15-02 Data vintage in testing properties of expectations

Transcription

1 Insiue of Economerics Warsaw School of Economics (SGH) ul. Madalińskiego 6/8, 02-5 Warsaw, oland A L I E D E C O N O M E T R I C S A E R S ISSN Daa vinage in esing properies of expecaions Emilia Tomczyk Warsaw School of Economics December 205 This paper is available a he Warsaw School of Economics (SGH), Insiue of Economerics websie a: This aricle has been submied for publicaion in The Quaniaive Mehods in Economics journal of he Warsaw Universiy of Life Sciences (SGGW). 0

2 Daa vinage in esing properies of expecaions Emilia Tomczyk Insiue of Economerics, Warsaw School of Economics Absrac In his paper, resuls of quanificaion procedures and properies of expecaions series obained for wo daa vinages are described. Volume index of producion sold in manufacuring is defined for end-of-sample and real ime daa, and evaluaed agains expecaions expressed in business endency surveys. Empirical analysis confirms ha while here are only minor differences in quanificaion resuls wih respec o daa vinage, properies of expecaions ime series obained on heir basis do diverge. Specifically, here exiss a coinegraing regression for one of he vinages only, ha is, end-of-sample daa. In his case, expecaions and observed changes in indusrial producion exhibi similar long-run properies. Neiher of he expecaions series, however, consiues predicion of changes in producion ha is unbiased or employs available informaion efficienly. Keywords: end-of-sample () daa, real ime () daa, daa revisions, quanificaion procedures, expecaions, unbiasedness, orhogonaliy JEL: C82, C8, D84

3 . Inroducion Tesing properies of economic expecaions series consiues a challenge for many reasons, among hem hose relaed o observing and measuring expecaions, reliabiliy of survey daa, and selecion of appropriae saisic and economeric mehods for he purposes of empirical analysis. In his paper, I propose o address one of he issues relaed o qualiy of daa employed o describe and evaluae expecaions processes, ha is, he subjec of daa revisions and daa vinages. Daa revision is defined as an adjusmen inroduced afer iniial announcemen had been published. End-of-sample () daa is usually described, following Koenig e al. (200), as daa provided in he mos recen announcemen. Real ime values () are iniial numbers, available o economic agens in real ime and (frequenly) subjec o revisions. The dae when a paricular daase was made available is ermed vinage of ha daa series. For deails on definiions and classificaions concerning daa revisions, see Tomczyk (20). As far as I am aware, he exen of daa revisions in oland and heir impac on predicive properies of ime series have been addressed in a single paper only (see Syczewska, 20). General lieraure peraining o daa revisions and heir influence on qualiy of forecass or properies of expecaions ime series is also limied. There is a coninuing (if somewha slowmoving) debae on wheher ess of expecaions should be based on iniial or revised daa (see Zarnowiz, 985; Keane and Runkle, 990; Croushore and Sark, 200, Mehra, 2002). Recen economeric analyses on impac of daa revisions on forecas qualiy include Croushore (20, 202) and Arnold (20). There remain many open quesions concerning appropriae daa vinage for scaling qualiaive survey daa, measuring accuracy of expecaions wih respec o observed values, or esing properies of expecaions ime series. In my previous papers (Tomczyk, 20, 204), review of lieraure and daabases relaed o economic daa revisions, reasons for inroducing adjusmens o already published economic daa, axonomy of revisions, and comparison of quanificaion resuls for iniial and revised daa on producion volume index in oland are presened. In his paper, I coninue his line of research by updaing resuls on quanificaion procedures and esing properies of expecaions obained for wo disincive daa vinages: end-of-sample () and real ime (). 2

