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 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 d