Volume 35, Issue 1. Nonlinear ARDL Approach and the Demand for Money in Iran

Transcription

1 Volume 35, Issue 1 Nonlnear ARDL Approach and he Demand for Money n Iran Mohsen Bahman-Oskooee The Unversy of Wsconsn-Mlwaukee Sahar Bahman The Unversy of Wsconsn- Parksde Absrac To accoun for currency subsuon, mos sudes oday nclude exchange rae as a deermnan of he demand for money, n addon o ncome and neres rae. Ths radon goes back o Rober Mundell who nroduced hs noon n In hs paper, we demonsrae ha he falure o fnd a sgnfcan relaonshp beween exchange rae and he demand for money could be due o assumng a lnear adjusmen mechansm among he varables. Once we nroduce nonlneary n he shor run as well as n he long run hrough paral sum concep, we show ha currency apprecaon or deprecaon could affec he demand for money n an asymmerc manner. Ths s demonsraed usng daa from Iran. Valuable commens from semnar parcpans a Tabrz Unversy n Iran on November 25, 2014 as well as from an anonymous referee are grealy apprecaed. Remanng errors are our own. Caon: Mohsen Bahman-Oskooee and Sahar Bahman, (2015) ''Nonlnear ARDL Approach and he Demand for Money n Iran'', Economcs Bullen, Volume 35, Issue 1, pages Conac: Mohsen Bahman-Oskooee - bahman@uwm.edu, Sahar Bahman - bahman@uwp.edu. Submed: May 23, Publshed: March 11, 2015.

2 1. Inroducon The demand for money s perhaps one of he areas n economcs whch has receved he greaes aenon. Idenfyng varables, oher han ncome and neres rae, esng for negrang properes of he relevan varables, esablshng conegrang properes of he varables, and fnally, esng for sably of he money demand funcon are some of he mporan aspecs of he leraure upon whch researchers have concenraed. Concenrang on he frs ssue of denfyng relevan varables, n 1963 he Nobel laureae Mundell (1963) conjecured ha n addon o ncome and neres raes, he exchange rae could ceranly be anoher deermnan of he demand for money. Subsequen sudes no only red o provde clear and nuve explanaons for hs assumpon, bu also emprcal suppor for Mundell s conjecure. Very brefly, he deprecaon of domesc currency, or he apprecaon of foregn currency, rases he domesc currency value of foregn asses held by domesc resdens. If hs s perceved as an ncrease n wealh, he demand for money should ncrease (Arango and Nadr, 1981). However, when foregn currency apprecaes, f here s he expecaon of furher apprecaon, domesc resdens may hold more foregn currency and reduce her demand for domesc currency (Bahman-Oskooee and Pourheydaran, 1990). Therefore, dependng upon he srengh of he wealh effec versus he expecaon effec, he demand for money could move n eher drecon. Example of sudes whch have ncluded he exchange rae n he money demand nclude McNown and Wallace (1992) for he U.S.; Lee and Chung (1995) for Korea, Myao (1996) for Japan, Chowdhury (1997) for Thaland, and Bahman-Oskooee and Gelan (2009) for Afrcan counres. The fndngs are mxed a bes. Falure o fnd suppor for he sgnfcance of he exchange rae n he demand for money could sem from assumng ha he shor-run dynamc adjusmen process follows a lnear pah. Once we nroduce he non-lnear adjusmen process no he esng procedure, we show ha currency deprecaon could have a sgnfcan effec on he demand for money. To ha end, we nroduce he model and mehods n Secon II. In secon III we presen our emprcal resuls followed by a summary and concludng remarks n Secon IV. Daa defnon and sources are ced n an Appendx. 2. The Model and Mehodology Ou of our neres and for demonsrave purpose, we use daa from Iran. Therefore, he specfcaon adoped n hs paper follows Bahman-Oskooee (1996) who esmaed he demand for money for Iran by ncludng real ncome as a scale varable, nflaon rae as a measure of he 1