4 2. Descripion of daa Analyses of indusrial producion are ypically based on volume index of producion sold in manufacuring provided by he Cenral Saisical Office (CSO). In oland, sysemaic daa revisions in he pas wo decades were due o changes in he base period for he index in 2004, 2009 and 20. In January 20, value of reference has been se as he average monhly indusrial producion of 200. To exend he sample, observaions daing back o January 2005 were recalculaed o be consisen wih he 200 base. Apar from sysemaic revisions reflecing updaes of he base period, frequen correcions of las monh s value of producion index is eviden in CSO daa. Table presens srucure of revisions in volume index of indusrial producion sold for he period of January 2005 November 204 (ha is, 9 observaions). Table. Direcion of revisions in volume index of indusrial producion Direcion of revision ercenage in sample Mean size of revision (in absolue values) Iniial value larger han final value 26% 0.20 Iniial value smaller han final value 4% 0.5 No revision % -- Source: own calculaions Resuls repored in Table sugges ha revisions in volume index of indusrial producion sold may no be unbiased as upward correcions (ha is, from lower iniial value o higher final value) are more frequen han he reverse adjusmens. Size of revisions, however, appears small: on average 0.20 of a percenage poin in case of overesimaion, and 0.5 of a percenage poin in case of underesimaion of final values. To evaluae properies of expecaions colleced hrough qualiaive business endency surveys, quanificaion of survey daa is necessary. In his paper, longer daa series is used han in an earlier paper (Tomczyk, 204), and an addiional issue is addressed: ha no only dependen variables in quanificaion models (ha is, CSO daa on volume index of indusrial producion) are subjec o revisions, bu so are explanaory variables (ha is, qualiaive daa on expecaions and assessmens of changes in economic variables). I would like o hank Mr Konrad Walczyk, hd (Research Insiue for Economic Developmen, Warsaw School of Economics) for his assisance wih compiling he daase.

5 Expecaions and subjecive assessmens of changes in producion are colleced by he Research Insiue for Economic Developmen (RIED, Warsaw School of Economics) hrough monhly business endency surveys. The survey comprises eigh quesions designed o evaluae boh curren siuaion (as compared o las monh) and expecaions for he nex 4 monhs by assigning hem o one of hree caegories: increase / improvemen, no change, or decrease / decline. revious sudies based on RIED survey daa show ha expecaions series defined for hree- and four-monh horizons exhibi only minor differences, wih a sligh superioriy of he hree-monh forecas horizon. Le us define he following: A percenage of respondens who observed increase beween and, 2 A percenage of respondens who observed no change beween and, A percenage of respondens who observed decrease beween and, percenage of respondens who expec increase beween and +, 2 percenage of respondens who expec no change beween and +, percenage of respondens who expec decrease beween and +. Balance saisics calculaed for observed changes: and for expecaions: BA A A B remain he simples mehod of quanificaion ha is, of convering qualiaive business survey daa ino quaniaive ime series. More sophisicaed procedures can be grouped ino probabilisic and regressive quanificaion mehods (for a concise review of basic quanificaion mehods and heir modificaions, see esaran, 989). In secion, wo versions of regression mehod are used o compare real ime and end-of-sample daa vinages. RIED business survey daa is also subjec o revisions. rior o 202 revisions were sporadic: jus a single one in 200 (in April) and anoher in 20 (in Ocober). From 202 on, adjusmens become frequen. In 5 monhs beween January 202 and November 204, balance saisics for assessmens of changes in producion has been revised a oal of 9 imes. In welve cases, correcions were posiive (ha is, final number was larger han iniial esimae by, on average, 0.64 of a percenage poin). In seven cases, final number was smaller han iniial esimae by, on average, 0.5 of a percenage poin. 4

6 Le us employ he following noaion: end-of-sample values will be marked wih superscrip (for example, A ), and real ime values wih superscrip (for example, A ). In he nex secion, boh real ime and end-of-sample daa is used in regression quanificaion models.. Quanificaion models Quanificaion procedures involve scaling qualiaive survey daa in a manner consisen wih observed quaniaive values, usually provided by governmen agencies ha is, widely available and officially endorsed daa. In my earlier paper (Tomczyk 20) I suggesed ha for quanificaion purposes, survey daa should be compared wih final () daa raher han values available in real ime because respondens are probably aiming o describe heir final assessmens and predicions raher han iniial esimaes subjec o revisions. Iniial aemp o es his proposiion (Tomczyk 204) has shown ha end-of-sample daa does indeed appear beer suied o quanificaion of RIED business endency survey daa on volume index of indusrial producion. However, his conclusion was of limied reliabiliy as none of he quanificaion models exhibied saisically saisfacory esimaion resuls. In his paper, I employ wo versions of he regression mehod, inroduced by O. Anderson (952) and D. G. Thomas (995), respecively. In Anderson s model, he following equaion is esimaed: y A A, () where y describes relaive change in value of variable y published by a saisical agency beween and, and is a whie noise error erm. arameers α and β are hen esimaed by OLS, and on he assumpion ha he same relaionship holds for expecaions repored in surveys, quaniaive measure of expecaions is consruced on he basis of he following equaion: 5 y, (2) where ˆ and ˆ are OLS esimaes of () and reflec average change in dependen variable y for respondens expecing, respecively, increase and decrease of dependen variable. In 995, D. G. Thomas offered a modificaion of he basic Anderson model o accoun for he special case in which normal or ypical siuaion ha respondens compare heir curren

