffce of ra 3 s 96% =.86/.896 of he coeffce of ra whereas R of ra 3 s 88% =.758/.865 of R of ra. 4 A deomaor s decal for boh models. 4 The coeffces o he eraco erms should be erpreed wh much care. Sce qule ras are scaled o le bewee ad for he resuls repored Table 3, ael B, he coeffces o he eraco erms represe he dfferece he coeffce bewee ra ad ra 5. 9

29 ha he coeffces ad R s are geerally decreasg as he measureme error proxy meproxy creases. Ths mples ha aalyss cosesus forecass ha coa larger measureme error expla less of he mare expecao of fuure eargs. Table 7, ael B provdes he evdece ha he adjused R s crease whe formao abou cross-secoal varao of he measureme error s corporaed. Ths mples ha osy measureme of he mare expecao of fuure eargs ca affec he resuls of value relevace sudes. 43 Therefore, mplcaos of he measureme error a depede varable should also be cosdered he value relevace sudes. 6.5 Effec of cross-secoal varao of measureme error aalyss cosesus forecass o predcably of fuure soc reurs Table 8 preses he resuls of he regressos for predcg oe year ad fve year fuure soc reurs wh eargs yeld. The resuls of Table 8, ael A show ha he coeffces ad R s geerally decrease as he measureme error proxy meproxy creases. I should be oed ha he coeffces of he predco model based o all observaos.e.,.49 for oe year fuure soc reurs predco ad.559 for fve year fuure soc reurs predco are oly greaer ha hose of he predco model for ra 5. Therefore, predcg fuure soc reurs based o he coeffce from he predco model ha gores cross-secoal varao of he measureme error would be effce ad msleadg. To exame wheher he specfcao of soc reurs predco models s mproved whe formao abou cross-secoal varao of he measureme error s corporaed, he regressos are coduced wh he eraco erm cluded bewee eargs yeld ad a dcaor for each ra as model ad 4 of Table 8, ael B. Cosse wh Hypohess 4, whe formao abou cross-secoal varao of he measureme error s corporaed as model ad 4, he adjused R s are larger ad mproveme s eve greaer ha he mproveme of he eargs predco models. Ths mples ha he sum of all squared predco errors.e., he squared dfferece bewee fuure soc reurs ad he predced value from each model s smaller for he predco model wh formao abou cross-secoal varao of he measureme error. The sgfcaly egave coeffces o he eraco erms cofrm he resuls repored Table 8, ael A. The predcably of fve year fuure soc reurs provdes he evdece ha he mpac of a gve year s osy measureme of he mare expecao of fuure eargs coues o exs for que a log perod. To exame wheher growh eargs s he ma drver of he resuls, acual eargs growh for he ex fve years s cluded each of he fuure soc reurs predco models ad resuls do o chage o repored. Cosse wh he fdgs Truema 993, he resuls Table 8 mply ha whe researchers measure he mare expecao of fuure eargs wh error ad hey do o corporae formao abou cross-secoal varao of he measureme error, spurous resuls ca arse he ess of a relao bewee eargs ad soc reurs, ad he framewor offered hs sudy helps o mgae relaed ssues. 6.6 Ou of sample ess for mproveme predcably of fuure eargs ad soc reurs 43 I her revew paper o he value relevace sudy, Holhouse ad Was quoes: If he amou s fraugh wh oo much measureme error, he researcher would o deec a sgfca relao.

30 To cofrm he resuls repored Table 6, he ou of sample ess for predcg fuure eargs are coduced accordg o he followg procedure: easureme error proxy s cosruced he same way as descrbed 6.. or each predco year, wo ypes of predco regressos are coduced usg he daa of daa years as Table 6, ael B. or each predco year, predced values are compued by mulplyg each depede varable by he respecve coeffce from sep for each of wo predco models. v ea absolue dfferece AD bewee he respecve predced values ad fuure eargs s compued for each model. AD deoes AD based o he predco model whou formao abou cross-secoal varao of he measureme error ad AD deoes AD based o he predco model wh formao abou crosssecoal varao of he measureme error. The resuls repored Table 9, ael A show ha AD s greaer ha AD for all years ad dffereces are sgfca a % level dfferece for he predco of oe year ahead acual eargs for 4 s sgfca a % level. To cofrm he resuls repored Table 8, he ou of sample ess for predcg fuure soc reurs are coduced based o he same procedure as hose for predcg fuure eargs. Table 9, ael B repors ha AD s geerally smaller ha AD wh some excepos. The resuls are weaer ha he predco of fuure eargs because he predco of fuure soc reurs would be affeced by more facors ha he predco of fuure eargs. I cocluso, he resuls Table 9 cofrm ha corporag formao abou crosssecoal varao of he measureme error mproves predcably of fuure eargs ad soc reurs.

