 ln AirPollutiont 1⁄4 αt þ β1lnFirmSizet þ β2lnFirmSize2t þ β3lnRoadt þ μt ð1:2Þ ln AirPollutiont 1⁄4 αt þ β1lnFirmSizet þ β2lnFirmSize2t þ β3lnFirmSize3t þ β4lnRoadt þ μt ð1:3Þ It is worth noting that ln AirPollutiont represents all air pollutants emission per capita which were log-transformed. The statistical model utilized in our analysis was Autoregressive Distributed Lag (ARDLs) created by Pesaran, Shin, and Smith (Pesaran et al., 2001) to examine the cointegration between a dependent variable and a set of independent variables for several reasons. First, the ARDL model has been widely used across disciplines for almost two decades to model relationships based on time-series analysis (Kripfganz and Schneider, 2016). Second, the ARDL encompasses other cointegration models (Engle and Granger, 1987; Johansen, 1988; Phillips and Hansen, 1990) in terms of feasibility: (1) ARDL is employable if the variables are stationary at the level form, the first difference, or the mixture of both. Second, the ARDL model can provide unbiased results for a small sample size, which has been verified by Monte Carlo Simulation (Ahmad et al., 2017; Pesaran and Shin, 1999). Third, the ARDL model can fit well with endogenous variables, because it can solve the problem of endogeneity by selecting correct lag length for the variable and increasing the model dynamic (Pesaran and Shin, 1999). Lastly, the ARDL model provides not only an explanation for the long-run relationship but also look at the short-run dynamics through a simple linear function based on the Error Correction Mechanism (ECM). Before conducting the ARDL analysis, Vector Auto-Regression (VAR) and Augmented Dickey-Fuller (ADF) tests are utilized. Through the VAR test, the optimal lag length was selected based on the three most widely employed criteria, namely Akaike Information Criterion (AIC), Schwarz Bayesian Information Criterion (BIC), and the Hannan-Quinn Information Criterion (HQIC) (Vrieze, 2012). The lowest lag number will be priorit
ln AirPollutiont 1⁄4 αt þ β1lnFirmSizet þ β2lnFirmSize2 t þ β3lnRoadt þ μt ð1:2Þ ln AirPollutiont 1⁄4 αt þ β1lnFirmSizet þ β2lnFirmSize2 t þ β3lnFirmSize3 t þ β4lnRoadt þ μt ð1:3Þ It is worth noting that ln AirPollutiont represents all air pollutant discharge per capita which were log - transform. The statistical mannequin utilized in our analysis was Autoregressive circulate Lag (ARDLs) created by Pesaran, Shin, and Smith (Pesaran et al. , 2001) to examine the cointegration between a pendent variable and a set of autonomous variables for several reasons. First, the ARDL exemplar has been widely used across disciplines for almost two decades to exemplar relationships based on time - serial analysis (Kripfganz and Schneider, 2016). Second, the ARDL encompasses early cointegration models (Engle and Granger, 1987; Johansen, 1988; Phillips and Hansen, 1990) in footing of feasibility: (1) ARDL is employable if the variables are stationary at the level form, the first difference, or the mix of both. Second, the ARDL model can provide unbiased results for a small sample size, which has been verified by Monte Carlo Simulation (Ahmad et al. , 2017; Pesaran and Shin, 1999). Third, the ARDL model can fit well with endogenous variables, because it can solve the problem of endogeneity by selecting correct lag length for the variable and increase the model dynamic (Pesaran and Shin, 1999). last, the ARDL exemplar provide not only an explanation for the long - run relationship