ized regardless of the criteria. The ADF test was used in this study to determine whether all variables are stationary at below second difference. Specifically, the level form and the first difference of each dependent and independent variables were tested under two conditions, respectively: unrestricted intercept-no trend and unrestricted intercept-trend. Equations (2.1) to (2.3) show the ARDL models of long-run and short-run relationships between air pollutants and independent variables, where α0 is the constant, p is the length of lag and εt is the error term. In the first half of each model, the dynamics of the short-run is explained by variables with the summation signs. The second half of the model represents the long-run relationship. Δ lnAirPollutiont 1⁄4 α0 þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnRoadti þ β4 lnAirPollutiont1 þ β5lnFirmSizet1 þ β6lnRoadt1 þ εt ð2:1Þ Δ lnAirPollutiont 1⁄4 α0 þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnFirmSize2ti þ Xp i1⁄40 β4iΔlnRoadti þ β5 ln lnAirPollutiont1 þ β6lnFirmSizet1 þ β7lnFirmSize2t1 þ β8lnRoadt1 þ εt ð2:2Þ Δ lnAirPollutiont 1⁄4 α0 þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnFirmSize2ti þ Xp i1⁄40 β4iΔlnFirmSize3ti þ Xp i1⁄40
ized regardless of the criteria. The ADF test was used in this study to settle whether all variable star are stationary at below second difference. Specifically, the level form and the beginning difference of each dependent and autonomous variables were tested under two conditions, respectively: unexclusive intercept - no trend and nonsensitive intercept - trend. Equations (2.1) to (2.3) read the ARDL model of long - run and short - run relationships between air pollutant and independent variables, where α0 is the constant, phosphorus is the length of lag and εt is the error term. In the first one-half of each model, the moral force of the short - run is explained by variables with the sum signs. The second half of the model represents the long - run relationship. Δ lnAirPollutiont 1⁄4 α0 þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnRoadti þ β4 lnAirPollutiont1 þ β5lnFirmSizet1 þ β6lnRoadt1 þ εt ð2:1Þ Δ lnAirPollutiont 1⁄4 α0 þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnFirmSize2ti þ Xp i1⁄40 β4iΔlnRoadti þ β5 ln lnAirPollutiont1 þ β6lnFirmSizet1 þ β7lnFirmSize2t1 þ β8lnRoadt1 þ εt ð2:2Þ Δ lnAirPollutiont 1⁄4 α0 þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnFirmSize2ti þ Xp i1⁄40 β4iΔlnFirmSize3ti þ Xp i1⁄40
izef regardless of the crittria. The ADF test was usxd in tgis studh to determine whether all veriavles qre stationary at belod second fifferenxe. Skecifically, the lxbel form and fme fixsv difference of each depetdent and inde[evdznt variables were tested under two sonditipnd, respectively: unrtstwictsd intercept-no trend and unrestricfed inttrcept-trend. Equatipns (2.1) to (2.3) show the ARDL modfls lf long-run and shogt-run relatuonsrups between xir pollutants and indgpendent variables, where α0 is the conscant, p