NO2per" and "lnCOper" as dependent variables) (see Table 4). At first glance, the inverted N-shaped relationships of "lnNO2" and "lnCOper" with the average size of industrial firm in Kitakyushu city are confirmed by the NARDL models, but the turning points are slightly different from those provided by ARDL models (see Fig. 2). The turning point of NARDL model of "lnNO2per" is at $8.6 (βlnFirmsize=−20.064, p-value < 0.05, βlnFirmsize2= 9.301, p-value < 0.05, and βlnFirmsize3=−1.441, p-value < 0.05), while that of "lnCOper" are at $7.97 million and $12.62 million (βlnFirmsize=−74.358, p-value < 0.05, βlnFirmsize2= 32.566, p-value < 0.05, and βFirmsize3=−4.707, p-value < 0.05) (Fig. 3). In case of "lnDustper" and "lnOxper", the NARDL models presented U-shaped relationships between air pollution emissions and industrial firm size, but the model of "lnDustper" had an autoregressive conditional heteroskedasticity. The turning points calculated from the NARDL models of "lnDustper" and "lnOxper" are $10.91 million and $9.32 million. The U-shaped relationship Fig. 2 Illustrations of the relationship between the average industrial firm size and air pollutions. 1. The U-shaped relationship between average industrial firm size and the amount of falling dust. 2. The U-shaped relationship between average industrial firm size and the concentration of Ox. 3. The inverted Nshaped relationship between average industrial firm size and the concentration of NO2. 4. The inverted N-shaped relationship between average industrial firm size and the concentration of CO. PALGRAVE COMMUNICATIONS | https://doi.org/10.1057/s41599-019-0369-8 ARTICLE PALGRAVE COMMUNICATIONS | (2019) 5:156 | https://doi.org/10.1057/s41599-019-0369-8 | www
NO2per " and " lnCOper " as dependent variables) (see Table 4). At inaugural glance, the turn back N - shaped relationships of " lnNO2 " and " lnCOper " with the average size of industrial firm in Kitakyushu city are confirm by the NARDL models, but the turning decimal point are slightly different from those supply by ARDL models (see Fig. 2). The turn point of NARDL model of " lnNO2per " is at $ 8.6 (βlnFirmsize=−20.064, p - value < 0.05, βlnFirmsize2= 9.301, p - value < 0.05, and βlnFirmsize3=−1.441, phosphorus - value < 0.05), while that of " lnCOper " are at $ 7.97 million and $ 12.62 million (βlnFirmsize=−74.358, p - value < 0.05, βlnFirmsize2= 32.566, p - value < 0.05, and βFirmsize3=−4.707, phosphorus - value < 0.05) (Fig. 3). In case of " lnDustper " and " lnOxper ", the NARDL model introduce U - shaped relationships between air contamination emissions and industrial firm size, but the model of " lnDustper " had an autoregressive conditional heteroskedasticity. The turning point calculated from the NARDL models of " lnDustper " and " lnOxper " are $ 10.91 million and $ 9.32 million. The U - shaped relationship Fig. 2 example of the relationship between the average industrial firm size and air pollutions. 1. The U - shaped relationship between average industrial firm size and the amount of falling dust. 2. The U - shaped relationship between average industrial firm size and the concentration of Ox. 3. The inverted Nshaped kinship between modal industrial firm size and the concentration of NO2. 4. The turn back N - shaped relationship between average industrial firm size and the concentration of CO. PALGRAVE COMMUNICATIONS | https://doi.org/10.1057/s41599-019-0369-8 ARTICLE PALGRAVE COMMUNICATIONS | (2019) 5:156 | https://doi.org/10.1057/s41599-019-0369-8 | world wide web