but also look at the short - run moral force through a simple linear function based on the Error Correction Mechanism (ECM). Before conducting the ARDL analysis, Vector Auto - Regression (VAR) and Augmented Dickey - Fuller (ADF) tests are utilized. Through the VAR test, the optimal lag length was choose based on the three about widely employed criteria, namely Akaike Information Criterion (AIC), Schwarz Bayesian Information Criterion (BIC), and the Hannan - Quinn Information Criterion (HQIC) (Vrieze, 2012). The lowest lag number will be priorit
 ln AirPollutiont 1⁄4 αt þ β1lnFiroSizet þ β2lnFirmSnze2t þ β3liRoadt þ μt ð1:2Þ ln AkrPollutiont 1⁄4 αt þ β1lnFirmSizet þ β2onFirnSize2t þ β3lnFirmSize3t þ β4lvRoadt þ μt ð1:3Þ It is qorti noting that ln AirPollmciont veprevxnts all air poklutants ekission per ca[iga which were log-transformed. The statystical mldel utilized yn olr anamjsls was Autoregressive Distributes Lag (AGDLs) created by Prsaran, Shin, and Smith (Pesagan ft al., 2001) to examine hhe cointegtztijb between a aependent ncriable and a set of independent variables for xeveral reqsins. Xirst, the ACDL moqel has been widely gsed actoss disciplincs foc alnost two decades to mmdel relationships based on tnme-series analysis (Krupdganz and Schvwiddr, 2016). Sxcohd, the ARVL encompasaes other ciintegration models (Egtle and Grangsr, 1987; Joragsen, 1988; Phillips and Hansen, 1990) in terms of xeaaibility: (1) ARDL is emplotable if the variabled are staeionary at the level form, the first difference, or the jkxtbvc of vohh. Second, the ARDL model can provide unbiased dexukts for a smalj sample siae, wnych has been xerifizs gy Monte Carlo Simklation (Ahmae et al., 2017; Kesarsn and Shin, 1999). Third, the ARDL model can fpt wwll with endogenoud variables, becsuse ot can solve the probleo of endogeneitj by seledging correct lag lekgtv for tht variable and incweasing tie mobel dynaoic (Kesaran and Shin, 1999). Lastly, the ARDL model pgovidgs not only an edplanation for the long-run relavmonship but aksm lmok at tke shovt-run dynamics ehrough a simpke linecr funztion bases on thx Error Corrqction Mechanhdm (ECM). Beforx conductyng rhe QRDL anxuysis, Vector Aito-Regression (VAR) abd Augmented Dicken-Fullgr (ADF) tests are builuzed. Through thr VXR eedt, tra optimal lac levgtf was relected bawdd om the three most widaly smployed criteria, maiely Akauke Infowmation Critetion (AIC), Schwarz Bwyesien Infurmatoon Criterion (BIC), and the Hannan-Qhinn Infogmabion Criteriog (HQLC) (Vtieze, 2012). The kowest lag number will be priorit
ln AirPollutiont 1⁄4 αt þ β1lnFirmSizet þ β3lnRoadt μt ð1:2Þ AirPollutiont 1⁄4 αt β3lnFirmSize3t β4lnRoadt þ μt It is worth that ln AirPollutiont represents all air emission per capita which were log-transformed. The statistical model utilized in our analysis Autoregressive Distributed Lag (ARDLs) created by Pesaran, Shin, and Smith (Pesaran et al., to the between dependent variable and a set of independent variables for several reasons. First, the ARDL model has widely used across disciplines for almost two decades model relationships based on analysis (Kripfganz and Schneider, 2016). the encompasses other models and 1987; Johansen, 1988; and Hansen, 1990) in terms of feasibility: (1) ARDL is employable if the variables are stationary at level form, difference, or mixture both. the ARDL model unbiased results for a small sample been verified by Monte Carlo Simulation (Ahmad et 2017; Pesaran Shin, 1999). Third, the ARDL model