3 opporuny cos of holdng money, and he black marke exchange rae, as n equaon (1): 1 LnM a blny c dlnex ( 1 ) where M s a measure of real M2 moneary aggregae, Y s a measure of real ncome, s he rae of nflaon, EX s he exchange rae, and ε s an error erm. We expec an esmae of b, whch measures ncome elascy of he demand for money, o be posve. The nflaon rae, raher han he neres rae, s ncluded n he specfcaon o measure he opporuny cos of holdng money due o he lack of well-developed fnancal markes n Iran. As Bahman-Oskooee (1996) argued, hsorcally n Iran real asses, such as land and housng, are he bes alernave for holdng cash. Therefore, we expec an esmae of c o be negave. As for an esmae of d, as menoned n he nroducon, could be negave or posve dependng on wheher he dollar apprecaon ncreases expecaons of furher apprecaon or s perceved as an ncrease n wealh (.e., an ncrease n domesc currency value of foregn asses). 2 Models such as (1) are labeled long-run models and her esmaes by any means wll yeld only long-run coeffcen esmaes once conegraon among he varables s esablshed. Snce sably of he money demand s anoher concern, Ladler (1993, p. 175) argued ha one source of nsably could sem from excludng shor-run dynamcs from long-run model. To ha end, we specfyng (1) n an error-correcon modelng forma as n equaon (2): LnM n1 1 LnM n 2 0 LnY n 3 n LnEX LnM 0 1 LnY LnEX 3 1 (2) Equaon (2) follows Pesaran e al. s (2001) bounds esng approach who offer a one-sep procedure n esmang he shor-run as well as he long-run effecs. The shor-run effecs are conaned n he coeffcens aached o he frs-dfferenced varables. The long-run effecs are obaned by he esmaes of ρ 1 -ρ 3, normalzed on ρ 0. 3 However, for he long-run esmaes o be vald, conegraon mus be esablshed. Pesaran e al. (2001) propose applyng he sandard F es for jon sgnfcance of he lagged level varables n (2). However, as hey demonsrae, hs 1 Ths specfcaon s followed by many ohers n he leraure. 2 Noe ha, alhough here are neher economc nor polcal relaons beween he U.S. and Iran, he U.S. dollar sll serves as a reserve currency and domnaes almos all nernaonal ransacons. For he hsory of he ral-dollar rae see Bahman-Oskooee (2005). 3 For he exac normalzaon procedure see Bahman-Oskooee and Tanku (2008) n hs journal. 2

4 F es has a new dsrbuon wh new crcal values ha hey abulae. An upper bound crcal value s provded by assumng all varables n a model o be I(1) and a lower bound crcal value s provded when all varables are assumed o be I(0). They demonsrae ha he upper bound crcal values could also be used f some varables are I(1) and some are I(0). Snce almos all macroeconomc me-seres varables are eher I(1) or I(0), here s acually no need for pre unroo esng under hs mehod. 4 Prevous sudes ha esmaed any of he above models usng any mehod, assumed ha exchange rae changes have symmerc effecs on he demand for money. To es hs hypohess, we decompose he movemen of he Ln EX varable no s negave (he deprecaon of he dollar) and posve (he apprecaon of he dollar) paral sum as: LnEX LnEX LnEX LnEX where Ln EX + 0 and LnEX - are he paral sum process of posve and negave changes n Ln EX. More precsely: LnEX j 1 LnEX j j 1 max( LnEX j,0), LnEX j 1 LnEX j j 1 mn( LnEX j,0) We hen follow Shn e al (2014) and replace Ln EX n equaon (2) by Ln EX + and Ln EX - as n (3) below: LnM a n1 1 b LnM n 2 0 c LnY n 3 0 d n 4 0 e LnEX n 5 0 f LnEX LnM 0 1 LnY LnEX 3 1 LnEX 4 1 (3) Equaon (3) now allows us o es wheher exchange rae changes have asymmerc or symmerc effecs on he demand for money n he shor run as well as n he long run. Shn e al. (2014) jusfy applyng Pesaran e al. s (2001) bounds esng approach o (3) n order o es he symmery hypohess. Equaon (3) s labeled as a Nonlnear ARDL model n whch nonlneary s bascally nroduced hrough paral sums The Resuls In hs secon, we frs ry o esmae he lnear ARDL model oulned by equaon (2). Quarerly daa from Iran s used for esmaon purposes. Followng ohers, we mpose a 4 For oher applcaons of hs approach see Bahman-Oskooee e al. (2005), Bahman-Oskooee and Hegery (2007), Halcoglu, F., (2007), Narayan e al. (2007), Tang (2007), Mohammad e al. (2008), Wong and Tang (2008), De Va and Kyaw (2008), Payne (2008), Chen and Chen (2012), and Wong (2013). 5 For anoher applcaon of paral sum see Apergs and Mller (2006). 3