7 circumsances o is subjec o a growh rae, making observing (or predicing) decreases in dependen variable more essenial han increases: 6 y A, () where < 0, consan γ is inerpreed as ypical growh rae, and is a whie noise error erm. Thomas quaniaive measure of expecaions is given by he formula y, (4) where ˆ and are OLS esimaes obained on he basis of (). For he purpose of comparing daa vinages, dependen and explanaory variables in quanificaion models () and () may be based on eiher or daa. In case of real ime daa, dependen variable in regression quanificaion models (ha is, changes in volume of indusrial producion) is ypically defined on he basis of volume index of indusrial producion sold available in real ime, I : I, (5) I Variable ( 00 ) is inerpreed as percenage change in volume of indusrial producion, available in real ime, as compared o las monh. For end-of-sample () daa, dependen variable in regression quanificaion models is defined on he basis of he final available announcemen of volume index of indusrial producion sold, I : I, (6) I However, previous research (Tomczyk 204) shows ha quanificaion models esimaed wih dependen variables defined by (5) and (6) exhibi unsaisfacory saisical properies. Exending he sample did no improve heir qualiy: deerminaion coefficiens for Anderson s and Thomas models esimaed on he basis of and daa range beween 0.02 and 0.06, and explanaory variables are generally no saisically significan. Exremely low values of a sandard measure of fi coupled wih insignificance of explanaory variables sugges ha business endency survey respondens do no consider heir variable of ineres o be similar o (5) or (6). I seems likely, however, ha respondens evaluae curren changes in producion agains recen averages, and one quarer appears a plausible observaion horizon. Le us define AV I (7) I s s

8 for real ime daa and AV I (8) I s s for end-of-sample daa. Formulas (7) and (8) reflec changes in volume of indusrial producion sold as compared o he average calculaed on he basis of las hree monhs, for real ime and end-of-sample daa. Tables 2 and presen resuls of quanificaion procedures obained for wo daa vinages: and. All quanificaion models are esimaed by OLS wih HAC sandard errors ha is, Newey-Wes heeroskedasiciy and serial correlaion consisen esimaors o accoun for possible serial correlaion and unsable variance of he error erm (due o ineria in processes describing behaviour of macroeconomic variables and probable learning paerns imbedded in expecaions formaion processes). All models are esimaed on sample from April 2005 ill November 204 (n = 6). Esimaed equaions ake he following form: AV Anderson s model for real ime daa:.288 A A Anderson s model for end-of-sample daa: Thomas model for real ime daa: Thomas model for end-of-sample daa: AV AV AV A A A A Esimaion resuls are summarized in Tables 2 and, and presened in more deail in Appendix (Anderson model) and Appendix 2 (Thomas model). Table 2. Anderson s model () wih HAC sandard errors Real ime daa End-of-sample daa cenered R AIC RESET p-value Source: own calculaions 7

9 Table. Thomas model () wih HAC sandard errors Real ime daa End-of-sample daa R AIC RESET p-value Source: own calculaions Inerpreaion of resuls for example, esimaes obained hrough Anderson s model () wih end-of-sample dependen variable AV is he following: for respondens ha wihin las monh noed increase in producion in comparison o he -monh average, ha increase amouned o approximaely 29%. For respondens ha wihin las monh noed decline in producion in comparison o he -monh average, decrease was equal o abou 25%. All he remaining parameer esimaes presened in Tables 2 and are similarly inerpreed. For boh daa vinages and boh quanificaion models, all esimaed parameers exhibi correc signs and are differen from zero a 0.0 significance level. RESET es allows o accep funcional form of all quanificaion models as adequae, and coefficiens of deerminaion of he models are accepable. To find basis for selecing eiher Anderson s or Thomas models for furher analysis, le us noe ha correlaion coefficiens beween explanaory variables in Anderson s equaions, boh based on and daa, are equal o approximaely High degree of mulicollineariy in Anderson s models allow o selec Thomas equaions as more reliable. Resuls presened in Tables and 4 do no confirm he preliminary hypohesis ha final () daases are beer suied o modeling assessmens of survey respondens. Models esimaed for wo daa vinages are very similar, boh from saisical poin of view and aking ino accoun heir economic inerpreaion. To summarize, comparison of regression quanificaion models across daa vinages does no provide immediae recommendaions as o wheher or daa should be used in quanificaion procedures. In secion 4, analysis is coninued wih expecaions series consruced on he basis of he wo daa vinages. 4. Tess of properies of expecaions 8