31 Chaper 7 Robusess checs 7. Effec of eargs perssece ror research cludg reema ad Tse 99 ad Das ad Lev 993 documes he S-shaped relao.e. o lear relao bewee uexpeced eargs ad uexpeced soc reurs, argug ha hs fdg s due o eargs perssece ad large uexpeced eargs coas more rasory compoes ha are more heavly dscoued by he mare. Sce he measureme error proxy meproxy used hs sudy s cosruced based o he uexpeced eargs ha pror research uses as a proxy for eargs perssece, oe mgh h resuls hs sudy are drve by eargs perssece.e. rasory eargs raher ha he measureme error a osy predcor. To exame wheher hs s he case, wo ess are coduced. Al ad Zarow 99 repors ha uexpeced eargs coverge o eargs level raher ha eargs chages f eargs follow IA, process ad ed o be rasory. Ther fdg mples ha f he resuls are erely drve by eargs perssece.e. f qule ras hs sudy represe he degree of eargs perssece, cludg eargs level should duce a smlar level of eargs respose coeffces across qule ras. Alhough s o plausble o clude fuure eargs level forecasg models, hs sudy arfcally cludes he fuure eargs level o vesgae wheher he resuls are drve by eargs perssece. year acual eargs deflaed by soc prce a he ed of hrd moh from pror fscal year ed s used as a proxy for he fuure eargs level. As show Table, ael A, eargs respose coeffces are sll decreasg as he measureme error proxy meproxy creases. Sum of wo eargs respose coeffces are also decreasg. Al ad Zarow 99 also cofrms hs resul. Ths suggess ha measureme error effecs seem domag eargs perssece effecs. Soc reurs represe he chage mare s expecao o fuure eargs.e. dvded or cash flows. Therefore, f eargs are less persse, soc reurs ed o be more volale. To corol for eargs perssece, soc reurs volaly defed as he sadard devao of daly raw soc reurs for he predco perod s cluded all predco models. 44 Table, ael B repors ha he forecasg coeffces ad R s are sll decreasg as he measureme error proxy meproxy creases. Ths aga cofrms ha he measureme error s he ma drver of he resuls. Tess are also coduced wh eargs volaly ad eargs growh for ex fve years ad he resuls are qualavely smlar o repored. Resuls repored Table are cosse wh he fdg of Das ad Lev 994. They fd ha a o lear relao bewee uexpeced eargs ad uexpeced soc reurs sll exss eve afer specal ems are removed. 7. Effec of egave aalyss cosesus forecass ad sze 44 or 5 year soc reurs forecasg, sadard devao of daly raw soc reurs over he ex 5 years are cluded. or he res of he ess, sadard devaos of daly raw soc reurs over he ex year are cluded.