5 maxmum of four lags on each frs-dfferenced varable and use Akake s Informaon Creron (AIC) o selec he opmum number of lags. The resuls from he opmum model are repored n Table 1. 6 Due o he volume of he resuls, hey are repored n hree panels. Panel A repors he shor-run coeffcen esmaes. Clearly, a majory of hese coeffcens are sgnfcan, excep he coeffcens obaned for nflaon rae and he exchange rae. Turnng o he long-run normalzed coeffcens n Panel B, appears ha only ncome carres a posve and sgnfcan coeffcen, supporng he ransacon demand for money. Bu hs long-run relaon beween money demand and ncome wll be meanngful only f conegraon s esablshed. From Panel C, s clear ha he varable addon F es for jon sgnfcance of lagged level varables a opmum lags s much less han s crcal value of 3.52, mplyng he lack of conegraon. However, followng Bahman-Oskooee and Tanku (2008) we use normalzed long-run coeffcens from Panel B and equaon (1) o generae he error erm, whch s normally referred o as error correcon erm ECM. We hen replace he lagged level varables n (2) by ECM -1 and esmae hs new specfcaon a he opmum lags. A sgnfcanly negave coeffcen obaned for ECM -1 wll suppor conegraon or convergence oward he long run. Ths s ndeed he case from Panel C. A few oher dagnosc sascs are also repored n Panel C. To make sure ha he resduals are auocorrelaon free, he Lagrange Mulpler (LM) sasc s repored, whch s dsrbued as χ 2 wh four degrees of freedom. Gven s crcal value of 9.48, repored a he boom of Table 1, clearly he repored LM sasc s nsgnfcan, supporng auocorrelaon free resduals. Ramsey s RESET sasc s also repored for judgng msspecfcaon. Ths sasc also has a χ 2 dsrbuon, bu only wh one degree of freedom. Gven s crcal value of 3.84 a he 5% level of sgnfcance, clearly our calculaed sasc s nsgnfcan, supporng he specfcaon of he opmum model. We also repor a es for normaly of he resduals, whch s based on skewness and kuross of he resduals. I has a χ 2 dsrbuon wh wo degrees of freedom and, as can be seen, he repored sasc s nsgnfcan, supporng he normaly assumpon. To es for he sably of shor-run and long-run coeffcens, followng ohers (e.g., Pesaran e al. 2001, Bahman-Oskooee and Bohl 2000) we apply CUSUM and CUSUMSQ ess o he resduals of he opmum model. As can be seen, all coeffcens are sable by boh crera. Fnally, adjused R 2 s also repored, whch shows a good f. 6 As a prelmnary exercse, we appled he ADF es o each varable and esed for un roos. The resuls, avalable upon reques, revealed ha all varables are I(1), excep he nflaon rae whch was I(0). 4

6 Concenrang on he effecs of exchange rae changes on he demand for money, based on he resuls so far, we may conclude ha has no sgnfcan effec durng he sudy perod. As menoned before, hs concluson s based on assumng ha he adjusmen of varables s n lnear fashon. Wll he resuls change f we shf o nonlnear ARDL approach and esmae equaon (3) by akng he same seps of mposng a maxmum of four lags on each frs dfferenced varable and usng he AIC creron? The resuls are repored n Table 2. From he shor-run resuls, repored n Panel A, we gaher ha he varable represenng negave paral sum,.e., ΔLnEX-, whch represens dollar deprecaon, carres a sgnfcanly posve coeffcen. The fac ha ΔLnEX- carres a sgnfcan coeffcen bu ΔLn EX + does no, suppors asymmery effecs of any exchange rae changes on he demand for money n he shor run. Does hs las no he long run? Long run coeffcen esmaes are repored n Panel B. Concenrang on he effecs of exchange rae changes, s clear ha a he 5% sgnfcan level he negave paral sum,.e., LnEX-, carres a hghly sgnfcan coeffcen bu he posve paral sum,.e., Ln EX+, does no. Ths s he same as he shor-run resuls and mples ha when he dollar deprecaes, Iranans hold less of her domesc currency. 7 If we consder he 10% level of sgnfcance, hen boh coeffcens are sgnfcan wh oppose sgns, supporng, agan, he asymmerc effecs. The negave coeffcen of posve paral sum, Ln EX+, mples ha when he dollar apprecaes, Iranans hold less of her own currency. The posve coeffcen of negave paral sum, Ln EX -, also mples ha when he dollar deprecaes, Iranans hold less of her own currency. The combned mplcaon of he resuls s ha exchange rae changes have her effecs on he demand for money n Iran hrough changes n expecaons and no hrough he wealh effec. When he dollar apprecaes, due o he expecaon of furher apprecaon, Iranan wll hold more dollars and less rals. When deprecaes, snce here s always expecaon of dollar apprecaon, hey wll hold more dollars and less ral. Hsorcally, due o nflaon n Iran dollar has always apprecaed. Any dollar deprecaon has been shor lved and here s a belef ha lke housng marke n Iran, he rend of he dollar s always upward. 8 Therefore, we conclude ha he exchange rae changes have an asymmerc effec on he demand for money n he long run. 7 Noe ha by way of consrucon, he negave paral sum can only declne. As does, because of posve slope coeffcen, so does he demand for ral. 8 The 70 rals per dollar rae ha exsed before 1979, sands a more han rals per dollar as of revsng hs paper. 5