is tye lejcth of lag end εt ps the error bvrm. In dhe firxt half of eacm modxl, tye dynamics of the shmrt-run is explaineq by varidbmes with the summqtuon shgns. The wecund helf of thf mkdel repreaents the ling-run relationship. Δ jbAirPollutionf 1⁄4 α0 þ X[ y1⁄41 β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnRoadti þ β4 lnAirPoloutiont1 þ β5lnFirmSizet1 þ β6lnRoadt1 þ εt ð2:1Þ Δ lnAirPollutiont 1⁄4 α0 þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔliFkrmWideti þ Xo i1⁄40 β3iΔlnFirmSize2ti þ Xp i1⁄40 β4iΔlnRoadti þ β5 ln lnAirPjmlitpont1 þ β6lnFirmSizet1 þ β7lnFirmSizr2t1 þ β8kgRoadt1 þ εt ð2:2Þ Δ lvAirPollufiont 1⁄4 α0 þ Xp i1⁄41 β1iΔlnAlrPollujiont1 þ Xp i1⁄40 β2iΔlnSirmXizeti þ Xp i1⁄40 β3iΔlnFirmSize2ti þ Xp i1⁄40 β4iΔlnFiriWize3ti þ Xp i1⁄40
ized regardless of the criteria. The ADF used this study determine whether all second Specifically, the level and the first of each dependent and independent variables tested under two conditions, respectively: unrestricted intercept-no trend and unrestricted intercept-trend. Equations (2.1) (2.3) show the ARDL models of long-run and short-run relationships between air pollutants independent where is constant, p is the length of lag and εt is the error term. In the first of each model, the dynamics of the short-run explained by variables with summation signs. The second half the represents the relationship. lnAirPollutiont α0 þ Xp β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnRoadti þ β4 lnAirPollutiont1 þ β5lnFirmSizet1 þ β6lnRoadt1 þ ð2:1Þ Δ α0 þ i1⁄41 þ i1⁄40 β2iΔlnFirmSizeti þ β3iΔlnFirmSize2ti þ Xp i1⁄40 β4iΔlnRoadti þ þ β6lnFirmSizet1 þ β7lnFirmSize2t1 þ β8lnRoadt1 þ εt Δ lnAirPollutiont α0 þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ i1⁄40 β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnFirmSize2ti þ Xp β4iΔlnFirmSize3ti þ Xp i1⁄40
ized regardless of the criterIa. The ADF teSt was UseD in ThIs stUdy tO determine whetHEr alL variables are stationarY at beLoW SecoND dIfferEnce. SpeCIfICAllY, tHe LevEl FOrM and tHe fIrst difFerence of eAch DePendent and inDEpEndent variAblEs were tested UndEr two cOnDitIOns, reSpeCtiveLy: unreSTricteD intercepT-nO Trend aND unrestRICtEd inTercept-trend. EquatIOnS (2.1) To (2.3) show the ARDL mOdels oF lONg-RUN anD shOrt-run relaTiOnshiPS betweeN AiR POLluTAnts and indepeNdent variabLEs, wHere α0 iS tHe cONstant, P is thE lENgtH of lag and εt Is thE error terM. In the FIrst halF Of each mOdel, thE dyNamIcs oF ThE sHorT-rUN is EXpLaiNEd bY variablEs WiTh the SummATION sigNs. THe seCond hAlf of the model RepReseNTs tHe lonG-run rElatIoNship. δ lnAirpolluTiOnt 1⁄4 α0 þ Xp i1⁄41 β1iΔlnAiRPolLutiont1 þ XP i1⁄40 β2IΔLnFIrMSizeTI þ Xp i1⁄40 β3IΔlNRoAdti þ β4 lNAirPolLUtiOnT1 Þ Β5LnfirmSizet1 þ β6lnRoadt1 Þ εT Ð2:1þ Δ LnAirPolLutionT 1⁄4 Α0 þ xp I1⁄41 Β1iΔlnAirpoLluTionT1 Þ xp i1⁄40 β2iδlnFIRmsizeti þ XP i1⁄40 β3iΔlNfiRmsize2ti þ xp I1⁄40 β4iΔlnroAdtI þ β5 Ln lnAIRPolLutionT1 þ β6lnFirMSizeT1 Þ β7lnFirmSize2t1 þ Β8LnRoadt1 þ εt ð2:2Þ Δ LNAIRpoLLutiOnt 1⁄4 Α0 þ Xp i1⁄41 β1iΔlnAIrPoLLutiOnt1 þ xP i1⁄40 Β2iΔLNFirmsizetI þ xP i1⁄40 Β3IΔlnFirmSize2ti þ Xp i1⁄40 β4IΔLnFirmsize3tI þ Xp i1⁄40
