. 2021 Apr 1;28(31):41965–41987. doi: 10.1007/s11356-021-13463-y

Table 2.

Cubic specification estimation results

Denmark
Scaling factor (a)	0.000017	0.001	0.01	1 (original data)	10	100	1000
$\hat{β_{1}}$	−0.2640	54.2493^**	141.9168^**	440.4372^**	651.2899^**	903.2044^**	1196.1807^**
t-value	(−0.3986)	(2.9750)	(2.7583)	(2.6165)	(2.5845)	(2.5625)	(2.5463)
$\hat{β_{2}}$	1.1996	−14.5786^***	−23.4950^***	−41.3279^***	−50.2443^***	−59.1608^***	−68.0772^***
t-value	(1.1072)	(−2.7052)	(−2.5990)	(−2.5289)	(−2.5130)	(−2.5020)	(−2.4940)
$\hat{β_{3}}$	1.2908^***	1.2908^***	1.2908^***	1.2908^***	1.2908^***	1.2908^***	1.2908^***
t-value	(2.4419)	(2.4419)	(2.4419)	(2.4419)	(2.4419)	(2.4419)	(2.4419)
$\hat{η}$	−0.4047^***	−0.4047^***	−0.4047^***	−0.4047^***	−0.4047^***	−0.4047^***	−0.4047^***
t-value	(−4.8716)	(−4.8716)	(−4.8716)	(−4.8716)	(−4.8716)	(−4.8716)	(−4.8716)
Sweden
Scaling factor (a)	0.000035	0.0000483	0.001	0.01	1 (original data)	100	1000
$\hat{β_{1}}$	−1.4409^***	−0.0417	153.3242^***	439.3269^***	1450.3580^***	3046.7567^***	4064.4689^***
t-value	(−13.4025)	(−0.4458)	(8.1970)	(8.0558)	(7.9585)	(7.9205)	(7.9091)
$\hat{β_{2}}$	0.0504	−4.3946^***	−46.2158^***	−77.9936^***	−141.5490^***	−205.1045^***	−236.8823^***
t-value	(0.2275)	(−9.9483)	(−8.0294)	(−7.9493)	(−7.8973)	(−7.8776)	(-7.8717)
$\hat{β_{3}}$	4.6003^***	4.6003^***	4.6003^***	4.6003^***	4.6003^***	4.6003^***	4.6003^***
t-value	(7.8326)	(7.8326)	(7.8326)	(7.8326)	(7.8326)	(7.8326)	(7.8326)
$\hat{η}$	−1.4410^***	−1.4410^***	−1.4410^***	−1.4410^***	−1.4410^***	−1.4410^***	−1.4410^***
t-value	(−13.1143)	(−13.1143)	(−13.1143)	(−13.1143)	(−13.1143)	(−13.1143)	(−13.1143)

Source: Data from Jaforullah and King (2017)

Notes: The values of the scaling factors are chosen to show the existence of coefficients with the opposite signs and with significant and insignificant values (according to t-values). The estimated elasticities $\hat{(η})$ are calculated at mean values as discussed in Gujarati and Porter (2009), inter alia