7 Turnng o he oher varables, s clear ha ncome elascy s hghly sgnfcan and as expeced, s posve. Inflaon rae carres s expecedly negave and sgnfcan coeffcen also. Lke before, hese long-run resuls wll be meanngful only f we esablsh conegraon among varables. From Panel C, of Table 2, s clear ha conegraon s suppored by a leas ECM -1 coeffcen. Furhermore, all dagnosc sascs are less han her crcal values, supporng auocorrelaon free resduals, a correcly specfed nonlnear ARDL model, normally dsrbued errors, and sable coeffcens Summary and Concluson The orgn of ncludng he exchange rae n he specfcaon of he money demand goes back o 1963 and Rober Mundell, who conjecured ha he demand for money could depend on he exchange rae n addon o ncome and neres rae. Subsequen sudes snce hen have red o provde a clear explanaon along wh emprcal suppor for Mundell s conjecure. In hs paper, we demonsrae ha falure o fnd a sgnfcan relaonshp beween he exchange rae and he demand for money could sem from assumng a lnear dynamc adjusmen process of varables oward her long run equlbrum varables. Once nonlneary s nroduced, usng he paral sum concep, exchange rae movemen could have a sgnfcan effec on he demand for money. We demonsrae hs usng Iranan daa and by esmang he demand for money n Iran. Separang he movemens n he value of he dollar no posve paral sum (apprecaon) and negave paral sum (deprecaon), helps us o nroduce nonlneary no he adjusmen mechansm, we hen fnd ha dollar apprecaon and dollar deprecaon have an asymmerc effec on he demand for money n Iran. Pror o he Iranan revoluon, here was free capal mobly n Iran and, as a maer of fac, he Iranan ral was converble and was one of he 16 currences ncluded n SDR (Specal Drawng Rghs) of he IMF. Iranans were allowed o hold asses abroad. Therefore, s no surprse why when Bahman-Oskooee (1996) used daa over he perod , whch was domnaed by he pre-revoluonary perod, suppor was found for he wealh effec of dollar apprecaon. Due o sancons, mos Iranans canno hold asses abroad, so he wealh effec s weakened. However, he expecaon effec s very srong. Many Iranans n large ces now speculae by buyng and sellng dollars. Ths s borne ou of our resuls n hs paper, whch used daa only from he pos- 9 For sensvy analyss, we carred ou he enre analyss by mposng a maxmum of egh lags on each frsdfferenced varable. There was no sgnfcan change n he resuls and concluson. More precsely, ncome elascy was wh a -rao of 25.26; he coeffcen obaned for nflaon rae was wh a -rao of 6

8 revoluonary perod. As he dollar apprecaes, Iranans expec furher apprecaon and herefore, hold more dollars and less of domesc currency. 10 The same s rue even when he dollar deprecaes, hence asymmerc effecs. Appendx All daa are quarerly and are colleced from he followng source. a. The Inernaonal Fnancal Sascs of he IMF. b. Bahman-Oskooee (2005). Varables: Real Money (M2): Nomnal moneary aggregae (M1) s added o quaz money o ge nomnal M2. Nomnal M2 s hen deflaed by CPI (he only avalable prce ndex n Iran) o oban real money. All daa come from source a. Real Income (Y): Ths varable s consruced by dvdng he nomnal GDP by he CPI. Quarerly nomnal GDP was no avalable for Iran. Therefore, we generaed he seres followng he mehod n Bahman-Oskooee (1998) usng annual daa. All annual daa came from source a. Inflaon Rae (Π) = Ths varable s defned as Ln P Ln P -1, where P s measured by he CPI ndex. All CPI daa come from source a. Exchange Rae (EX) = Ths varable s defned as he number of Iranan rals per U.S. dollar, uns of domesc currency per U.S. dollar. In lne wh Bahman-Oskooee (1996), he black marke exchange rae s used. Of course, snce 2001 he offcal and he black marke raes have been unfed. The daa come from sources (a) and (b) , he coeffcen of posve paral sum,.e., LnEX +, was wh a -rao of -1.52, and fnally he coeffcen of negave paral sum, Ln EX-, was wh a -rao of Recen nuclear deals wh he Uned Naons and he wes and easng of sancons has creaed opmsm n Iran and has helped he dollar o come down from a hgh of 38,000 rals o almos 30,000.Par of ha drop s due o he 7