10 In his secion, unbiasedness and weak-form orhogonaliy of expecaions are esed. These properies are ypically verified wihin he framework of Raional Expecaions Hypohesis, and have been previously analyzed for olish business survey respondens (see Tomczyk, 20 for review of lieraure). Noneheless, ess of raionaliy of expecaions in oland have failed o provide conclusive resuls. Wheher expecaions on producion, prices, employmen and general business condiions can be considered raional or no depends on various facors, including sample size, frequency of available daa, empirical mehods employed, and ype of variables included in he analysis. No consisen resuls on raionaliy (or, more precisely, is fundamenal componens: unbiasedness and orhogonaliy of expecaions errors o widely available informaion) emerge from he lieraure. Nardo (200) gives one likely reason for his impasse: The presence of measuremen error in he quanified daa is cerainly refleced in he general disappoining performance of he sandard ess of raionaliy in he applied lieraure. (p. 658) In his secion, anoher possible reason relaed o daa qualiy in addressed, ha is, he issue of selecing appropriae daa vinage for empirical analysis of expecaions ime series. On he basis of esimaion resuls repored in Table (ha is, Thomas quanificaion model), expecaion series for boh daa vinages have been consruced. I is assumed ha onemonh observed changes and hree-monh expeced changes in producion are described by he same regression parameers. This simplificaion consiues a subsanial weakness of regression mehod, shared by all commonly used quanificaion mehods. I canno be esed, however, on he basis of daase available from he RIED business endency survey as deailed daa on individual survey respondens would be required for his purpose. Two expecaions ime series have been consruced, ha is: for real ime daa and E (9) E (0) for end-of-sample daa. As menioned in commens o Tables 2 and, esimaed coefficiens are very similar for boh daa vinages and so far do no imply ha here are significan differences in properies of expecaions ime series consruced on he basis of or daa. To es for unbiasedness, I employ procedure based on uni roo ess of expecaions and corresponding observed ime series (see Liu, Maddala, 992; Maddala, Kim, 998; Da 9

11 Silva Lopes, 998) which has been exensively used in empirical ess of raionaliy of expecaions. Resuls of he Augmened Dickey-Fuller es of nonsaionariy of expecaions series ( E, E ) and observed changes in indusrial producion ( AV, AV ) are presened in Table 5. All es equaions have been esimaed wih a consan and maximum lag se o 2 on he basis of he modified AIC crierion. Deailed resuls are repored in Appendix. Table 5. Resuls (p-values) of ADF es for expecaions and observed producion series Expecaions series Observed variable Levels Firs differences Degree of inegraion E I() AV I() Expecaions series Observed variable E I() AV I() Source: own calculaions I is clear from Table 5 ha all series are inegraed of order one. reliminary condiion for expecaions series being unbiased predicors of observed series is herefore me, and subsequen condiions may be esed: wheher expecaions and realized changes in producion are coinegraed, and wheher he coinegraing parameer is equal o (see Da Silva Lopes, 998). The following equaions are herefore esimaed: and AV E AV 2 2 E 2 (), (2) in which explanaory variables have been lagged hree monhs o accoun for he -monh forecas horizon used in RIED business endency surveys. Models have been esimaed by OLS wih HAC sandard errors. Resuls of he ADF es for residuals in models for boh daa vinages, and of he es of linear resricion reflecing he posulaed coinegraing vecor, are presened in Table 6; deailed resuls are repored in Appendix 4. 20