32 Resuls repored Table 6, 7 ad 8 reveal ha as he measureme error proxy meproxy becomes larger, aalyss cosesus forecass ed o be more egave. Therefore, o vesgae wheher he resuls repored Table 6, 7 ad 8 are drve by he egave aalyss cosesus forecass, he same aalyses are coduced oly wh he posve aalyss cosesus forecass. Resuls repored Table sugges ha he egave aalyss cosesus forecass are o a ma drver of he resuls preseed Table 6, 7 ad 8. Resuls repored Table 6, 7 ad 8 also reveal ha as he measureme error proxy meproxy becomes larger, a frm sze measured as he pror fscal year ed oal asses eds o be smaller. 45 oreover, eve afer he egave aalyss cosesus forecass are removed, he paer of a frm sze does o dsappear o repored. 46 To see wheher he frm sze accous for resuls, he whole ess are aga coduced wh he formao o frm sze corporaed. or hs ed, qule ras are formed based o he oal asses as of pror fscal year ed ad qule ras are scaled o be le bewee ad. The, he formao o he frm sze varably s corporaed as a eraco erm wh respecve predcors. To remove he effec of egave aalyss cosesus forecass, oly posve aalyss cosesus forecass are used. The resuls preseed Table sll show he sgfcaly egave eraco erms bewee respecve predcor ad qule ras based o he measureme error proxy meproxy all forecasg models alhough resuls become weaer. Ths mples ha frm sze s o a ma drver of he resuls. 7.3 Tess wh udeflaed measureme error Cheog ad Thomas repors ha aalyss forecas error ad dsperso do o vary wh he scale. To reflec hs fdg, all ess are repeaed wh he measureme error proxy meproxy based o udeflaed measureme error regressos ad he resuls are smlar excep for he year soc reurs forecasg. or year soc reurs forecasg, forecasg coeffce of ra s smaller ha ha of ra ad 3 o repored. 7.4 Tess wh deflaed eargs a purpose of ess repored Table 6 s o docume he evdece ha measureme error aalyss cosesus forecas has mplcaos forecasg udeflaed fuure perodc or permae eargs. ay pror sudes exame forecasably of fuure eargs based o he eargs deflaed by soc prce. To be cosse wh pror sudes, he same ess are coduced wh aalyss cosesus forecass, year acual eargs ad 5 year mea acual eargs scaled by soc prce a he ed of hrd moh afer fscal year ed. Resuls are qualavely smlar o he ess wh udeflaed eargs alhough resuls are weaer o repored. 45 Tes wh mare value a pror year fscal year ed produces smlar resuls. 46 eda oal asses as of pror fscal year ed for ra s abou 8m ad for ra 5 s abou 6m. 3

33 Chaper 8 Cocludg remars Usg aalyss cosesus forecass, hs sudy vesgaes mplcaos of measurg he mare expecao of fuure eargs wh error for predcg fuure eargs ad soc reurs. Wh he framewor ha esmaes cross-secoal varao of he measureme error aalyss cosesus forecass based o he errors--varables approach, hs sudy repors ha he measureme error aalyss cosesus forecass mpars he predcably of fuure eargs ad soc reurs ad causes ferece problems. Ths sudy also documes ha corporag formao abou cross-secoal varao of he measureme error ca geerae beer specfed predco models ad mproved predcos of fuure eargs ad soc reurs. The fdgs of hs sudy ca be readly exeded o oher accoug research ha reles o he mare expecao of fuure eargs. A fruful fuure research area exedg he resuls of hs sudy cludes fdg a mehod o corol for ex-pos eargs ews capurg he ex-ae measureme error aalyss cosesus forecass o geerae beer specfed predco models. Aoher suggesed research area s he es of he mare level predcably of fuure soc reurs based o eargs yeld. Some rece research cludg Ag ad Beaer 7 argues ha eargs yeld has lle or o predcve ably of fuure soc reurs The fdgs of hs sudy sugges ha he resuls of pror sudes may be due o he observaos ha measure he mare expecao of fuure eargs wh much error ad corporag formao abou crosssecoal varao of measureme error.e., less wegh s gve o he observaos wh large measureme error would brg dffere resuls. 47 Refer o Goyal ad Welch 3, Ag ad Beaer 7, Cochrae 8, Goyal ad Welch 7 ad Campbell ad Thomso 7 amog ohers. 48 I s fully recogzed ha he resuls of hs sudy are based o he frm specfc predcos ad he debae o he predcably of fuure soc reurs usg eargs yeld s maly based o he mare daa. However, f mare dex were re-cosruced by corporag formao abou cross-secoal varao of he measureme error, more sgfca ad meagful resuls should be oed. 4