9 References Apergs, N., and S. Mller (2006) Consumpon Asymmery and he Sock Marke: Emprcal Evdence Economcs Leers 93, Arango, S. and M. Ishaq Nadr (1981) "Demand for Money n Open economes" Journal of Moneary Economcs 7, Bahman-Oskooee, M. (1996) "The Black Marke Exchange Rae and Demand for Money n Iran" Journal of Macroeconomcs 18, Bahman-Oskooee, M. (1998) "Are Devaluaons Conraconary n LDCs?" Journal of Economc Developmen 23, Bahman-Oskooee, M. (2005) Hsory of he Ral and Foregn Exchange Polcy n Iran Iranan Economc Revew 10, Bahman-Oskooee, M. and M. Pourheydaran (1990) "Exchange Rae Sensvy of he Demand for Money and Effecveness of Fscal and Moneary Polces" Appled Economcs 22, Bahman-Oskooee, M. and M. Bohl (2000) "German Unfcaon and he Sably of Long-Run German Money Demand Funcon" Economcs Leers 66, Bahman-Oskooee, M. and S.W. Hegery (2007) Exchange Rae Volaly and Trade Flows: a Revew Arcle, Journal of Economc Sudes 34, Bahman-Oskooee, M. and A. Tanku (2008) The Black Marke Exchange Rae vs. he Offcal Rae n Tesng PPP: Whch Rae Fosers he Adjusmen Process Economcs Leers 99, Bahman-Oskooee, M. and A. Gelan (2009) How Sable s he Demand for Money n Afrcan Counres? Journal of Economc Sudes 36, Bahman-Oskooee, M. and H. Fardavana, Do Exchange Rae Changes have Symmerc Effec on he S-Curve?, Economcs Bullen, Vol. 34 (2014), Issue 1, pp Bahman-Oskooee, M., C. Economdou, and G. G. Goswam. (2005), How Sensve are Bran s Inpaymens and Oupaymens o he Value of he Brsh Pound Journal of Economc Sudes 32, Chen, S.-W. and T.-C. Chen, (2012) Unanglng he Non-Lnear Causal Nexus beween Exchange Raes and Sock Prces: New Evdence from he OECD Counres Journl of Economc Sudes 39, Chowdhury, A. (1997) The Fnancal Srucure and he Demand for Money n Thaland Appled Economcs 29, De Va, G. and K. S. Kyaw, (2008) Deermnans of Capal Flows o Developng Counres: A dollar sellng by speculaors. However, due o drop n ol prces and herefore, ol revenues whch has reduced he supply of dollar o foregn exchange marke, he rae s back o around rals per dollar. 8

