Spatial productivity and efficiency spillovers in the presence of transient and persistent efficiency: Evidence from China’s provinces

Figures & data

Table 1. Summary statistics

Variable	Description	Mean	SD	Min.	Max
y	Real GDP (100 mil. Yuan)	7151.22	11288.95	15.39	83446.73
k	Real capital stock(100 mil. Yuan)	288.46	389.14	1.16	2794.64
l	Labour employed (per 10,000 people)	2216.66	1508.27	105.72	6963.00
gov	Ratio of government spending to GDP	0.14	0.05	0.05	0.52
opn	Ratio of imports and exports to GDP	0.25	0.35	0.02	3.69

N = 990 and is the number of observations from 30 provinces during the period 1985–2017. Real GDP, real capital stock and labour employed are reported in levels. The dummy variable Coast includes Fujian, Guangdong, Guangxi, Hebei, Jiangsu, Liaoning, Shandong, Shanghai, Tianjin and Zhejiang

Table 2. Spatial Durbin production frontier coefficients and associated parameters

Variable	Model Coeff.	Direct Parameter	Indirect Parameter	Total Parameter	Variable	Model Coeff.
k	0.393***	0.405***	0.491*	0.896*	Wk	−0.063
	(0.024)	(0.027)	(0.267)	(0.281)		(0.116)
l	0.331***	0.315***	0.618	0.933*	Wl	−0.043**
	(0.037)	(0.036)	(0.351)	(0.361)		(0.148)
k^2	−0.161***	−0.181***	−0.927**	−1.108*	Wk^2	−0.224*
	(0.018)	(0.024)	(0.358)	(0.376)		(0.135)
l^2	0.027	0.041	−0.572*	−0.531	Wl^2	−0.139
	(0.025)	(0.029)	(0.368)	(0.386)		(0.148)
kl	0.090	0.132**	0.868***	1.000*	Wkl	0.040**
	(0.034)	(0.042)	(0.561)	(0.591)		(0.218)
t	0.021*	0.022**	0.026*	0.048*	Wkt	0.027*
	(0.014)	(0.014)	(0.020)	(0.033)		(0.029)
t^2	−0.005**	−0.005**	−0.006**	−0.011**	Wlt	−0.041*
	(0.002)	(0.002)	(0.003)	(0.005)		(0.023)
kt	0.045***	0.048***	0.156*	0.204**	Wgov	−0.087***
	(0.004)	(0.005)	(0.076)	(0.080)		(0.090)
lt	−0.018***	−0.022***	−0.182**	−0.204**	Wopn	0.052**
	(0.003)	(0.004)	(0.057)	(0.060)		(0.027)
gov	−0.052***	−0.072***	−0.091***	−0.163***	constant	−0.203***
	(0.017)	(0.017)	(0.174)	(0.180)		(0.029)
opn	0.005**	0.002**	0.125**	0.127**
	(0.010)	(0.010)	(0.059)	(0.060)
coast	0.427***	0.510***	0.308**	0.818***
	(0.097)	(0.105)	(1.353)	(1.378)
$v_{0i}$	0.89				LL	809.71
	(0.016)
$v_{it}$	0.246				$W\rho$	0.549***
	(0.002)
$u_{0i}$	0.079				$u_{it}$	0.006
	(0.030)					(0.062)

Definition of variables is in Table 1. *, **, *** denote statistical significance at the 10%, 5%, and 1% levels, respectively. Standard errors are in parenthesis. The dummy variable Coast includes Fujian, Guangdong, Guangxi, Hebei, Jiangsu, Liaoning, Shandong, Shanghai, Tianjin and Zhejiang. Standard errors are in parenthesis. Variables are log-transformed prior to estimation. ${\nu }_{0i}$ captures country-specific effects. ${\mu }_{0i}$ captures long-run (persistent) efficiency. ${\nu }_{it}$ captures random noise or idiosyncratic error while ${\mu }_{it}$ captures short-run time-varying (transient) efficiency.

