Estimation of the aggregate import demand function for Mexico: A cointegration analysis

Rome o, José; Alipha , Rod igo A icle Es ima ion o he agg ega e impo demand unc ion o Mexico: Acoin eg a ion analysis Jou nal o Economics, Finance and Adminis a i e Science P o ided in Coope a ion wi h: Uni e sidad ESAN, Lima Sugges ed Ci a ion: Rome o, José; Alipha , Rod igo (2023) : Es ima ion o he agg ega e impo demand unc ion o Mexico: Acoin eg a ion analysis, Jou nal o Economics, Finance and Adminis a i e Science, ISSN 2218-0648, Eme ald Publishing Limi ed, Bingley, Vol. 28, Iss. 56, pp. 372-385, h ps://doi.o g/10.1108/JEFAS-08-2020-0302 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/289664 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. 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I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ Es ima ion o he agg ega e impo demand unc ion o Mexico: a coin eg a ion analysis Jos e An onio Rome o Tellaeche Cen o de Es udios Econ omicos, El Colegio de Mexico AC, Mexico Ci y, Mexico, and Rod igo Alipha Facul ad de Econom ıa, Uni e sidad Nacional Au  onoma de M exico, Mexico Ci y, Mexico Abs ac Pu pose –This s udy es ima ed o al impo demand elas ici ies conce ning income, impo p ices and domes ic p ices. A high p opensi y o impo cons i u es a signi ican obs acle o economic g ow h in Mexico since he bene i s o inc eased expo s o any o he agg ega e demand expansion leak o he es o he wo ld. Design/me hodology/app oach –This pape es ima ed a Vec o E o Co ec ion Model o he o al impo demand elas ici ies conce ning income, impo p ices and domes ic p ices. To al impo s a e a dependen a iable, while G oss Domes ic P oduc (GDP) and impo and domes ic p ices a e he independen a iables. Findings –The p incipal inding is ha an inc ease o 1 peso in he Mexican GDP leads o a ise o 0.50 pesos in Mexican impo s; he elas ici y o impo demand o p ices is low. S ill, he elas ici y o impo demand o domes ic p ices is 2.14 imes g ea e han ha o impo p ices. These esul s ha e signi ican economic policy implica ions, such as p omo ing he expansion o he domes ic ma ke and he na ional con en o expo s. Resea ch limi a ions/implica ions –I is emp ing o es ima e he impo demand unc ion o he en i e 1993–2019 pe iod since such da a is a ailable. Bu by doing so, he au ho s would o e es ima e he p opensi y o impo , gi en ha om 1993 o 2019, he p opo ion o impo s as a pe cen age o GDP wen om 11.37 in 1993 o 29.66 in 2019. The e o e, i makes mo e sense o es ima e he impo demand unc ion om 2000 o 2019, a pe iod wi h a s able p opo ion o impo s o GDP. O iginali y/ alue –A high le el o impo s in de eloping coun ies means ha much o hei agg ega e demand is il e ed ab oad. The e o e, he low impac o i s expo s on GDP is ela ed o he Mexican economy’s high impo s. The au ho s calcula e his ela ionship wi h new da a and me hods. Keywo ds Mexico, Impo demand, Elas ici ies, Indus ial policy Pape ype Resea ch pape 1. In oduc ion In Mexico and o he eme ging economies, impo s ad e sely in luence economic g ow h. Thus, i is essen ial o co ec ly quan i y he elas ici y o impo demand and he p opensi y o impo . Acco ding o San os-Paulino (2002), iden i ying he main a iables a ec ing impo beha iou can help policymake s design and