10 Srucural VAR Analyss Journal of Economc Sudes 35, Halcoglu, F. (2007) The J-Curve Dynamcs of Turksh Blaeral Trade: A Conegraon Approach Journal of Economc Sudes 34, Ladler, E.W.D. (1993) The Demand for Money: Theores Evdence and Problems, 4 h Edon, Harper Collns College Publshers. Lee, T. H. and K. J. Chung (1995) "Furher Resuls on he Long-Run Demand for Money n Korea: A Conegraon Analyss" Inernaonal Economc Journal 9, McNown, R. and M.S. Wallace (1992) "Conegraon Tess of a Long-Run Relaonshp beween Money Demand and he Effecve Exchange Rae" Journal of Inernaonal Money and Fnance 11, Myao, R. (1996) "Does a Conegrang M2 Demand Relaon Really Exs n Japan? Journal of he Japanese and Inernaonal Economes 10, Mohammad, H., M. Cak, and D. Cak, (2008), Wagner s Hypohess: New Evdence from Turkey usng he Bounds Tesng Approach Journal of Economc Sudes 35, Mundell, R.A. (1963) Capal Mobly and Sablzaon Polcy under Fxed and Flexble Exchange Raes Canadan Journal of Economcs and Polcal Scence 29, Narayan, P.K., S. Narayan, B.C. Prasad, and A. Prasad (2007) Expor-led Growh Hypohess: Evdence from Papua New Gunea and Fj Journal of Economc Sudes 34, Payne, J. E. (2008) Inflaon and Inflaon Uncerany: Evdence from he Carbbean Regon Journal of Economc Sudes 35, Pesaran, M. H., Y. Shn and R. J. Smh (2001) "Bounds Tesng Approaches o he Analyss of Level Relaonshps" Journal of Appled Economercs 16, Shn, Y, B. C. Yu, and M. Greenwood-Nmmo (2014) Modellng Asymmerc Conegraon and Dynamc Mulplers n a Nonlnear ARDL Framework Fesschrf n Honor of Peer Schmd: Economerc Mehods and Applcaons, eds. by R. Sckels and W. Horrace: Sprnger, Tang, T.C. (2007) Money Demand Funcon for Souheas Asan Counres: An Emprcal Vew from Expendure Componens Journal of Economc Sudes 34, Wong, K. N.. and T. C. Tang (2008) The Effecs of Exchange Rae Varably on Malaysa s Dsaggregaed Elecrcal Expors Journal of Economc Sudes 35, Wong, H. T. (2013) Real Exchange Rae Msalgnmen and Economc Growh n Malaysa Journal of Economcs Sudes 40,

11 Table 1: Full-Informaon Esmae of Lnear ARDL Equaon (3). Panel A: Shor-Run Coeffcen Esmaes Lag Order Ln M (3.56) (4.42) (3.90) Ln Y (62.8) (3.99) (4.42) (3.82) Δπ (0.49) Ln EX (0.29) Panel B: Long-Run Coeffcen Esmaes Consan Ln Y π Ln EX (2.01) (4.62) (1.04) (0.66) Panel C: Dagnosc Sascs F ECM -1 LM RESET Normaly CUS (CUS 2 ) Adj. R Sable 0.99 (2.14) Noes: a. The number nsde he parenheses are he absolue value of -raos. b. The upper bound crcal value of he F sasc a he usual 5% level of sgnfcance s Ths comes from Pesaran e al. (2001, Table CI-Case III, p. 300). c. LM s he Lagrange mulpler es for seral correlaon. I has a 2 dsrbuon wh four degrees of freedom. The crcal value a he 5% level of sgnfcance s d. RESET s Ramsey's specfcaon es. I has a 2 dsrbuon wh only one degree of freedom. The crcal value a he 5% level of sgnfcance s e. The normaly es s based on a es of skewness and kuross of resduals. I has a 2 dsrbuon wh only wo degrees of freedom. The crcal value a he 5% level of sgnfcance s

12 Table 2: Full-Informaon Esmae of Nonlnear ARDL Equaon (5). Panel A: Shor-Run Coeffcen Esmaes Lag Order Ln M (3.86) (3.82) (4.32) Ln Y (66.7) (4.25) (3.82) (4.28) Δπ (0.67) Ln EX (1.30) Ln EX (2.73) Panel B: Long-Run Coeffcen Esmaes Consan Ln Y π Ln EX + Ln EX (15.1) (37.9) (1.96) (1.85) (4.77) Panel C: Dagnosc Sascs F ECM -1 LM RESET Normaly CUSUM (CUSSUM 2 ) Adj. R Sable 0.99 (2.81) Noes: a. The number nsde he parenheses are he absolue value of -raos. b. The upper bound crcal value of he F sasc a he usual 5% level of sgnfcance s Ths comes from Pesaran e al. (2001, Table CI-Case III, p. 300). c. LM s he Lagrange mulpler es for seral correlaon. I has a 2 dsrbuon wh four degrees of freedom. The crcal value a he 5% level of sgnfcance s d. RESET s Ramsey's specfcaon es. I has a 2 dsrbuon wh only one degree of freedom. The crcal value a he 5% level of sgnfcance s e. The normaly es s based on a es of skewness and kuross of resduals. I has a 2 dsrbuon wh only wo degrees of freedom. The crcal value a he 5% level of sgnfcance s