34 Refereces Abarbaell, J., ad V. Berard. 99. Tess of aalyss overreaco/uderreaco o eargs formao as a explaao for aomalous soc prce behavor. The Joural of ace 47 5: 8-7. Abarbaell, S., W. Lae, ad R.Verreccha Aalyss' forecass as proxes for vesor belefs emprcal research. Joural of Accoug ad Ecoomcs, 7: 3-6. Al, A., A. Kle, ad J. Rosefeld. 99. Aalyss use of formao abou permae ad rasory eargs compoes forecasg aual ES. The Accoug Revew 67 : Al, A., ad. Zarow. 99. The role of eargs levels aual eargs-reurs sudes. Joural of Accoug Research 3 : Ag, A., ad G. Beaer. ay 7. Soc reur predcably: Is here? Revew of acal Sudes 3: Barro, O., O. Km, S. Lm, ad D. Seves Usg aalyss forecass o measure properes of aalyss formao evrome. The Accoug Revew 73 4: Barro, O.,. Saford, ad Y. Yog. 9. urher evdece of he relao bewee aalyss forecas dsperso ad soc reurs. Coemporary Accoug Research 6 : Barro, O., ad. Suere Dsperso aalyss eargs forecass as a measure of uceray. Joural of Accoug, Audg ad ace 3 3: Barh,., 99. Relave measureme errors amog alerave peso asse ad lably measures. The Accoug Revew Vol. 66, No. 3, Barov, E., S. Ly, ad R. Joshua.. Reurs-eargs regressos: A egraed approach. Worg aper, Cy Uversy of Hog Kog ad New Yor Uversy. Basu, S Ivesme performace of commo socs relao o her prce-eargs raos: A es of he effce mare hypohess. The Joural of ace 3 3: Beaver, W., R. Lamber, ad D. orse. 98. The formao coe of secury prces. Joural of Accoug ad Ecoomcs : 3-8. Beaver, W.,. cnchols, ad R. rce. 7. Delsg reurs ad her effec o accougbased mare aomales. Joural of Accoug ad Ecoomcs 43: Beesh,., ad C. Harvey easureme error ad oleary he eargs-reurs relaos. Revew of Quaave ace ad Accoug 3: Bolfare, H., A. Lemoe, ad A. eroa. 9. Improved maxmum lelhood esmaors a heerosedasc errors--varables model. Sascal apers 5 3: Brow, L Eargs forecasg research: Is mplcaos for capal mares research. Ieraoal Joural of orecasg 9: Brow, L., R. Hagerma,. Grff, ad. Zmjews A evaluao of alerave proxes for he mare s assessme of uexpeced eargs. Joural of Accoug ad Ecoomcs 9: Burgsahler, D., ad E. Chu.. Eargs precso ad he relao bewee eargs ad reurs. Worg aper, ad Uversy of Souher Calfora ad Uversy of Washgo a Seale. Campbell, Y., ad S. Thompso. 8. redcg excess soc reurs ou of sample: Ca ayhg bea he hsorcal average? Revew of acal Sudes 4: Cheg, C., W. Hopwood, ad J. ckeow. 99. No-leary ad specfcao problems uexpeced eargs respose regresso model. The Accoug Revew 67 3:

35 Cheg, C., ad J. Ru. 6. O esmag lear relaoshps whe boh varables are subjec o heeroscedasc measureme errors. Techomercs 48 4: Cheog,., ad J. Thomas.. Why do ES forecas error ad dsperso o vary wh scale? Implcaos for aalys ad maageral behavor. Worg aper, Rugers Uversy ad Yale Uversy. Cleme,., ad S. Tse. 3. Do vesors respod o aalyss forecas revso as f forecas accuracy s all ha maers? The Accoug Revew 78 : Cochrae, H. 8. The dog ha dd o bar: A defese of reur predcably. Revew of acal Sudes 4: Cohe, D., R. Ha, ad. Ogeva. 7. Aoher loo a GAA versus he Sree: a emprcal assessme of measureme error bas. Revew of Accoug Sudes : Colls, D., S.. Kohar, J. Shae, ad R. Sloa Lac of meless ad ose as explaao for he low coemporaeous reur-eargs assocao. Joural of Accoug ad Ecoomcs 8: Das, S., ad B. Lev Noleary he reurs-eargs relao: Tess of alerave specfcaos ad explaaos. Coemporary Accoug Research : Das, S., C. Leve, ad K. Svaramarsha Eargs predcably ad bas aalyss eargs forecass. The Accoug Revew 73 : Dechow,., A. Huo, ad R. Sloa A emprcal assessme of he resdual come valuao model. Joural of Accoug ad Ecoomcs 6: -34. Dchev, I., ad V. Tag. 9. Eargs volaly ad eargs predcably. Joural of Accoug ad Ecoomcs 47: 6-8. Deher, K., C. alloy, ad A. Scherba.. Dffereces of opo ad he cross seco of soc reurs. The Joural of ace 57 5: 3-4. Easo,. 7. Esmag he cos of capal mpled by mare prces ad accoug daa. oudaos ad Treds Accoug 4: Easo,., ad S. oaha. 5. A evaluao of accoug-based measures of expeced reurs. The Accoug Revew 8 : Easo,., ad G. Sommers. 7. Effec of aalyss opmsm o esmaes of he expeced rae of reur mpled by eargs forecass. Joural of Accoug Research 45 5: Elgers,., ad. Lo Reducos aalyss aual eargs forecas errors usg formao pror eargs ad secury reurs. Joural of Accoug Research 3 : ama, E. 99. Effce capal mares: II. The Joural of ace 46 5: ama, E., ad K. rech Dvded yelds ad expeced soc reurs. Joural of acal Ecoomcs : 3-5. rael, R., ad C. Lee Accoug valuao, mare expecao, ad cross-secoal soc reurs. Joural of Accoug ad Ecoomcs 5: rael, R., ad L. Lov. 9. Eargs perssece. Joural of Accoug ad Ecoomcs 47: 8-9. reema, R., ad S. Tse. 99. A olear model of secury prce resposes o uexpeced eargs. Joural of Accoug Research 3 : red, D., ad D. Gvoly. 98. acal aalyss forecass of eargs: A beer surrogae for mare expecaos. Joural of Accoug ad Ecoomcs 4:

36 Gasbarra, D., S. B. Kulahal, ad K. Kuulasmaa.. Esmao of a errors--varables regresso model whe he varaces of he measureme errors vary bewee he observaos. Sascs edce 8: 89-. Gode, D., ad. oharam. 8. Improvg he relaoshp bewee mpled cos of capal ad realzed reurs by removg predcable aalys forecas errors. Worg aper, New Yor Uversy. Goyal, A., ad I. Welch. 3. redcg he equy premum wh dvded raos. aageme Scece 49 5: Greee, W. 3. Ecoomerc aalyss. rece Hall 5h Edo. Guay, W., S.. Kohar, ad S. Shu. 5. roperes of mpled cos of capal usg aalyss forecass. Worg aper, assachuses Isue of Techology. Holhause, R., ad R. Was.. The relevace of he value-relevace leraure for facal accoug sadard seg. Joural of Accoug ad Ecoomcs 3: Hughes, J., J. Lu, ad W. Su. 8. O he relao bewee predcable mare reurs ad predcable aalys forecas errors. Revew of Accoug Sudes -3: Imhoff, E., ad G. Lobo. 99. The effec of ex ae eargs uceray o eargs respose coeffces. The Accoug Revew 67 : Jag, G., C. Lee, ad Y. Zhag. 5. Iformao uceray ad expeced reurs. Revew of Accoug Sudes : 85-. Key, W., D. Burgsahler, ad R. ar.. Eargs surprse maeraly as measured by soc reurs. Joural of Accoug Research 4 5: Kormed, R., ad R. Lpe Eargs ovaos, eargs perssece, ad soc reurs. Joural of Busess 6 3: Kohar, S... Capal mares research accoug. Joural of Accoug ad Ecoomcs 3: 5-3. Kohar, S.., ad J. Shae Boo-o-mare, dvded yeld, ad expeced mare reurs: A me-seres aalyss. Joural of acal Ecoomcs 44 : Kohar, S.., ad R. Sloa. 99. Iformao prces abou fuure eargs: Implcaos for eargs respose coeffces. Joural of Accoug ad Ecoomcs 5: Kohar, S.., ad J. Zmmerma rce ad reur models. Joural of Accoug ad Ecoomcs : Kormed, R. ad Lpe, R., 987. Eargs Iovaos, Eargs erssece, ad Soc Reurs. Joural of Busess Vol. 6, No. 3, Lamo, O Eargs ad expeced reurs. The Joural of ace 53 5: Lewelle, J., ad J. Shae.. Learg, asse-prcg ess, ad mare effcecy. The Joural of ace 57 3: Lu, J., ad J. Thomas.. Soc reurs ad accoug eargs. Joural of Accoug Research 38 : 7-. achuga, S.. Use of uller s echque o reduce measureme error he reurs/eargs assocao. Revew of Quaave ace ad Accoug 4: addala, G.. Iroduco o ecoomercs. Wley 3rd Edo. edehall, R. 99. Evdece o he possble uderweghg of eargs-relaed formao. Joural of Accoug Research 9 : O Bre, Aalyss forecass as eargs expecaos. Joural of Accoug ad Ecoomcs :

