Table 12 Robustness tests for threshold model regression result.

From: Ecological footprints, carbon emissions, and energy transitions: the impact of artificial intelligence (AI)

Thresholds

IND

OPEN

Dependents

EF

CE

ETR

EF

CE

ETR

Model

RT1

RT2

RT3

RT4

RT5

RT6

Result

Lower

Higher

Lower

Higher

Lower

Higher

Lower

Higher

Lower

Higher

Lower

Higher

lnai

−0.0222***

0.0234***

−0.0125***

0.0158***

−0.0244***

0.0297***

0.0025***

−0.0014

0.0153***

−0.0196***

−0.0002

0.0206***

 

(−6.88)

(7.51)

(−4.86)

(5.42)

(−5.67)

(5.59)

(3.43)

(−0.50)

(10.16)

(−7.60)

(−0.15)

(7.84)

Sup Wald p

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

γ

3.1057***

3.1819***

3.2115***

4.1403***

4.0026***

4.4158***

Thresholds

ai

ETR

Dependents

EF

CE

ETR

EF

CE

ETR

Model

RT7

RT8

RT9

RT10

RT11

RT12

Result

Lower

Higher

Lower

Higher

Lower

Higher

Lower

Higher

Lower

Higher

Lower

Higher

lnai

0.0119***

−0.0567**

0.0014***

−0.1239***

−0.0522***

0.033

0.0302***

−0.0445***

0.0103***

−0.0107***

0.0226***

−0.0335***

 

(5.06)

(−2.14)

(6.78)

(−3.52)

(−2.82)

(1.17)

(4.41)

(−4.78)

(5.64)

(−5.28)

(10.69)

(−12.21)

Sup Wald p

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

γ

7.8276***

6.7628***

−1.8279

1.3581**

1.3581***

2.2916***

  1. z-statistic in parentheses. Lower represents the lower regime result and Higher represents the threshold effect estimator consistent with Model 6–9. γ represents the estimated threshold value. Due to space limitations, the regression results of the control variable and the lagged dependent variables are not reported. Complete regression results are made on request.
  2. ***p < 0.01; **p < 0.05.
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