e alua e he sus ainabili y o an economic s a egy, such as in oducing an ac i e indus ial policy. JEFAS 28,56 372 JEL Classi ica ion —E23, F13, F41. © Jos e An onio Rome o Tellaeche and Rod igo Alipha . Published in Jou nal o Economics, Finance and Adminis a i e Science. Published by Eme ald Publishing Limi ed. This a icle is published unde he C ea i e Commons A ibu ion (CC BY 4.0) licence. Anyone may ep oduce, dis ibu e, ansla e and c ea e de i a i e wo ks o his a icle ( o bo h comme cial and non-comme cial pu poses), subjec o ull a ibu ion o he o iginal publica ion and au ho s. The ull e ms o his licence maybe seen a h p://c ea i ecommons.o g/licences/by/4.0/legalcode Funding: This esea ch did no ecei e any speci ic g an om unding agencies in he public, comme cial o no - o -p o i sec o s. The cu en issue and ull ex a chi e o his jou nal is a ailable on Eme ald Insigh a : h ps://www.eme ald.com/insigh /2077-1886.h m Recei ed 19 Augus 2020 Re ised 8 July 2021 7 Oc obe 2021 Accep ed 27 Janua y 2022 Jou nal o Economics, Finance and Adminis a i e Science Vol. 28 No. 56, 2023 pp. 372-385 Eme ald Publishing Limi ed 2077-1886 DOI 10.1108/JEFAS-08-2020-0302 A p emise in expo -based g ow h models is ha a coun y’s g ow h and de elopmen expec a ions imp o e when i s expo s inc ease and in eg a e in o global alue chains. Howe e , as Roca and Simabuko (2015) men ion, a pa adox a ises in Mexico because high expo g ow h a es a e no ela ed o highe G oss Domes ic P oduc (GDP) g ow h a es; among o he easons, hey explain ha i may be due o he inc eased p opensi y o impo ( he li e a u e e iew deepens on he subjec ). The p oblem o he p opo ions o impo , which we will s udy and calcula e in his documen , has been a opic o in e es in he s udy o eme ging economies. Fo example, Ko a c and Ko a c (2013) e alua e he e ec s o in e na ional ade in C oa ia, inding ha he ise in expo s has been es ic ed by lowe added alue due o he g ow h o impo s. In addi ion, Kaplinsky and Messne (2008) men ion ha a high le el o impo s could nega i ely a ec he in e nal p oduc i e ab ic. This pape aims o es ima e he o al impo demand elas ici ies o income, impo p ices and domes ic p ices. A high p opensi y o impo cons i u es a signi ican obs acle o economic g ow h in Mexico since he bene i s o inc eased expo s o any o he agg ega e demand expansion leak o he es o he wo ld. This s udy’s main indings a e ha an inc ease o 1 peso in he Mexican GDP leads o a ise o 0.50 pesos in Mexican impo s. This esul has signi ican implica ions o he low impac o inc eased agg ega e demand on GDP and economic policy (i.e. go e nmen spending o s abilize he economy). Fu he mo e, hese indings call o a change in Mexican mone a y policy ega ding i s economic s uc u e o encou age an inc ease in he na ional con en o i s expo s and domes ic p oduc ion. The impo demand unc ion is es ima ed using a Vec o E o Co ec ion (VEC) model. A e an in oduc ion, Sec ion 2 e iews ele an li e a u e. Sec ion 3 con ains a b ie discussion o he ends in impo s, ade balance and GDP o e he s udy pe iod; hen, we p esen he econome ic model speci ica ion and a iables. Then, Sec ion 4 p esen s he esul s o he VEC model; and inally, Sec ion 5 discusses he signi ican indings and Sec ion 6 concludes wi h policy ecommenda ions. 