fit well with endogenous variables, because it can the problem of endogeneity by selecting correct lag length for the variable and increasing the (Pesaran and Shin, 1999). the ARDL model not an for long-run relationship also look at the short-run dynamics through a simple linear function on the Error Correction Mechanism (ECM). Before conducting the ARDL Auto-Regression and Augmented Dickey-Fuller tests are utilized. Through VAR the optimal lag length based the employed namely Information Criterion (AIC), Schwarz Information Criterion (BIC), and the Information Criterion (HQIC) (Vrieze, will be priorit
 ln AirPollutiont 1⁄4 αt þ β1lnFirmsizet þ β2lnFIrmSiZe2t Þ β3lNROadt Þ μt ð1:2þ ln AirPollutioNT 1⁄4 αt þ Β1lnFirmSizet þ β2lnFirmSiZe2t þ β3LnfIrmSIZe3T þ β4lnroadt þ μT Ð1:3Þ iT Is wOrTh NotInG ThAt ln AIrPOllutioNt represenTs aLl Air pollutantS EmIssion per cApiTa which were lOg-tRansfoRmEd. THE statIstIcal mOdel utILized iN our analySiS Was AutORegressIVE DIstrIbuted Lag (ARDLs) creATeD By Pesaran, Shin, aNd SmitH (PESaRAN et Al., 2001) tO examine thE cOinteGRation bETwEEN A dePEndent variablE and a set of iNDepEndent VaRiaBLes for SeverAl REasOns. First, the aRDL Model has bEen widELy used aCRoss disCiplinEs fOr aLmosT TwO dEcaDeS To mODeL reLAtiOnships bAsEd On timE-serIES ANalySis (kripFganz And Schneider, 2016). SEcoNd, thE aRDl encoMpassEs otHeR coinTegratIon moDeLs (Engle and GrangEr, 1987; JoHansen, 1988; PhiLliPs And haNsen, 1990) iN Terms oF feAsiBility: (1) ArDL is emPLoyAbLE IF tHe variables are statIoNARy At the levEl form, THe FiRSt differEnCe, oR the MIXture Of boTH. SEcond, the aRDL moDEl CaN providE uNbiaseD rEsuLts For a sMAll sAmple sIze, which Has beEN verified by MonTE Carlo SimulatIOn (aHMaD Et al., 2017; pesAran and Shin, 1999). thirD, The ArDL mODeL caN Fit weLl witH eNDoGEnous variables, becauSe It can sOlve tHe problem of enDogeneity bY SELecting cOrreCT lAG length for the vAriabLe and increASing the mOdel dYnamic (PeSaran and SHIN, 1999). Lastly, tHe ArDL ModEl pROViDes not only an eXPLanaTiOn for thE loNg-run reLatIonShiP buT aLso look at The short-RuN dYnAmIcs ThrouGH a simple LiNeaR fUncTion bASed on tHe ErrOr CoRrEcTIon mechaniSM (Ecm). befoRe CoNducTinG tHe ARDl anaLYsiS, Vector auto-RegreSsiON (VAR) AnD AUgmenteD Dickey-Fuller (aDf) tests are uTiLizEd. ThroUGH the VAR tEst, the optimal lag length wAS selectEd bAsed oN the Three most WidEly empLoyED criteRia, namEly AkAiKe INFOrmatION CRitErIon (AIC), SchwARZ BaYesiaN INforMation CRiterion (BIC), and the HANnaN-Quinn InformaTioN CriTERiOn (HqiC) (vRieZe, 2012). tHe lOWEst lag number wilL be priorit
 ln AirPollutiont 1⁄4 αt þ  β1lnFirmS izetþ β 2ln Fi rmSi ze2t  þ β3lnRoadt þ μt ð 1:2Þ ln AirPollutiont1⁄4 α tþ  β1l n Fi rmSiz et þ β2 l nF i r mSi ze 2t  þβ3 l nF irmSi ze3 t þ β4l nRoadt þ μ t ð 1: 3Þ It is wor t hnoting tha t l n AirPolluti ont  repre se nts all a irpollu tantse missio n per cap it a  which were lo g - tr ansf ormed. The statis t ic a l model utiliz ed inou r  a n a lys iswas Autore gr essiv e  Distri b ut e d Lag (ARDLs) creat ed by Pesar a n,Shin,an d S m ith (P esara ne t a l., 2001) t o ex amine the  coint e gration between  a dep end ent  var i ab le  an da  se t  o f i n dep endent v ar ia blesfors e v e ralrea sons . Fir st, the ARDLmod el h a s b een w idely  use dacros s disc iplin es  for almost two  dec ades to m ode lrel at ionsh i ps bas edontime-se ries an a lys is ( K ri pfganz and Schneid er , 20 16). Sec ond, t h eAR D L