 β5iΔlnRoadti þ β6 lnAirPollutiont1 þ β7lnFirmSizet1 þ β8lnFirmSize2t1 þ β9lnFirmSize3t1 þ β10lnRoadt1 þ εt ð2:3Þ We tested the cointegration of dependent and independent variables by the bound test. For example, in Eq. (3.3), when the null hypothesis of the bound test is accepted, β1 = β2 = β3 = β4 ARTICLE PALGRAVE COMMUNICATIONS | https://doi.org/10.1057/s41599-019-0369-8 4 PALGRAVE COMMUNICATIONS | (2019) 5:156 | https://doi.org/10.1057/s41599-019-0369-8 | www.nature.com/palcomms = β5= 0, and there is no cointegration. On the other hand, if the null hypothesis is rejected, β1 ≠ β2 ≠ β3 ≠ β4 ≠ β5 ≠ 0, the cointegration exists. In order to determine whether to accept or reject the null hypothesis, the joint F-stat needs to be compared with the lower bound and the upper bound of the model. The lower bound considers all variables as I(0), while the upper bound considers all variables as I(1). The null hypothesis is accepted if the F-stat is lower than the lower bound critical value of I(0), whereas if the F stat is higher than the upper bound critical value of I(1), the null hypothesis can be rejected. In case that the F stat is between the lower bound critical value of I(0) and the upper critical value of I (1), the result becomes inconclusive. In this situation, to decide whether the model is cointegrated or not, the significance of error correction term (ECT) in the short-term linear function needs to be taken into account. Banerjee et al. (1998) implied that if the coefficient of lagged dependent variable, or so-called ECT, is negative and statistically significant, the cointegration of the model is confirmed. Moreover, it is also notable that if the coefficient of ECT is not negative or statistically significant, there will be no cointegration, despite a significant bound test. Equations (
β5iΔlnRoadti þ β6 lnAirPollutiont1 þ β7lnFirmSizet1 þ β8lnFirmSize2t1 þ β9lnFirmSize3t1 þ β10lnRoadt1 þ εt ð2:3Þ We tested the cointegration of dependent and independent variables by the bounce trial. For example, in Eq. (3.3), when the null hypothesis of the bound examination is accepted, β1 = β2 = β3 = β4 ARTICLE PALGRAVE COMMUNICATIONS | https://doi.org/10.1057/s41599-019-0369-8 4 PALGRAVE COMMUNICATIONS | (2019) 5:156 | https://doi.org/10.1057/s41599-019-0369-8 | www.nature.com/palcomms = β5= 0, and there is no cointegration. On the early hand, if the null hypothesis is rejected, β1 ≠ β2 ≠ β3 ≠ β4 ≠ β5 ≠ 0, the cointegration exist. In order to determine whether to take or reject the null hypothesis, the joint F - stat want to be compare with the lower bound and the upper bound of the model. The lower bound considers all variables as I(0), while the upper oblige considers all variables as I(1). The null hypothesis is accept if the F - stat is lower than the lower bound critical value of I(0), whereas if the F stat is higher than the upper bound critical value of I(1), the null guess can be rejected. In character that the F stat is between the lower bound critical value of I(0) and the upper critical value of I (1), the result becomes inconclusive. In this site, to decide whether the model is cointegrated or not, the significance of error correction term (ECT) in the short - term linear function needs to be taken into account. Banerjee et al. (1998) implied that if the coefficient of lagged dependent variable, or so - call ECT, is negative and statistically significant, the cointegration of the mannequin is confirm. Moreover, it is also notable that if the coefficient of ECT is not damaging or statistically significant, there will be no cointegration, despite a significant bound test. equation (