Table 3. Average efficiencies of provinces

	Gross Efficiency	Persistent Efficiency	Transient Efficiency	$\mathit{G}V{E}^{Dir}$	$\mathit{G}V{E}^{Ind}$	$\mathit{G}V{E}^{Tot}$
Total average	93.55%	94.08%	99.51%	93.71%	18.98%	112.69%

Persistent efficiency scores are derived from (1—exp (${\mu }_{0i}$)) and transient efficiency scores are derived from (1—exp (${\mu }_{it}$)). Gross efficiency is the interaction between persistent and transient efficiency.

Table 4. Gross time-varying efficiency of provinces

Province	Total gross time-varying efficiency	Indirect gross time-varying efficiency	Direct gross varying efficiency
Sichuan	112.99%	18.93%	94.06%
Xinjiang	112.98%	19.07%	93.90%
Hunan	112.94%	18.99%	93.96%
Henan	112.94%	18.99%	93.96%
Guangdong*	112.94%	19.02%	93.92%
Jiangxi	112.91%	18.97%	93.94%
Qinghai	112.91%	19.04%	93.87%
Gansu	112.91%	19.01%	93.89%
Shandong*	112.87%	18.99%	93.88%
Hebei*	112.87%	18.94%	93.93%
Tianjin*	112.82%	18.87%	93.95%
Beijing	112.79%	18.88%	93.91%
Chongqing	112.76%	18.92%	93.84%
Guizhou	112.76%	18.98%	93.78%
Jilin	112.76%	18.99%	93.77%
Hubei	112.75%	18.99%	93.76%
Shanxi	112.75%	18.96%	93.79%
Anhui	112.74%	18.90%	93.84%
Shanghai*	112.71%	18.88%	93.84%
Shaanxi	112.69%	18.99%	93.71%
Guangxi*	112.68%	19.01%	93.67%
Yunnan	112.68%	19.05%	93.63%
Jiangsu*	112.60%	18.85%	93.76%
Ningxia	112.52%	19.00%	93.53%
Zhejiang*	112.52%	18.96%	93.56%
Tibet	112.40%	19.07%	93.33%
Fujian*	112.32%	19.00%	93.31%
Liaoning*	112.20%	19.01%	93.18%
Inner Mongolia	112.07%	19.01%	93.06%
Heilongjiang	111.91%	19.04%	92.87%
Total average	112.69%	18.98%	93.71%

Gross time-varying scores are unbounded as it takes into account the own net time-invariant, own net time-varying and gross time-varying efficiency. This is calculated using the spatial multiplier matrix which passes through a provinces’ first order and neighbouring provinces and rebounds back to the unit. The scores above 1 suggests that the efficiency spillover is sufficiently large and has pushed the province beyond the best practice frontier.

Table 5. Gross time-varying efficiency over time

Year	Total gross time-varying efficiency	Indirect gross time-varying efficiency	Direct gross time-varying efficiency
1985	112.82%	18.99%	93.83%
1986	112.75%	18.98%	93.77%
1987	110.77%	18.64%	92.13%
1988	111.39%	18.74%	92.65%
1989	113.53%	19.11%	94.42%
1990	113.30%	19.05%	94.25%
1991	112.86%	18.97%	93.89%
1992	110.72%	18.59%	92.13%
1993	111.46%	18.74%	92.71%
1994	112.66%	18.96%	93.70%
1995	112.89%	19.01%	93.88%
1996	113.60%	19.14%	94.46%
1997	113.55%	19.12%	94.43%
1998	113.28%	19.08%	94.20%
1999	113.45%	19.10%	94.35%
2000	113.14%	19.04%	94.09%
2001	113.73%	19.14%	94.59%
2002	112.81%	18.98%	93.83%
2003	111.76%	18.80%	92.96%
2004	111.75%	18.80%	92.94%
2005	112.24%	18.89%	93.34%
2006	112.47%	18.93%	93.53%
2007	112.85%	19.00%	93.85%
2008	113.43%	19.10%	94.33%
2009	112.78%	19.00%	93.78%
2010	112.56%	18.97%	93.59%
2011	113.01%	19.05%	93.96%
2012	113.24%	19.09%	94.15%
2013	112.86%	19.04%	93.83%
2014	111.96%	18.89%	93.07%
2015	112.87%	19.05%	93.83%
2016	113.06%	19.09%	93.97%
2017	113.23%	19.13%	94.10%
Total average	112.69%	18.98%	93.71%

Gross time-varying scores are unbounded as it takes into account the own net time-invariant, own net time-varying and gross time-varying efficiency. This is calculated using the spatial multiplier matrix which passes through a provinces’ first order and neighbouring provinces and rebounds back to the unit. The scores above 1 suggests that the efficiency spillover is sufficiently large and has pushed the province beyond the best practice frontier.