2. Li e a u e e iew Acco ding o he ecen app oaches o indus ial policy published by Aiginge and Rod ik (2020), ade policy mus a icula e he objec i es o encou aging inno a ion and include a na ional p oduc ion policy beyond seeking o co ec ma ke ailu es. Rela ed o his, Gu u and Yada (2019) ound a posi i e and signi ican ela ionship be ween inancial in e media iesandeconomicg ow hineme ging economies. In he absence o inancial in e media ies, Chang and And eoni (2020) sugges ha ade libe aliza ion allows companies inanced mainly wi h o eign capi al o be inco po a ed in o global alue chains. This also a ec s in e nal p oduc ion chains because companies wi h g ea e expo ac i i y end o depend mo e on impo ed inpu s. In addi ion, a weakening o he na ional p oduc i e s uc u e causes he demand o consume and in es men goods o be me h ough impo s. And eoni (2019) explained ha in an eme ging economy, he posi i e e ec s o ade libe aliza ion would only happen i he p oduc i e in e nal s uc u e had a minimum le el o echnological capaci y and human capi al. Acco ding o Cas illo and de V ies (2018), Mexico is an example o p ema u e libe aliza ion since p oduc i i y le els and he use o skilled wo ke s in maquila indus ies ha e ba ely imp o ed pos -NAFTA. While o al impo s inc eased be ween 1993 and 2020 (Figu e 1), hey do no ind a sys ema ic endency o inc eased domes ic sou cing o inpu s. The e o e, libe alisa ion is no isible. This p opensi y o impo could be an indica o o di e en ia e be ween an economy wi h an expo oca ion o added alue and a maquilado a o an expo e o aw ma e ials. The analysis o he impo demand unc ion has become ele an in he s udy o eme ging economies and hei e olu ion. The e o e, he e is a cons an need o es ima e he impo Es ima ion o impo demand unc ion 373 demand unc ion as new da a a i es and new me hods de elop. Examples o his include Galindo and Ca de o (1999), who ale s o a s uc u al ela ionship be ween he inc ease o impo con en in Mexican expo s; Zhou and Dube (2011) ound a simila pa e n o China, India, B azil and Sou h A ica when analyzing hei impo demand beha iou . Min e al. (2002) ound o Sou h Ko ea ha he p incipal de e minan s o impo s a e he inal consump ion expendi u e and expo demand; ela ed esul s had Kalyoncu (2006) o Tu key; Na ayan and Na ayan (2010) o Sou h A ica; Wang and Lee (2012) o China; and Du maz and Lee (2015) o Tu key. Calcula ing he Mexican impo demand is essen ial o i s economic policy issues; since expo s ha e expanded apidly du ing he las 36 yea s, economic g ow h has s agna ed. Fo yea s, many au ho s ha e blamed he indus ializa ion pa e n adop ed by M exico as he sou ce o low economic g ow h (Puyana and Rome o, 2009;Mo eno-B id and Ros, 2009; Puyana and Rome o, 2009;Rome o, 2014). Since 1983, Mexican au ho i ies ha e adop ed an expo -led g ow h s a egy in which ansna ional co po a ions ha e led he expo p ocess wi h weak in eg a ion wi h he es o he Mexican economy. This has esul ed in Mexico ha ing an ex emely high impo - o-expo a io (Ruiz-Napoles, 2004). The expo a ion pa e n which de eloped could be cha ac e ized as he “expo o impo s”(Rome o, 2019; Ruiz-Napoles, 2020). Ib ahim (2015) o Saudi A abia, Ogbonna (2016) o Nige ia, Muhammad and Za a (2016) o Pakis an, Mish a and Mohan y (2017) o