12 Table 6. Coinegraing regressions p-value for ADF es of residuals Real ime daa p = 0.56 End-of-sample daa p = Source: own calculaions p-value for resricion H 0: µ = in () p = H 0: µ 2 = in (2) p = In case of real ime daa, null hypohesis of nonsaionariy of he residuals in equaion () canno be rejeced, ha is, expecaions and corresponding observed changes in producion are no coinegraed. For end-of-sample daa, however, null hypohesis is rejeced a every ypical significance level. I follows ha expecaions and observed changes in producion are in fac coinegraed for series based on he end-of-sample daa. Ye, he null hypohesis of coinegraing parameer being equal o one is rejeced, and consequenly neiher of he daa vinages lead o unbiased expecaions of changes in producion. To summarize: here is a noable difference beween and daa vinages: a coinegraing relaion exiss only for daa. In his case, here is a sable linear combinaion (ha is, expecaions and observed series do no diverge in he long run) bu i does no suppor he hypohesis of unbiasedness of expecaions. Unbiasedness ess are considered o be very sensiive o measuremen errors and are ofen supplemened wih ess of orhogonaliy (someimes also called informaional efficiency) of expecaions errors wih respec o freely available informaion (see esaran, 989; Da Silva Lopes, 998). Tess of orhogonaliy are classified as weak, when informaion se includes only lagged values of variable being forecased, or srong, when he informaion se conains addiional exogenous variables. I propose o es weak-form orhogonaliy of expecaions errors wih respec o producion volume daa lagged up o hree monhs. I believe ha his ses he upper limi on informaion se of business endency survey respondens who are no professional forecasers. The orhogonaliy hypohesis for daa may be herefore wrien as follows: H0: κ = κ2 = κ = 0 where AV AV AV AV E and for end-of-sample daa as 2, ()

13 where H0: ω = ω 2 = ω = 0 AV AV AV AV E (4) Equaions () and (4) have been esimaed by OLS wih HAC sandard errors. Since hree lagged variables are used and herefore mulicollineariy of explanaory variables may pose a problem, Variance Inflaion Facors are also verified, and found o be equal o.8.22 and o indicae absence of serious mulicollineariy. Resuls of orhogonaliy ess are presened in Table 7; esimaion deails are repored in Appendix 5. Table 7. Resuls of orhogonaliy ess p-value for resricion Real ime daa H 0: κ = κ 2 = κ = 0 in () p = End-of-sample daa H 0: ω = ω 2 = ω = 0 in (4) p = Source: own calculaions From Table 7 i is clear ha he null hypohesis of insignificance of explanaory variables is rejeced. Expecaion errors are herefore no orhogonal o easily available informaion on changes in producion index. I follows ha RIED business endency survey respondens do no efficienly make use of available daa, and from deailed resuls repored in Appendix 5 i is eviden ha second and hird lags of explanaory variables AV and AV are saisically significan. I seems ha when forming heir expecaions peraining o volume of indusrial producion, business endency survey respondens do no ake daa older ha one monh ino accoun. 4. Conclusions and direcions for fuure research In his paper, resuls of quanificaion procedures and properies of expecaions series obained for wo daa vinages are described. Empirical analysis confirms ha while here are only minor differences in quanificaion resuls wih respec o daa vinage, properies of expecaions ime series obained on heir basis do diverge. Specifically, here exiss 22

14 a coinegraing regression for one of he vinages only, ha is, end-of-sample daa. In his case, expecaions and observed changes in indusrial producion exhibi similar long-run properies. Neiher of he expecaions series, however, consiues predicion of changes in producion ha is unbiased or employs available informaion efficienly. The research projec on impac of daa vinage on properies of expecaions is coninued wih he following poins considered for furher analysis: use of oher business endency survey series o scale Cenral Saisical Office daa, exending he es of orhogonaliy o include addiional variables in he informaion se of survey respondens, describing and evaluaing exen of daa revisions in Research Insiue for Economic Developmen business endency survey daa. Empirical sudies of impac of daa revisions on expecaions promise o assis economiss in drawing more general conclusions on behavior and properies of expecaions series, including predicive qualiy, unbiasedness and efficien use of available informaion. Based on analysis presened in his paper, daa vinage does maer in deermining basic properies of expecaions ime series. 2