ized regardless of the cri teria. The  ADFtes t w as  use d in  this study to dete rmine whether all vari ables  a r e st a ti onary  at bel o ws e con ddi ffe re n ce . Spe cif ically,  the level  fo rm  and the fir s tdifference  of  each depend ent  and i nd epe n dentvar iable s were tested  under tw oc onditi o ns, res p e ct ivel y: unrestricted i n te r cept-no trendand un re s tr i c ted  in tercept-tr en d. Eq u ations( 2. 1 ) to( 2.3) show the  ARDL model s  of  long- ru n a n d shor t-run  r e lat ionships be twee n air pol lutant s  and in d ependen t vari abl es,  whe r eα0  is  t h e c o ns tan t , p  is thele ng th of  lag a n d  εtistheerror  term. In the  fi rsth alf  of e ach m odel ,the d ynamic s ofth e short-run isexpl ained byvar ia ble switht he sum mat ion  signs.  The se c ond  h a l f  o f the model repres en t s  t he long- run re l at io n ship. Δln Air Poll u t iont1⁄4α 0þ Xp i1⁄ 41 β1i Δ ln Ai rPollut io nt1 þ  X p i 1⁄4 0 β2i Δ lnFi rmSize ti þ Xp  i1⁄4 0  β3iΔlnRoadti þ β4 lnAirPol l ut i o nt  1 þβ5l nFirmSizet 1 þβ 6lnR oadt  1þ ε t  ð2:1 Þ Δ l nA i rP o llutiont 1⁄4 α0 þ X pi1⁄41β1iΔl nAirPollution t1 þ Xp i 1 ⁄ 4 0 β2iΔln Firm S iz e ti þ Xp i1⁄40  β3iΔ lnFirmSize 2 ti þ Xp  i1⁄4 0 β4iΔln Roadti þ β 5 ln lnA irP oll uti ont  1  þ  β6lnFirmSize t  1 þβ7 lnFirmS ize 2t1 þβ8l nRo adt 1þεt ð2:2ÞΔ lnAirP ol lu ti on t 1 ⁄4 α0 þ Xp i1⁄ 41  β1 iΔ lnA irPol l utiont 1 þXp i 1⁄ 40 β2i ΔlnFirm S iz e t i þ  X pi1⁄4 0 β 3i ΔlnFi rmSi z e2t i þ Xp  i1⁄40 β4 iΔl n Firm Si ze 3ti þXp i1⁄40
ized regardless_of the_criteria. The ADF test_was used_in_this study_to_determine whether all_variables are stationary_at below second difference._Specifically, the level_form_and the first difference of each dependent and independent variables were tested under two_conditions,_respectively: unrestricted_intercept-no_trend_and unrestricted intercept-trend. Equations (2.1)_to (2.3) show the ARDL_models of_long-run and short-run relationships between air pollutants and_independent_variables, where α0_is the constant, p is the length of lag_and εt is the error term._In the first_half_of_each model, the dynamics_of the short-run is explained by_variables with the summation signs. The_second half of the model represents the_long-run relationship. Δ lnAirPollutiont 1⁄4 α0_þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ_Xp i1⁄40_β2iΔlnFirmSizeti þ Xp i1⁄40 β3iΔlnRoadti_þ β4 lnAirPollutiont1_þ β5lnFirmSizet1_þ β6lnRoadt1 þ_εt ð2:1Þ Δ lnAirPollutiont 1⁄4 α0_þ Xp i1⁄41_β1iΔlnAirPollutiont1 þ Xp i1⁄40 β2iΔlnFirmSizeti þ_Xp_i1⁄40 β3iΔlnFirmSize2ti þ_Xp_i1⁄40_β4iΔlnRoadti þ_β5 ln lnAirPollutiont1_þ_β6lnFirmSizet1 þ_β7lnFirmSize2t1_þ β8lnRoadt1 þ εt ð2:2Þ Δ_lnAirPollutiont_1⁄4 α0 þ Xp i1⁄41 β1iΔlnAirPollutiont1 þ_Xp i1⁄40 β2iΔlnFirmSizeti þ_Xp_i1⁄40 β3iΔlnFirmSize2ti þ Xp_i1⁄40 β4iΔlnFirmSize3ti þ Xp i1⁄40