India and Ce me~ no and Ri e a (2016) o M exico ound in di e en s udies a posi i e long- e m ela ionship be ween na ional income o domes ic consump ion and he g ow h o impo s; u he mo e, all he s udies epo ha ade balances a e cons an ly ad e sely a ec ed by highe income g ow h. Since Leame and S e n (1970) published hei es ima ion o income and p ice elas ici ies o agg ega e impo demand, many empi ical s udies ha e been published examining he de e minan s o impo demand and es ima ing impo demand unc ions (Khan, 1974;Sa mad, 1988;Gio anne i, 1989;Mo an, 1989;Em an and Shilpi, 1996; Abbo and Seddighi, 1996;Ko an and Saygih, 1999;Lo ia, 2001;Lind e al., 2005;Ho, 2004;Dash, 2005;andDu a and Ahmed, 2004, among o he s). A gene al p oblem esea che s ace is choosing he o m o he demand unc ion o es ima e agg ega e demand models o impo s. Un o una ely, in e na ional ade heo y does no p o ide many clues abou he app op ia e ype o speci ica ion o which equa ions should be used o es ima e impo demand. Two o he unc ional o ms used mos o his a e linea and loga i hmic. Figu e 1. Mexico’s o al expo s, impo s and ade balance 1993–2020 JEFAS 28,56 374 3. Me hod 3.1 Da a analysis Mexico’s ade opening began 36 yea s ago, eaching an imp essi e expo le el equi alen o 30% o i s GDP in ecen yea s. A he same ime, i s impo s eached he same p opo ion o GDP. Du ing Mexico’s indus ializa ion pe iod (1940–1970), i s a e age annual GDP g ow h a e was 5.99%, i s pe capi a income 3.01% and labou p oduc i i y 2.96%. I s pe capi a income in 1970 was only 2.47 imes g ea e han i s 1940 GDP (Rome o, 2021). This high le el o impo s means ha much o he e ec s o i s inc eased expo s and o he componen s o agg ega ed demand leaked o he es o he wo ld. Figu e 1 shows he e olu ion o he Mexican ade balance and i s componen s since 1993. Despi e he apid inc ease in expo s, Mexico’s GDP has g own a an annual a e age a e o only 2.34% annually. I s GDP pe capi a in 2019 was only 1.3 imes g ea e han in 1993 (see Figu e 2). The low impac o i s expo s on GDP is ela ed o he Mexican economy’s high le els o impo s. This esul jus i ies a pe manen need o es ima e he impo demand unc ion o Mexico due o i s essen ial implica ions o economic g ow h. Since his da a is a ailable, es ima ing he impo demand unc ion o he en i e 1993– 2019 pe iod is emp ing. Howe e , we would o e es ima e he p opensi y o consume gi en ha om 1993 o 2019, he p opo ion o impo s as a pe cen age o GDP wen om 11.37 in Janua y 1993 o 29.66 in Janua y 2019. The e o e, i makes mo e sense o es ima e he impo demand unc ion om Janua y 2000 o Decembe 2019 when he p opo ion o impo s o GDP wen om 21.9 in Janua y (see Figu e 3). 3.2 Model speci ica ion and a iables Following Leame and S e n (1970), i is possible o speci y he impo demand equa ion, which ela es he demanded quan i y o impo s o income, he p ice o impo s and he p ice o domes ic subs i u es. The impo demand equa ion o e ime is as ollows: M ¼ Y ;Pm ;Pd (1) wi h M being he eal demand o impo s in o eign cu ency, Y , he na ional eal income in o eign cu ency, Pm ; he p ice o impo s and Pd ; he p ice o domes ic goods in o eign cu ency. Figu e 2. Mexico’s GDP pe capi a: 1993–2019 Es ima ion o impo demand unc ion 375 The linea o mula ion o agg ega e impo demand is exp