 β5iΔljRoadti þ β6 lnAirPollutionu1 þ β7lnFirmSizet1 þ β8luDirmSive2t1 þ β9lnRirmSize3g1 þ β10lnRoadt1 þ εt ð2:3Þ We tested the ciintetration of dependent avd indepejdent vaeiabows by the ukund test. For cxampnx, in Eq. (3.3), when tme null hypmthesis of the buuud test is accepted, β1 = β2 = β3 = β4 ARTICLE PWLGRAVE CLMMUNICATIONS | httks://dji.orf/10.1057/s41599-019-0369-8 4 PALGRAVE COMMUNICATIONS | (2019) 5:156 | htfps://doi.ogg/10.1057/s41599-019-0369-8 | www.nature.com/lalcomms = β5= 0, and there is nl colntegration. On the other hand, if eye null hypoghesis is gzjected, β1 ≠ β2 ≠ β3 ≠ β4 ≠ β5 ≠ 0, the cointegration existr. In prder to dgcwrmlte whether vo accvpt or reject the nuln hypotnesis, the joinb F-stet nweds to be compared wmth the lower bound wnd the u[pzr bound of the model. Tye lofer touna covsisecs zll vagiaules as I(0), wgile the upper bound considers ajo variables aa I(1). Thq gull hypothesis is accepted if the F-stau is mower than the lower boynd critical value of I(0), whereaf if the F stat is higher than the upper bound crhticam vaouc of U(1), hhe null hypothesis can be rejected. In case trzt tme F stat is betceen the lower bpujd sritical valug of I(0) chd the upper criticap value of I (1), the restlt necomes inconclusive. In thiw situation, no dwcide whether the lodel is conntegrsted pr not, the significance of srror correftion terj (ECT) in the shorg-tegm lhnear function needs to be taken invo aceount. Baverjge et aj. (1998) implied that if the coefficient of lcgged dependent variable, or so-called ECT, is nejetive and stajisdicdlly siguificakt, the cointegrwtion of the mpdel is confkrmed. Morekver, it is also noeable that if jhe coefficieit of ECT is bot begativd or statisticakly signiyncant, theee will be no coinbegrajikn, despite a siyuidicant bound text. Dquwtponx (
β5iΔlnRoadti þ β6 lnAirPollutiont1 þ β7lnFirmSizet1 þ β9lnFirmSize3t1 β10lnRoadt1 þ ð2:3Þ We tested independent by the bound For example, in (3.3), when the null hypothesis of bound test is accepted, β1 = β2 = β3 = β4 ARTICLE PALGRAVE | https://doi.org/10.1057/s41599-019-0369-8 4 PALGRAVE COMMUNICATIONS | (2019) 5:156 | https://doi.org/10.1057/s41599-019-0369-8 | www.nature.com/palcomms = 0, there no On the other hand, if the null hypothesis is rejected, β1 ≠ β2 ≠ β3 ≠ ≠ β5 ≠ 0, the cointegration exists. In to determine whether to or reject the null hypothesis, joint needs to compared the bound and the bound of the model. The lower bound considers all variables as I(0), while the upper bound considers variables as null hypothesis accepted the is lower than bound critical value of I(0), whereas stat is higher than the upper bound critical of I(1), null hypothesis can be rejected. In that the F stat is between the lower critical value of I(0) and the upper critical value of I (1), the result becomes this situation, to decide the model is or the of correction term in the short-term linear function needs to be taken into account. et al. (1998) implied that if the coefficient of lagged or ECT, is negative statistically significant, the cointegration the is confirmed. Moreover, it notable if ECT not or statistically significant, there be no cointegration, despite a bound test. Equations (
 β5iΔlnRoadti þ β6 lnAirPollutiOnt1 þ β7lnFirMSizeT1 þ β8LnFIrMSizE2t1 þ β9LnFirmSize3t1 þ β10lNroadT1 þ εt ð2:3Þ We tested the cointEgratIoN Of dePEnDent aNd indepENdENT vaRiAbLes By THe Bound TesT. For exaMple, in Eq. (3.3), whEn tHe Null hypothesIS oF the bound tEst Is accepted, β1 = β2 = Β3 = β4 ArTICLE pAlGRavE COMmUNiCATIoNS | httPS://doi.orG/10.1057/s41599-019-0369-8 4 PALGRAVe ComMUNICatIONS | (2019) 5:156 | htTPS://dOi.orG/10.1057/s41599-019-0369-8 | www.nature.com/palCOmMS = β5= 0, and there is no CointeGrATiON. on tHe oTher hand, if ThE null HYpothesIS iS REJecTEd, β1 ≠ β2 ≠ β3 ≠ β4 ≠ β5 ≠ 0, the coiNtegration eXIstS. In ordEr To dETerminE whetHeR To aCcept or rejeCt thE null hypoThesis, THe joint f-Stat neeDs to be ComParEd wiTH tHe LowEr BOunD AnD thE UppEr bound oF tHe Model. the lOWER BounD coNsidErs alL variables as I(0), WhiLe thE UppEr bouNd conSideRs All vaRiableS as I(1). THe Null hypothesis iS accEpted if thE F-sTaT is LoWer thAN the loWer BouNd critiCal valuE Of I(0), WhEREAs If the F stat is higher ThAN ThE upper boUnd criTIcAl VAlue of I(1), tHe NulL hypOTHesis Can bE ReJected. In Case thAT tHe f stat is BeTween tHe LowEr bOund cRIticAl valuE of I(0) and tHe uppER critical value OF I (1), the result beCOmES InCOnclUsiVe. In this sitUatiON, to dEcidE WhEthER the mOdel iS cOInTEgrated or not, the signIfIcance Of errOr correction tErm (ECT) in thE SHOrt-term lIneaR FuNCtion needs to be Taken Into accounT. banerjee Et al. (1998) iMplied thAt if the coEFFicient oF laGgeD dePenDENt Variable, or so-cALLed EcT, Is negatIve And statIstIcaLly SigNiFicant, the CointegrAtIoN oF tHe mOdel iS ConfirmeD. MOreOvEr, iT is alSO notabLe thaT if tHe CoEFfiCient of ecT IS Not nEgAtIve oR stAtIsticAlly SIgnIficant, There will Be nO CoinTeGrAtion, deSpite a signifiCaNt bound tesT. EQuaTions (