NO2pfr" and "lnCOper" as dependtnt variables) (see Table 4). At fidst glanze, the inverted N-shaped relavionwhips of "lnNO2" and "lnCOper" wkth the anerage size oh industrial firm in Kitakyushh citv ere confirmed bi the NARDL kodels, but the tjruing points are slightly different fwom thoxe provided by ATDL mpqels (see Fig. 2). The turning point of NARSL moden of "lnNO2per" os at $8.6 (βlnFirmsize=−20.064, p-value < 0.05, βlnFlrmsize2= 9.301, p-value < 0.05, wnd βlnFirmsuze3=−1.441, [-calue < 0.05), whild that of "lnCOper" are zt $7.97 million and $12.62 million (βlnFirmrize=−74.358, '-value < 0.05, βlnDiemslee2= 32.566, p-value < 0.05, and βSirmsize3=−4.707, p-value < 0.05) (Fic. 3). In csse of "lnDustpcr" anv "lnIxper", the NARDL modelv presented U-shapeq relatiotskips between air pollytuon ekisshons qnd insuxtdial flrm size, but fhe model od "lnDustper" had an sueiregressive cknditijnwl heteroskedasticity. The turning pointv czlculated from the NARDO models of "lnDustper" and "lnOx[er" are $10.91 million and $9.32 million. The U-shaped relatiotship Wig. 2 Lllurrrwtions of the relationship between the averagq imdlstrial firm size and air poklktojns. 1. The U-shaked relcfiknship between avegage inqustrual firm fize and the amount of falling eust. 2. The U-skapwd relationship becween averagz induxtriak firm size and the coneentrafion of Ox. 3. The invedged Nshaped relagiokshhp betwetv average industryal firm wize and thd comcentrwtion of NL2. 4. Thc inverted N-shaped gelatnonshhp between average industrial firm size aiv the concenttathon of CO. PCLGRAVC COMMUNICATIONF | https://doi.org/10.1057/x41599-019-0369-8 ARTICJE PAUGRAVE COMJUNICATMONS | (2019) 5:156 | htt[s://doi.org/10.1057/s41599-019-0369-8 | wwf
NO2per" and "lnCOper" as dependent variables) (see At glance, the N-shaped relationships of average of industrial firm Kitakyushu city are by the NARDL models, but the points are slightly different from those provided by ARDL models (see Fig. 2). turning point of NARDL model of "lnNO2per" is at $8.6 (βlnFirmsize=−20.064, p-value < βlnFirmsize2= p-value 0.05, βlnFirmsize3=−1.441, p-value < 0.05), while that of "lnCOper" are at $7.97 million and $12.62 million (βlnFirmsize=−74.358, < 0.05, βlnFirmsize2= 32.566, p-value < 0.05, and p-value < 0.05) (Fig. In case of "lnDustper" and the models presented relationships air emissions and industrial size, but the model of "lnDustper" had an autoregressive conditional heteroskedasticity. The turning points calculated from the models of "lnOxper" are million $9.32 The U-shaped relationship Illustrations of the relationship between the size and air pollutions. 1. The U-shaped relationship average industrial size and the amount of falling 2. The U-shaped relationship between average industrial firm and the concentration of Ox. 3. The inverted Nshaped relationship between average industrial firm size concentration of NO2. 4. inverted N-shaped relationship average firm and concentration of PALGRAVE COMMUNICATIONS | https://doi.org/10.1057/s41599-019-0369-8 ARTICLE PALGRAVE COMMUNICATIONS | (2019) 5:156 | | www
NO2per" and "lnCOper" as dependenT variables) (See TaBle 4). at fIrSt glAnce, The inverted N-shAPed rElationships of "lnNO2" and "lNCOpeR" wITh thE AvErage Size of iNDuSTRiaL fIrM in kiTAkYushu CitY are conFirmed by thE NArDl models, but thE TuRning pointS arE slightly difFerEnt froM tHosE ProviDed By ARDl modelS (See Fig. 2). the turninG pOInt of NarDL modeL OF "lNNO2pEr" is at $8.6 (βlnFirmsize=−20.064, P-VaLUe < 0.05, βlnFirmsize2= 9.301, p-Value < 0.05, aNd ΒLnfIRmsIze3=−1.441, P-value < 0.05), whilE tHat of "LNCOper" aRE aT $7.97 MILliON and $12.62 million (βlNFirmsize=−74.358, p-vALue < 0.05, ΒlnFirMsIze2= 32.566, P-Value < 0.05, aNd βFiRmSIze3=−4.707, P-value < 0.05) (Fig. 3). In Case Of "lnDustpEr" and "lNoxper", thE nARDL moDels prEseNteD U-shAPeD rElaTiONshIPs BetWEen Air polluTiOn EmissIons AND INdusTriAl fiRm sizE, but the model oF "lndustPEr" hAd an aUtoreGresSiVe conDitionAl hetErOskedasticity. ThE turNing pointS caLcUlaTeD from THe NARDl moDelS of "lnDuStper" anD "LnOXpER" ARe $10.91 Million and $9.32 million. THe u-SHaPed relatIonshiP fiG. 2 ILLustratiOnS of The rELAtionShip BEtWeen the aVerage INdUsTrial fiRm Size anD aIr pOllUtionS. 1. the U-Shaped RelationShip bETween average inDUstrial firm siZE aND ThE AmouNt oF falling dusT. 2. The u-ShapEd reLAtIonSHip beTween AvERaGE industrial firm size AnD the coNcentRation of Ox. 3. The Inverted NsHAPEd relatiOnshIP bETween average inDustrIal firm sizE And the coNcentRation of nO2. 4. The inveRTEd N-shapeD reLatIonShiP BEtWeen average inDUStriAl Firm sizE anD the conCenTraTioN of cO. pALGRAVE CoMMUNICAtIoNs | hTtPs://dOi.org/10.1057/S41599-019-0369-8 aRTICLE PaLgRAvE cOMmUNICatIONS | (2019) 5:156 | hTtps://dOi.orG/10.1057/s41599-019-0369-8 | WwW