essed as ollows: M ¼ α 0þ α 1Y þ α 2Pm þ α 3Pd þ ε (2) α 0is he cons an e m in he eg ession, α 1is he ma ginal p opensi y o impo , α 2is he coe icien o impo s o o eign p ices, α 2is he coe icien o domes ic p ices and ε is he e o e m. Economic heo y expec s ha α 1>0, α 2< 0 and α 3> 0. Howe e , Golds ein and Khan (1976) a gued ha i impo s ep esen he di e ence be ween domes ic consump ion and p oduc ion, p oduc ion may g ow as e o slowe han consump ion in esponse o inc eased eal income. The e o e, impo s can ei he inc ease o dec ease as he ac ual income inc eases, esul ing in he coe icien o α 1 ha is ei he posi i e o nega i e. The loga i hmic e sion o Equa ion (3) is w i en as ollows: lnM ¼β0þβ1lnY þβ2lnPm þβ3lnPd þu (3) whe e ln ep esen s he na u al loga i hm and u is he e o e m. Again, acco ding o economic heo y, i is expec ed ha β1>0,β2< 0 and β3> 0 al hough β1can be nega i e. In p e ious esea ch, o example, Khan and Ross (1977),Boylan e al. (1980) and Do oodian e al. (1994) ha e a gued ha he speci ica ion o he loga i hmic o m is p e e able when impo demand unc ions a e es ima ed, as hese o ms o es ima ion allow he coe icien s o be in e p e ed as elas ici ies o he dependen a iable conce ning he independen a iable. This o mula ion mi iga es he he e oscedas ici y p oblem. This pape uses mon hly da a se ies o o al impo s wi h hei p ices and he nominal exchange a e; hese wo se ies we e ob ained om he Bank o Mexico (Sys em o Economic In o ma ion). The es ima ion uses qua e ly da a o eal GDP in 2013 domes ic p ices and mon hly da a o he Mexican Consume P ice Index. Bo h se ies we e ob ained om INEGI (Bank o Economic In o ma ion), and he Two-P ice Index was ans o med o he 2013 base (2013M6 51). Real impo s we e ob ained by di iding o al nominal impo s by he P ice Index o Impo s. To con e he eal peso alue o he GDP a 2013 p ices, we di ided he se ies by he nominal exchange a e o he second qua e o 2013. Also, we use he linea e sion o he “low o high- equency me hod” o ans o m qua e ly da a in o mon hly da a. Finally, he Consume P ice Index is di ided by he no malized nominal exchange a e o ob ain he Domes ic P ice Index (1996M6 51). Table 1 p o ides he da a de ini ions and desc ip i e s a is ics o he s udied a iables. Figu e 3. Value o impo s as a pe cen age o GDP JEFAS 28,56 376 The pe iod used o he es ima ion was om Janua y 2000 o Decembe 2019, and o al impo s and he eal GDP we e seasonally adjus ed. Figu e 4 shows he a iables used in he model. 3.3 Model es ima ion The Augmen ed Dickey–Fulle es o uni oo es s indica es ha all se ies ha e he same le el o in eg a ion I(1) (Phillips and Hansen, 1990). These es s (Table 2) use he ou -mon hly se ies exp essed in loga i hms o he 2000M01–2019M02 pe iod (240 obse a ions). As he a iables a e o o de I(1) a 1% o signi icance, we es ima e a Vec o Au o Reg ession model (VAR). The VAR includes he a iables ln(M), ln(GDP), ln(PM) and ln(PD). Fi s , he co ec numbe o lags is de ined (see Table 3). The C i e ion SC and HQ sugges wo lags; AIK c i e ia indica e 13, LR 15 and FPE 12. To es ima e he model, we used 12 lags since we wo ked wi h mon hly da a. A decision based on Asgha and Abid (2007) ensu es he VAR sys em is s able and ob ains a co ec es ima ion. Addi ionally, hey ound ha he FPE has a 0.85 p obabili y o co ec ly es ima ing wi h 240 sample sizes. Thus, FPE is p e e ed o e o he c i e ia because i pe mi s s abili y and co ec assessmen in ou model. Finally, he oo s o he cha ac e is ic polynomial es show ha no oo lies ou side he uni ci cle. Thus, we conclude ha he VAR model sa is ies he s abili y condi ion (Pesa an and Pesa an, 1997). 