Measuring and decomposing TFP incorporating environmental components: applications for rice farmers in Hubei Province, China

Figures & data

Table 1. Statistical description of the variables.

Variables	Unit	Mean	Std. Dev	Min	Max
Observation n = 1822
Rice output	kg	1840.19	1741.77	0	9989
Land	mu	3.36	2.42	0.2	15
Labor	day	59.16	46.93	1	378
Intermediate input	yuan	585.53	643.66	4.39	4794.70
Capital	yuan	4.17	11.73	0	133
Fertilizer	kg	317.78	276.93	4	2689
Land N content	g/mu	22075.17	4227.79	0	70272.35
Fertilizer N content	g/kg	139.44	76.50	0	515.7

Table 2. Parameter estimates.

Parameters	Coef	Std. Err
Nutrient frontier function
$\mathit{\text{ln}}(a_2)$	0.34***	(0.02)
$\mathit{\text{ln}}(q)$	0.49***	(0.02)
$\mathit{\text{ln}}(z_1)$	0.28***	(0.02)
$\mathit{\text{ln}}(z_2)$	0.16***	(0.02)
$\mathit{\text{ln}}(z_3)$	−0.05***	(0.01)
$0\text{.5ln}{(a_2)}^2$	0.17***	(0.03)
$0\text{.5ln}{(q)}^2$	−0.11***	(0.03)
$0\text{.5ln}{(z_1)}^2$	0.01	(0.02)
$0\text{.5ln}{(z_2)}^2$	0.03	(0.02)
$0\text{.5ln}{(z_3)}^2$	−0.01	(0.01)
$\mathit{\text{ln}}(a_2)\ast \mathit{\text{ln}}(q)$	−0.05*	(0.03)
$\mathit{\text{ln}}(a_2)\ast \mathit{\text{ln}}(z_1)$	−0.01	(0.02)
$\mathit{\text{ln}}(a_2)\ast \mathit{\text{ln}}(z_2)$	0.05**	(0.02)
$\mathit{\text{ln}}(a_2)\ast \mathit{\text{ln}}(z_3)$	−0.04**	(0.02)
$\mathit{\text{ln}}(q)\ast \mathit{\text{ln}}(z_1)$	0.04**	(0.02)
$\mathit{\text{ln}}(q)\ast \mathit{\text{ln}}(z_2)$	−0.02	(0.02)
$\mathit{\text{ln}}(q)\ast \mathit{\text{ln}}(z_3)$	0.15***	(0.01)
$\mathit{\text{ln}}(z_1)\ast \mathit{\text{ln}}(z_2)$	0.02	(0.01)
$\mathit{\text{ln}}(z_1)\ast \mathit{\text{ln}}(z_3)$	−0.06***	(0.01)
$\mathit{\text{ln}}(z_2)\ast \mathit{\text{ln}}(z_3)$	−0.09***	(0.01)
$t$	0.01***	(0.00)
$t^2$	−0.00	(0.00)
${\alpha }_0$	−0.01	(0.02)
${\beta }_0$	−0.01	(0.02)
$\text{lnsig2v}$	−3.02***	(0.05)
$\mathit{\text{lnsig}}2u$
Technical inefficiency model
$\mathit{\text{ln}}(\overline{x_1})$	1.96***	(0.41)
$\mathit{\text{ln}}(\overline{x_2})$	−1.80***	(0.35)
$\mathit{\text{ln}}(\overline{x_3})$	−2.61***	(0.24)
$\mathit{\text{ln}}(\overline{x_4})$	0.34***	(0.08)
$\mathit{\text{ln}}(\overline{x_5})$	2.65***	(0.33)
constant	2.02	(1.61)

* p < 0.10; **p < 0.05; ***p < 0.01.

Table 3. Nutrient elasticities.

	Mean	Std. Err	Std. Dev	[95% Conf. interval]
N in fertilizer	0.33	0.00	0.09	[0.33, 0.34]
N in land	0.67	0.00	0.09	[0.33, 0.34]
Rice output	0.54	0.00	0.15	[0.53, 0.55]
Labor	0.25	0.00	0.07	[0.25, 0.25]
Intermediate	0.14	0.00	0.07	[0.14, 0.15]
Capital	−0.04	0.00	0.08	[−0.05, −0.04]

Table 4. Components of TFP.

	Mean	Std. Dev	Min	Max
TC	−0.007	0.007	−0.019	0.003
SE	0.012	0.240	−1.121	1.443
TEC	−0.004	0.101	−1.053	0.795
AE of land nutrient	−0.003	0.035	−0.471	0.100
AE of fertilizer nutrient	−0.011	0.066	−0.634	0.289
effect of labor	0.007	0.140	−0.624	0.403
effect of intermediate input	0.001	0.110	−0.485	0.516
effect of capital	−0.023	0.303	−0.900	0.684
TFP	−0.028	0.385	−1.391	1.429

Note: In total, 834 observations were used to calculate the TFP and its components, which is lower than the number of observations (1707) in the regression due to excluding zero values for capital and first-year values in the calculation of instant changes in inputs and their N content.