37 Rchardso, S., Sloa, R. Solma,. ad Tua, I. 5. Accrual Relably, Eargs erssece ad Soc rces. Joural of Accoug ad Ecoomcs Vol. 39, Rya, S., ad. Zarow O he ably of he classcal errors varables approach o expla eargs respose coeffces ad R s alerave valuao models. Joural of Accoug, Audg ad ace : Sheffr, S Raoal expecaos. Cambrdge Uversy ress d Edo. Shumway, T The delsg bas CRS daa. The Joural of ace 5 : Shumway, T. ad V. Warher The delsg bas CRS s Nasdaq daa ad s mplcaos for he sze effec. The Joural of ace 54 6: Subramayam, K Ucera precso ad prce reacos o formao. The Accoug Revew 7 : 7-9. Truema, B Aalys forecass ad herdg behavor. Revew of acal Sudes 7 : Welch, I., ad A. Goyal. 8. A comprehesve loo a he emprcal performace of equy premum predco. Revew of acal Sudes 4: Wooldrdge, J.. Ecoomerc aalyss of cross seco ad pael daa. The IT ress. Wooldrdge, J. 6. Iroducory ecoomercs: A moder approach. Thomso Souh-Weser 3rd Edo. Yeug,. 9. Uceray ad expecao revsos afer eargs aouceme. Coemporary Accoug Research 6 : Zhag, X.. 6. Iformao uceray ad soc reurs. The Joural of ace 6 :

38 gure. Illusrao of sources of error measurg mare expecao of fuure eargs are expecao of fuure eargs Case Correc ad raoal forecas by each aalys Aalys Aalys Aalys 3 Aalys 4 Aalyss cosesus forecas Case Nosy forecas by each aalys Opmsc bas 9 Saleess 8 Iably 8 Herdg 9 Dsperso.4 Eargs ews Acual eargs Ths fgure llusraes a suao where he aalyss cosesus forecas measures he mare expecao of fuure eargs wh error. Ths fgure also shows how he fuure acual eargs become dffere from he mare expecao of fuure eargs. Noe: I s possble ha aalyss cosesus forecass happe o cocde wh he mare expecao of fuure eargs alhough each aalys s forecas measures he mare expecao of fuure eargs wh error. However, hs s o lely he case for mos of he frms covered by may aalyss. 9

39 gure. Tmele of predco of oe year ahead acual eargs where A : Acual eargs a me + : are expecao a me of acual eargs a me + : Aalyss cosesus forecas a me for acual eargs a me + e : easureme error aalyss cosesus forecas a me. : Eargs ews durg me + 3

40 gure 3. Tmele of predco of oe year fuure soc reurs where Re : Oe year fuure soc reurs : Soc prce a me : are expecao a me of acual eargs a me + : Aalyss cosesus forecas a me for acual eargs a me + e : easureme error aalyss cosesus forecas a me : Eargs ews durg me +. 3

41 gure 4. aer of coeffce esmaes ad R s e / x * whe all observaos coa measureme error gure 4A. aer of Coeffce Esmaes e / x * gure 4B. aer of R e / x * gure 4 shows he paer of he coeffce esmaes ad R s from he predco model below as he relave measureme error varace e o he varace of he rue predcor creases. y EIV x w 3

42 gure 5. aer of coeffce esmaes ad R s e / x * whe half of observaos are measured wh error ad observaos wh measureme error are defed wh dcaor varable gure 5A. aer of Coeffce Esmaes e / x * gure 5B. aer of R e / x * gure 5 shows he paer of he coeffce esmaes ad R s from he predco models below as he relave measureme error varace e o he varace of he rue predcor creases.. y EIV x w. y x D 3xD where D = whe observaos coa measureme error or hs aalyss, he half of he observaos s assumed o be measured wh error. The frs predco model does o use ay measureme error dcaor. The frs predco model assumes he suao where he observaos wh he measureme error cao be defed. The secod predco model uses he dcaor for he observaos ha coa he measureme error. The secod predco model assumes he suao where he observaos wh he measureme error ca be dsgushed from hose whou measureme error. 33

43 gure 6. aer of coeffce esmaes ad R s e / x * whe sample cosss of four groups wh dscve measureme error dsrbuo ad observaos wh each dscve measureme error dsrbuo are defed wh respecve dcaor varable gure 6A. aer of Coeffce Esmaes e / x * gure 6B. aer of R e / x * gure 6 shows he paer of he coeffce esmaes ad R s from he predco models below as he relave measureme error varace of he secod group e o he varace of he rue predcor creases. or hs aalyss, he sample cosss of four groups wh equal umber of observaos. The frs group of observaos coas o measureme error. The secod group of observaos coas he measureme error wh zero mea ad varace of e. The hrd group of observaos coas he measureme error wh zero mea ad varace of 4e. The las group of observaos coas he measureme error wh zero mea ad varace of 9e. 34