3.4 Es ima ion o he VEC model The nex s ep o cons uc ing he VEC model is o e i y ha a iables a e coin eg a ed. Fo ha pu pose, he Juselius–Johansen es pe o ms ou lags o he a iables ln(M), ln(GDP), ln(PM) and ln(P.D.), and i assumes in e cep (Model 3); VEC model allows o a linea de e minis ic end. Included obse a ions: 227 a e adjus men s. T end assump ion: Linea de e minis ic end. Lags in e al (in i s di e ences): 1 o 12. The esul s sugges wo s a is ics o de e mine he numbe o coin eg a ion ec o s: he ace s a is ic and he p oo o he maximum eigen alue (Johansen and Juselius, 1990). The c i ical alues app op ia e o he es a e hose gi en by Os e wald-Lenum (1992). Finally, he null hypo hesis and al e na i e a e es ed using hese s a is ics (Table 4). The hypo hesis o a no-coin eg a ion can be ejec ed a leas a 0.05 P ob. Thus, acco ding o Johansen’s coin eg a ion es , he model has a coin eg a ion equa ion. The p esence o a leas one ela ion coin eg a ion be ween he a iables in le els jus i ies using a VEC model, combining he sho - e m p ope ies o economic ela ionships wi h long- e m da a in o ma ion in he o m o a le el p o ided by he Johansen es . The nex s ep is o es ima e a VEC and hen concen a e on he i s equa ion: Δy ¼β0þX N i¼1 βiΔy −iþX N i¼1 δ1;iΔx1; −iþþX N i¼1 δj;iΔxj; −iþX M i¼1 θiDiþwZ −1þ μ (4) Va iable De ini ion Mean S anda d de ia ion Minimum Maximum Ln (M) To al impo s 10.22069 0.21075 9.83677 10.59288 Ln (GDP) G oss Domes ic P oduc 11.52701 0.12325 11.33623 11.73186 Ln (PM) P ice o impo s 0.14111 0.15236 0.40657 0.03367 Ln (PD) Domes ic p ices 0.13390 0.09224 0.36386 0.06393 Sou ce(s): Own elabo a ion Table 1. Desc ip i e s a is ics o s udied a iables Es ima ion o impo demand unc ion 377 whe e yis he dependen a iable in he i s equa ion o he VEC, a iables xi,i51,...,4 appea as dependen on he o he equa ions o he VEC, bu as independen in he i s equa ion, Dia e exogenous a iables o all he VEC and Z −1is he esidual o he coin eg a ion equa ion. The e o -co ec ion e m, w, is ela ed o he de ia ion o he las pe iod o he long- e m equilib ium ( he e o ). The e o e, i in luences he sho - e m Se ies Le els Fi s di e ence In e cep T end and in e cep None In e cep T end and in e cep None ln (M) 1.340899 3.087814 1.192696 9.212733 9.195900 9.121987 ln(GDP) 0.127110 3.095650 2.847940 15.39461 15.37598 14.92836 ln(PM) 1.348340 1.224444 2.222534 5.681698 5.763045 5.348924 ln(PD) 2.964677 2.929914 1.896442 12.01026 11.99558 12.03028 No e(s): The c i ical alues o he Augmen ed Dickey–Fulle es o in e cep , end, and in e cep and none a signi icance le els o 1, 5 and 10% a e, espec i ely: 3.457984, 2.873596, 2.573270; 3.997418, 3.428981, 3.137946; 2.574797, 1.942176, 1.615803 Sou ce(s): Own elabo a ion Endogenous a iables: ln(M), ln(GDP), ln(PM) and ln(PD) Lag LogL LR FPE AIC SC HQ 1 2377.514 NA 3.75e-15 21.86587 21.61585 21.76486 3 2517.411 127.7568 1.38e-15 22.86491 22.11485* 22.56189* 12 