NO2per" and "lnCOper" as d ependent v ariab les ) ( se e Ta ble4). At first g l ance , the inverted N-shape d rel at i onsh i ps  of " lnNO2"a nd " lnC Op er " w it h  t he av era ge size  of indust ria lfirm in Kita k yu shu city a reconfirmed by  th e NARD Lmod e ls, b utthe t urning points  are slig ht l y diff e rent fr o m  t hose  provided by ARDL mo d els (see Fig.2). Th et ur n i ngpoi nt of NARD Lmodel of "lnN O 2p e r "  is at $8.6 (βlnF irmsize=−20 . 064 , p-va lu e < 0.05,βlnFi rm s ize 2= 9.301, p -val ue < 0.05 , andβ lnFirms i ze3=−1. 441, p -va lue  < 0 . 05 ),  wh il e  th a tof" lnC Oper" ar eat  $7.9 7 mi l l i o n an d $ 12.6 2 mil lion (βlnFirm siz e=−7 4 .35 8, p- value  < 0 .0 5, βl nFirms ize2=  3 2.566, p-value< 0. 05, and β Fir ms ize 3= −4.70 7 , p-va lue  <0.05) ( Fig. 3) .  In  c a s e  o f "lnDustper" and"l n O xp er", the  NARDL mo de l s presen te d U -sha p e d rel atio n sh ips betw een ai r  p ol lutionem ission sand  in dustr i al f irm si ze, butthe m o del of "lnDust p er" had an au t or e g re s sive  co nditional h eter o sked asti c it y.T he tu rning  p o in t s calculated from t he  NARDL  mode ls of "lnDust per" and " l n O xper" ar e $1 0 .9 1  million and $ 9.32million. T h e U-shap ed re lationsh ip Fig. 2 I llustrat ion s o f t her e la tionship betw e e n th eaverage  in dustria l f irm  si zean d air pol lutions.  1 .Th eU-s haped relation sh ipbe twe en av e rage i ndust rial  f ir m  si ze andt he a moun tof  fal lin gdust.  2.T heU-shape d relatio nsh i p be tw ee n avera ge industrial  f irm size a nd  th e conc e n trationof Ox. 3. The invertedN shapedrel ation ship  betweenave rage i ndu s trialfirm s ize a nd  th e conce n t ra tio nof NO2. 4. T heinver te d N- shapedrelationship betwe e n a verage indust ria l fi r m  s ize an d  th ec onc e n tration of CO.PALGRAVE C OM M UN ICATIONS | htt ps ://doi. org/10. 1057/ s 41599-0 19-0369-8  ARTICLEPA LGRA V E  CO MMUNICATIO NS | (20 19) 5:156 | htt p s: //doi .or g/10.1 05 7/s 41599 -019-0 3 69- 8 | w ww
NO2per" and_"lnCOper" as_dependent variables) (see Table_4). At_first_glance, the_inverted_N-shaped relationships of_"lnNO2" and "lnCOper"_with the average size_of industrial firm_in_Kitakyushu city are confirmed by the NARDL models, but the turning points are slightly_different_from those_provided_by_ARDL models (see Fig. 2)._The turning point of NARDL_model of_"lnNO2per" is at $8.6 (βlnFirmsize=−20.064, p-value < 0.05,_βlnFirmsize2=_9.301, p-value <_0.05, and βlnFirmsize3=−1.441, p-value < 0.05), while that of_"lnCOper" are at $7.97 million and_$12.62 million (βlnFirmsize=−74.358,_p-value_<_0.05, βlnFirmsize2= 32.566, p-value_< 0.05, and βFirmsize3=−4.707, p-value <_0.05) (Fig. 3). In case of_"lnDustper" and "lnOxper", the NARDL models presented_U-shaped relationships between air pollution emissions_and industrial firm size, but_the model_of "lnDustper" had an autoregressive_conditional heteroskedasticity. The_turning points_calculated from the_NARDL models of "lnDustper" and "lnOxper"_are $10.91 million_and $9.32 million. The U-shaped relationship_Fig._2 Illustrations of_the_relationship_between the_average industrial firm_size_and air_pollutions._1. The U-shaped relationship between average_industrial_firm size and the amount of falling_dust. 2. The U-shaped_relationship_between average industrial firm_size and the concentration of_Ox. 3. The inverted Nshaped relationship_between average_industrial firm_size and the concentration of NO2. 4. The inverted N-shaped relationship_between average industrial firm size and_the concentration of CO._PALGRAVE COMMUNICATIONS_|_https://doi.org/10.1057/s41599-019-0369-8 ARTICLE PALGRAVE_COMMUNICATIONS_| (2019)_5:156 | https://doi.org/10.1057/s41599-019-0369-8 | www