15 5. References Anderson O. (952) The business es of he IFO-Insiue for Economic Research, Munich, and is heoreical model, Revue de l Insiu Inernaional de Saisique 20: 7 Arnold E. A. (20) The role of revisions and disagreemen in professional forecass, Naional Bank of oland Working aper No. 5, Warsaw 20 Croushore D. (20). Froniers of real-ime daa analysis, Journal of Economic Lieraure 49:72-00 Croushore D. (202) Forecas bias in wo dimensions, Federal Reserve Bank of hiladelphia Working aper No. 2-9 Croushore D., Sark T. (200) A real-ime daa se for macroeconomiss, Journal of Economerics 05:-0 Da Silva Lopes A. C. B. (998) On he resriced coinegraion es as a es of he raional expecaions hypohesis, Applied Economics 0: Keane M.., Runkle D. E. (990) Tesing he raionaliy of price forecass: new evidence from panel daa, American Economic Review 80:74-75 Koenig E. F., Dolmas S., iger J. (200) The use and abuse of real-ime daa in economic forecasing, The Review of Economic and Saisics 85: Liu. C., Maddala G. S. (992) Raionaliy of survey daa and ess for marke efficiency in he foreign exchange markes, Journal of Inernaional Money and Finance :66 8 Maddala G. S., Kim I.-M. (998) Uni Roos, Coinegraion, and Srucural Change, Cambridge Universiy ress, Cambridge Mehra Y.. (2002) Survey Measures of Expeced Inflaion: Revisiing he Issues of redicive Conen and Raionaliy, Federal Reserve Bank of Richmond Economic Quarerly, Vol. 88/ Nardo M. (200) The quanificaion of qualiaive survey daa: A criical assessmen, Journal of Economic Surveys 7: Orphanides A. (200) Moneary policy rules based on realime daa, American Economic Review 9: esaran M. H. (989) The Limis o Raional Expecaions, Basil Blackwell, Oxford Syczewska E. M. (20) Wpływ akualizacji danych makroekonomicznych bazy AMECO na dokładność prognoz [Influence of updaes in AMECO macroeconomic daabase on forecas accuracy], Badania Sauowe nr KAE/S/07/, KAE SGH, Warszawa Thomas D. G. (995) Oupu expecaions wihin manufacuring indusry, Applied Economics 27: Tomczyk E. (20) Oczekiwania w ekonomii. Idea, pomiar, analiza [Expecaions in Economics. Definiions, Measuremen, Analysis], Oficyna Wydawnicza SGH, Warszawa Tomczyk E. (20) End-of-sample vs. real ime daa: perspecives for analysis of expecaions, in: K. Walczyk (ed.) Expecaions and Forecasing, race i Maeriały Insyuu Rozwoju Gospodarczego SGH No 9, Warsaw School of Economics, p Tomczyk E. (204) Influence of daa vinage on quanificaion of expecaions, Applied Economerics apers No 4-04 Zarnowiz V. (985) Recen Work on Business Cycles in Hisorical erspecive: Review of Theories and Evidence, NBER Working aper No

16 Appendix. Esimaion resuls: Anderson s model Dependen variable: AV OLS, using observaions 2005:04-204: (T = 6) HAC sandard errors, bandwidh (Barle kernel) Coefficien Sd. Error -raio p-value < *** A A *** Mean dependen var S.D. dependen var Sum squared resid S.E. of regression R-squared Adjused R-squared F(2, 4) value(f) 6.47e- Log-likelihood Akaike crierion RESET es for specificaion Tes saisic: F(2, 2) =.056 wih p-value = (F(2, 2) >.056) = Dependen variable: AV OLS, using observaions 2005:04-204: (T = 6) HAC sandard errors, bandwidh (Barle kernel) Coefficien Sd. Error -raio p-value < *** A A *** Mean dependen var S.D. dependen var Sum squared resid S.E. of regression R-squared Adjused R-squared F(2, 4) value(f) 4.77e- Log-likelihood Akaike crierion RESET es for specificaion Tes saisic: F(2, 2) = wih p-value = (F(2, 2) > ) =

17 Appendix 2. Esimaion resuls: Thomas model Dependen variable: AV OLS, using observaions 2005:04-204: (T = 6) HAC sandard errors, bandwidh (Barle kernel) Coefficien Sd. Error -raio p-value cons < *** *** A Mean dependen var S.D. dependen var Sum squared resid S.E. of regression R-squared Adjused R-squared F(, 4) value(f) Log-likelihood Akaike crierion RESET es for specificaion Tes saisic: F(2, 2) = wih p-value = (F(2, 2) > ) = Dependen variable: AV OLS, using observaions 2005:04-204: (T = 6) HAC sandard errors, bandwidh (Barle kernel) Coefficien Sd. Error -raio p-value cons < *** *** A Mean dependen var S.D. dependen var Sum squared resid S.E. of regression R-squared Adjused R-squared F(, 4) value(f) Log-likelihood Akaike crierion RESET es for specificaion Tes saisic: F(2, 2) = wih p-value = (F(2, 2) > ) =

