. 2022 Oct 14;30(8):19737–19748. doi: 10.1007/s11356-022-23519-2

Table 3.

Results of the Kao and Pedroni cointegration tests

Kao test H₀: no cointegration	Pedroni test H₀: no cointegration
NO_x emissions, population, income per taxpayer, car ownership, houses per capita, industrial manufacturing, urban density (all variables logged)
Modified Dickey-Fuller t Dickey-Fuller t Augmented Dickey-Fuller t	− 19.58* − 12.61* − 7.14***	Modified Phillips-Perron t Phillips-Perron t Augmented Dickey-Fuller t	− 19.39* − 18.70* − 12.39***

Kao test
H₀: no cointegration

Pedroni test
H₀: no cointegration

NO_x emissions, population, income per taxpayer, car ownership, houses per capita, industrial manufacturing, urban density (all variables logged)

Modified Dickey-Fuller t

Dickey-Fuller t

Augmented Dickey-Fuller t

− 19.58***

− 12.61***

− 7.14***

Modified Phillips-Perron t

Phillips-Perron t

Augmented Dickey-Fuller t

− 19.39***

− 18.70***

− 12.39***

The Kao test assumes a constant cointegration vector, and the Pedroni-test assumes panel-specific AR parameters. Cross-sectional averages are substracted

***p < 0.01