2673.873 37.45154 1.27e-15* 22.98030 19.98006 21.76820 13 2689.911 24.35481 1.28e-15 22.98066* 19.73039 21.66754 15 2720.349 26.98793* 1.32e-15 22.96619 19.21588 21.45106 No e(s): * indica es lag o de selec ed by he c i e ion LR: sequen ially modi ied LR es s a is ic (each es a 5% le el); FPE: Final p edic ion e o ; AIC: Akaike in o ma ion c i e ion; SC: Schwa z in o ma ion c i e ion; HQ: Hannan–Quinn in o ma ion c i e ion Sou ce(s): Own elabo a ion Figu e 4. Va iables included in he model Table 2. Augmen ed Dickey– Fulle es Table 3. VAR lag o de selec ion c i e ia JEFAS 28,56 378 dynamics o he dependen a iable (s anda d VEC es ima ion can be seen in Be asaluce and Rome o, 2022). Thus, he coe icien wmeasu es he speed o adjus men o which he ln(M) a iable e u ns o equilib ium a e a change in he independen a iables. 4. Resul s As a esul o he es ima ion o Equa ion (4),Table 5 shows he long- e m ela ionship. The adjus ed R 2 is 0.67, abo e 50%, so we ha e a good i . We also ind ha he i s e m o e o co ec ion, w, has he expec ed sign and is signi ican : 0.622, (0.141), [4.398]; his implies ha he model e u ns o i s equilib ium le el a e o 62.2% pe mon h. The ac ha w is less han one, s a is ically signi ican and he expec ed nega i e sign con i ms a long- e m join causali y o all independen a iables owa ds impo s. Also, all es esul s p esen ed in Table 6 conclude ha he model es ima ion is e icien . Fu he mo e, he long- e m pa ame e s o he dependen alues a e signi ican and ha e he expec ed signs acco ding o Equa ion (3). The subsequen diagnosis o he esiduals consis s o h ee pa s: (a) an au oco ela ion es , (b) a he e oscedas ici y es and (c) a no mali y es . Fo he B eusch–God ey au oco ela ion es wi h h ee lags, he p obabili y is 10.7% highe han he equi ed 5%. The e o e, a null hypo hesis is accep ed, and he model has no se ial co ela ion in he esiduals a he 5% con idence le el. Hypo hesized no. o CE(s) T ace Maximum eigen alue T ace s a is ic C i ical alue P ob** Max-Eigen s a is ic C i ical alue P ob None 59.85346 47.85613 0.0025* 33.10555 27.58434 0.0088* A mos 1 26.74790 29.79707 0.1079 21.41346 21.13162 0.0457* A mos 2 5.334449 15.49471 0.7723 4.042296 14.26460 0.8549 A mos 3 1.292154 3.841466 0.2557 1.292154 3.841466 0.2557 No e(s): T ace es indica es one coin eg a ing eqn(s) a he 0.05 le el * deno es ejec ion o he hypo hesis a he 0.05 le el Sou ce(s): Own elabo a ion M −1510.791 þ1:825 lnðGDPÞ −1 −0:187 lnðPMÞ −1þ0:401 lnðDPÞ −1 (0.099) (0.087) (0.071) [18.439] [2.136] [5.679] No e(s): *S anda d e o s in () and -s a is ics in [ ]. All he coe icien s a e signi ican and ha e he expec ed signs Sou ce(s): Own elabo a ion Sample (adjus ed): 2001 M02 2019 M12 Me hod: LS (Gauss–New on/Ma qua d ) s eps D(lnM)5C(1)*(lnM(1) 1.8250*lnGDP(1) þ0.1865*lnMP(1) 0.40134*lnDP(1) þ10.7914) Adjus ed R-squa ed 0.671075 Akaike in o c i e ion 3.588224 S.E. o eg ession 0.036556 Schwa z c i e ion 2.833830 Sum squa ed esid 0.236530 Hannan–Quinn c i e ia 3.283815 Log-likelihood 457.2634 Du bin–Wa son s a 2.011451 F-s a is ic 10.40992 P ob(F-s a is ic) 0.000000 Sou ce(s): Own elabo a ion Table 4. Un es ic ed coin eg a ion ank es Table 5. Coin eg a ion equa ion* Table 6. P incipal esul s VEC lnM, lnGDP, MP and lnDP Es ima ion o impo demand unc ion 379