18 Appendix. Resuls of he Augmened Dickey-Fuller es of nonsaionariy Observed changes in producion (real ime daa) Variable: levels of AV Variable: firs differences of AV model: (-L)y = b0 + (a-)*y(-) e esimaed value of (a - ): es saisic: au_c() = -.75 asympoic p-value model: (-L)y = b0 + (a-)*y(-) e esimaed value of (a - ): es saisic: au_c() = -0.7 asympoic p-value.647e-02 Observed changes in producion (end-of-sample daa) Variable: levels of AV Variable: firs differences of AV model: (-L)y = b0 + (a-)*y(-) e esimaed value of (a - ): es saisic: au_c() = asympoic p-value model: (-L)y = b0 + (a-)*y(-) e esimaed value of (a - ): es saisic: au_c() = asympoic p-value.564e-02 Expecaions series (real ime daa) Variable: levels of E Variable: firs differences of model: (-L)y = b0 + (a-)*y(-) e esimaed value of (a - ): es saisic: au_c() = asympoic p-value E model: (-L)y = b0 + (a-)*y(-) e esimaed value of (a - ): es saisic: au_c() = asympoic p-value 7.692e-0 Expecaions series (end-of-sample daa) Variable: levels of E Variable: firs differences of model: (-L)y = b0 + (a-)*y(-) e esimaed value of (a - ): es saisic: au_c() = asympoic p-value E model: (-L)y = b0 + (a-)*y(-) e esimaed value of (a - ): -.09 es saisic: au_c() = asympoic p-value 6.74e-0 27

19 Appendix 4. Coinegraing regressions esimaion resuls Dependen variable: AV OLS, using observaions 2005:07-204: (T = ) HAC sandard errors, bandwidh (Barle kernel) Coefficien Sd. Error -raio p-value cons * E Mean dependen var S.D. dependen var Sum squared resid S.E. of regression R-squared Adjused R-squared F(, ) value(f) Log-likelihood Akaike crierion E Resricion: b[ ] = Tes saisic: Robus F(, ) = , wih p-value = e-00 Resriced esimaes: Augmened Dickey-Fuller es for residuals model: (-L)y = b0 + (a-)*y(-) e esimaed value of (a - ): es saisic: au_c() = asympoic p-value 0.56 Dependen variable: AV OLS, using observaions 2005:07-204: (T = ) HAC sandard errors, bandwidh (Barle kernel) Coefficien Sd. Error -raio p-value cons E Mean dependen var S.D. dependen var Sum squared resid S.E. of regression R-squared Adjused R-squared F(, ) value(f) Log-likelihood Akaike crierion E Resricion: b[ ] = Tes saisic: Robus F(, ) = , wih p-value =.57672e-007 Augmened Dickey-Fuller es for residuals model: (-L)y = b0 + (a-)*y(-) e es saisic: au_c() = asympoic p-value 6.509e-08 28

20 Appendix 5. Orhogonaliy esimaion resuls Dependen variable: AV E OLS, using observaions 2005:07-204: (T = ) HAC sandard errors, bandwidh (Barle kernel) Coefficien Sd. Error -raio p-value cons AV AV < *** AV < *** Mean dependen var S.D. dependen var Sum squared resid S.E. of regression R-squared Adjused R-squared F(, 09) value(f) 7.66e- Log-likelihood Akaike crierion Variance Inflaion Facors: AV.22 AV 2.8 AV.2 Dependen variable: AV E OLS, using observaions 2005:07-204: (T = ) HAC sandard errors, bandwidh (Barle kernel) Coefficien Sd. Error -raio p-value cons * AV * AV *** AV *** Mean dependen var S.D. dependen var Sum squared resid S.E. of regression R-squared Adjused R-squared F(, 09) value(f) 8.07e-07 Log-likelihood Akaike crierion Variance Inflaion Facors: AV.220 AV 2.8 AV.22 29