Figure 1. Spatial distribution of total technological progress

Source: Author’s compilation from Table 6 using total technological progress.

Table 6. Technological progress of provinces

Province	Total technological progress	Indirect technological progress	Direct technological progress
Beijing	1.341	1.256	1.066
Shanghai*	1.315	1.237	1.062
Tianjin*	1.286	1.234	1.044
Guangdong*	1.260	1.183	1.077
Zhejiang*	1.228	1.174	1.054
Jiangsu*	1.198	1.138	1.060
Shandong*	1.156	1.099	1.056
Fujian*	1.152	1.121	1.031
Liaoning*	1.141	1.105	1.036
Ningxia	1.105	1.102	1.002
Shanxi	1.066	1.040	1.026
Inner Mongolia	1.059	1.045	1.015
Heilongjiang	1.050	1.026	1.025
Shaanxi	1.049	1.024	1.027
Jilin	1.025	1.017	1.010
Guangxi*	1.024	1.012	1.012
Hebei*	1.023	0.987	1.038
Hubei	1.001	0.977	1.027
Yunnan	0.959	0.947	1.012
Gansu	0.957	0.961	0.997
Jiangxi	0.956	0.949	1.008
Henan	0.954	0.927	1.032
Tibet	0.949	1.012	0.938
Chongqing	0.946	0.949	0.999
Sichuan	0.946	0.923	1.026
Hunan	0.939	0.924	1.018
Guizhou	0.923	0.927	0.997
Anhui	0.906	0.901	1.008
Xinjiang	0.904	0.891	1.013
Qinghai	0.901	0.895	1.006
Total average	1.057	1.031	1.024

Total factor productivity growth index is decomposed using a Malmquist index. The direct and indirect effect is calculated using the spatial multiplier matrix which passes through a provinces’ first order and neighbouring provinces and rebounds back to the unit.

Table 7. Technological progress over time

Year	Total technological progress	Indirect technological progress	Direct technological progress
1986	1.142	1.015	1.123
1987	1.134	1.014	1.116
1988	1.127	1.014	1.109
1989	1.119	1.013	1.102
1990	1.108	1.011	1.095
1991	1.095	1.006	1.087
1992	1.084	1.003	1.079
1993	1.078	1.004	1.072
1994	1.075	1.006	1.066
1995	1.074	1.010	1.061
1996	1.072	1.015	1.055
1997	1.068	1.017	1.049
1998	1.069	1.023	1.043
1999	1.072	1.030	1.038
2000	1.068	1.033	1.031
2001	1.063	1.035	1.025
2002	1.055	1.034	1.018
2003	1.046	1.033	1.012
2004	1.037	1.031	1.005
2005	1.028	1.029	0.998
2006	1.017	1.025	0.992
2007	1.013	1.026	0.986
2008	1.016	1.034	0.982
2009	1.016	1.039	0.977
2010	1.018	1.046	0.973
2011	1.018	1.050	0.969
2012	1.017	1.054	0.964
2013	1.020	1.062	0.961
2014	1.022	1.068	0.956
2015	1.020	1.072	0.951
2016	1.015	1.073	0.946
2017	1.008	1.073	0.939
Total average	1.057	1.031	1.024

Total factor productivity growth index is decomposed using a Malmquist index. The direct and indirect effect is calculated using the spatial multiplier matrix which passes through a provinces’ first order and neighbouring provinces and rebounds back to the unit.

Figure 2. Technological progress over time

Source: Author’s compilation from Table 5 using total technological progress.