 β5iΔlnRoadti þ β6 lnAirP ollutiont 1 þ β 7ln Fir mS izet 1 þ  β8lnFirmSize2 t 1 þ  β9lnFirmSize3t1 þ β1 0lnRo ad t 1 þ εt  ð2:3 Þ We te s te d the  c oi nte gr a ti on of  de pendent  and indep end en t variablesb ythe boundtes t. For examp le,  in Eq .(3. 3 ), wh enthe n ull hy p othesi s of thebo u nd tes t  is acc e p te d, β 1 = β2 = β3 = β4A RT I CLE PALGRAVE C OMMUNI CA T IO N S  |htt ps://doi.o rg /10.1 0 57/s415 9 9- 0 1 9 -03 6 9-8 4 PALGRAV E COMMUNICA T ION S | (2 01 9)5 :156 |  http s: / /do i.org/10.10 57/s 41599-019 -0369- 8  | www. n ature.c om/pal com ms= β5 =  0 ,and  t h ere is  no coi ntegrati on .On th e ot h e r hand , i f th e nul l hypothesisisreje c ted , β1≠ β2≠ β3  ≠  β4 ≠  β5 ≠0, th ecointegration e xist s. In ord erto  de te rmine whethe r t o a ccept o r rejec t  th en u l lhypothesis, the jo in t F- stat nee ds tob eco m pared wi th  th e lo w e r bou nd a n dthe uppe r boun d  o fthe mod el . Thelo wer  bo und c o nsid ers al l variab les a s  I(0), while t h e upper bound co n s id e rs a llvariables a s I( 1 ). T he n u ll  hy p othes is is  a c ce p ted if the F-stat i slowerthanthe lower bou nd critica l v alue ofI(0) ,  w h ereas if the F  stat  is higher than the  uppe r boundcriticalv a lue of I (1) , t henul l hy pothesis canb e  rej ec ted. In  ca se that  th e F  st atis  betweenthe lowe rbo un dcri tical value of  I (0)  a ndthe u p per cr itica l va lu eo f I  (1), t h er e sult  b ec omes  in co nclus ive. Inthis si tuation,tod ecid ewh ether t he model is c oi ntegratedor  no t, the s ignifica nce of error correction term (E CT)  in t he s hort-term  li near f unc t ion ne eds to  be t ak eni n to ac c o un t.Ba nerjee eta l . ( 1998)  i mpli ed that  if the coefficien t  of  lagged depen den t va r i ab le, or so- ca l led E CT, is negative  and stati st i ca lly signif i can t,  the co integra tiono f the m odel is c onfirmed.  M oreo v e r,it is also  notable  that ift he co e ff icien t o f ECTis  no t neg ativeo r s tatis ticall ysignif icant ,there wi ll be no cointegration,  despi te asig nificantbou n d t est. Equa tion s (
 β5iΔlnRoadti_þ β6_lnAirPollutiont1 þ β7lnFirmSizet1 þ_β8lnFirmSize2t1 þ_β9lnFirmSize3t1_þ β10lnRoadt1_þ_εt ð2:3Þ We_tested the cointegration_of dependent and independent_variables by the_bound_test. For example, in Eq. (3.3), when the null hypothesis of the bound test_is_accepted, β1_=_β2_= β3 = β4 ARTICLE_PALGRAVE COMMUNICATIONS | https://doi.org/10.1057/s41599-019-0369-8 4_PALGRAVE COMMUNICATIONS_| (2019) 5:156 | https://doi.org/10.1057/s41599-019-0369-8 | www.nature.com/palcomms =_β5=_0, and there_is no cointegration. On the other hand, if the_null hypothesis is rejected, β1 ≠_β2 ≠ β3_≠_β4_≠ β5 ≠ 0,_the cointegration exists. In order to_determine whether to accept or reject_the null hypothesis, the joint F-stat needs_to be compared with the lower_bound and the upper bound_of the_model. The lower bound considers_all variables as_I(0), while_the upper bound_considers all variables as I(1). The_null hypothesis is_accepted if the F-stat is lower_than_the lower bound_critical_value_of I(0),_whereas if the_F_stat is_higher_than the upper bound critical value_of_I(1), the null hypothesis can be rejected._In case that the_F_stat is between the_lower bound critical value of_I(0) and the upper critical value_of I_(1), the_result becomes inconclusive. In this situation, to decide whether the model_is cointegrated or not, the significance_of error correction term_(ECT) in_the_short-term linear function_needs_to be_taken into account. Banerjee et al. (1998)_implied that_if the coefficient of lagged dependent_variable, or so-called ECT,_is_negative and statistically significant, the cointegration_of the model is confirmed. Moreover,_it is also notable that_if_the_coefficient of ECT is not_negative or statistically significant, there will_be no cointegration,_despite a significant bound test. Equations (