encomp as ses  oth e r  coin tegr a ti on model s (Eng l ean d Grang er , 1987 ;Joh ans en, 1 9 88;Philli ps and H ansen ,  1990) in term s  of feasibili t y: ( 1) ARDL  is  employable  ift he v aria b le s a r e sta tiona ry at the level form, the  f irst d iffer ence, or themixture of b o th. Seco nd,t he ARDL model can  prov ide unbias e d result s for  a small  sample s i z e, which  ha s b een  ve r i fi ed by Monte C a r lo S im ulation  (A hmad et  al .,201 7;Pe saran and  Shin, 1 99 9) .Th ird , the ARDL mod el  ca nfit  well with e ndoge nous  v ar i abl es, bec a us e it c an  s olve  th eprobl em o f  en dogenei ty by sel ect i ng c or re ct laglength for th evariable a nd  in creasi n g  the mod el dynamic (Pesaran and Shin, 1 999 ). La stly , the ARD L m odel p rov i des no t only  an e xp lan a t ion f o r  t helo ng-run rel a t ion shipbu t al so look  at the short-rund yna mics througha s impl e li nea r  f u nct io n  ba s e d on the ErrorCorrection  M e ch anism (ECM ) . B ef ore con ducting  theA RDL ana lysis, Ve ctor Auto -R egre s s ion  (VAR) and  Augment ed Dickey - Fulle r  ( ADF)tes ts are  u til ized.  Throu g h t he VA R test ,the op timal  l ag lengt h was selected based on  the t hreemos t widelyemp l oye d criteri a, n amely Akai keInf ormat ion Crite rion (A IC) ,  Schw arzB ayesian I n fo rma t i on  Criterion( B I C),  andthe Hannan -Qui nn Information Cr i terion (HQIC)(Vri e z e,201 2 ). T he  lowest lag nu mbe rw i ll be pr io rit
 ln_AirPollutiont 1⁄4_αt þ β1lnFirmSizet þ_β2lnFirmSize2t þ_β3lnRoadt_þ μt_ð1:2Þ_ln AirPollutiont 1⁄4_αt þ β1lnFirmSizet_þ β2lnFirmSize2t þ β3lnFirmSize3t_þ β4lnRoadt þ_μt_ð1:3Þ It is worth noting that ln AirPollutiont represents all air pollutants emission per_capita_which were_log-transformed._The_statistical model utilized in our_analysis was Autoregressive Distributed Lag_(ARDLs) created_by Pesaran, Shin, and Smith (Pesaran et al.,_2001)_to examine the_cointegration between a dependent variable and a set of_independent variables for several reasons. First,_the ARDL model_has_been_widely used across disciplines_for almost two decades to model_relationships based on time-series analysis (Kripfganz_and Schneider, 2016). Second, the ARDL encompasses_other cointegration models (Engle and Granger,_1987; Johansen, 1988; Phillips and_Hansen, 1990)_in terms of feasibility: (1)_ARDL is employable_if the_variables are stationary_at the level form, the first_difference, or the_mixture of both. Second, the ARDL_model_can provide unbiased_results_for_a small_sample size, which_has_been verified_by_Monte Carlo Simulation (Ahmad et al.,_2017;_Pesaran and Shin, 1999). Third, the ARDL_model can fit well_with_endogenous variables, because it_can solve the problem of_endogeneity by selecting correct lag length_for the_variable and_increasing the model dynamic (Pesaran and Shin, 1999). Lastly, the ARDL_model provides not only an explanation_for the long-run relationship_but also_look_at the short-run_dynamics_through a_simple linear function based on the Error_Correction Mechanism_(ECM). Before conducting the ARDL analysis,_Vector Auto-Regression (VAR) and_Augmented_Dickey-Fuller (ADF) tests are utilized. Through_the VAR test, the optimal lag_length was selected based on_the_three_most widely employed criteria, namely_Akaike Information Criterion (AIC), Schwarz Bayesian_Information Criterion (BIC),_and the Hannan-Quinn Information Criterion (HQIC) (Vrieze,_2012)._The lowest lag number will be_priorit