Evaluation of green innovation efficiency in catering industry based on data envelopment analysis

Figure 1.

Figure 2.

Figure 3.

The fitting results of the national spatial absolute β convergence model

Variables	Spatial fixed effect	Time-fixed effect	Double fixed effect
ln(yi,t)	-0.2614*** (0.000)	-0.0683*** (0.000)	-0.2641*** (0.000)
R2	0.531	0.259	0.672
F	7.544	1.926	3.795
Convergence velocity θ	0.0979	0.0241	0.0997
Half life cycle τ	7.0624	28.9867	6.8945

Estimation results of β convergence model under traditional panel model

Variables	National absolute β convergence	Eastern absolute beta convergence	Midsection absolute β convergence	Western absolute β convergence
ln(yi,t)	-0.098*** (0.000)	-0.045*** (0.007)	-0.141*** (0.000)	-0.172*** (0.000)
R2	0.1672	0.0651	0.1834	0.2085
F	58.39	7.38	18.26	4.03
Convergence velocity θ	0.036	0.015	0.051	0.062
Half life cycle τ	21.41	49.23	14.65	12.24

Dynamic efficiency of green technology innovation

Dynamic year	Changes in technical efficiency (EC)	Changes in technical level (TC)	M-index (TFP)
2014-2015	0.9584	1.0254	0.9707
2015-2016	0.9801	1.3889	1.3529
2016-2017	1.2528	0.6272	0.8067
2017-2018	1.0578	1.0717	1.1330
2018-2019	1.0989	0.9846	1.0819
2019-2020	0.9166	1.1019	0.9953
2020-2021	1.1864	0.8932	1.0671
2021-2022	0.9473	1.1257	1.0733
2022-2023	1.0280	1.0802	1.1012

Green technology innovation dynamic efficiency values

DMU	Changes in technical efficiency (EC)	Changes in technical level (TC)	M-index (TFP)
Anhui	1.0615	1.1144	1.1796
Beijing	0.9927	0.6893	0.6950
Fujian	0.9621	1.2152	1.1520
Gansu	1.0162	0.9362	0.9578
Guangdong	0.9996	1.0473	1.0426
Guangxi	1.0399	1.1443	1.1824
Guizhou	0.9805	0.9641	0.9277
Hainan	1.6016	0.7065	1.1182
Hebei	0.9834	1.1334	1.1376
Henan	1.0001	1.0101	1.0064
Heilongjiang	0.9522	1.0950	1.0321
Hubei	1.0870	1.1458	1.2845
Hunan	1.0727	1.1096	1.1668
Jilin	0.9897	1.0173	1.0179
Jiangsu	1.0240	1.0033	1.0578
Jiangxi	1.0214	1.1124	1.1675
Liaoning	0.9491	1.1546	1.1165
Inner Mongolia	1.0108	0.8928	0.9122
Ningxia	1.2735	0.7203	0.8955
Qinghai	1.0818	0.9321	1.0128
Shandong	0.9806	1.0157	1.0002
Shanxi	0.9928	1.0467	1.0354
Shaanxi	1.1166	1.1335	1.2722
Shanghai	0.9935	1.1019	1.1013
Sichuan	1.0694	1.1486	1.2077
Tianjin	0.9883	0.9477	0.9792
Xinjiang	1.0517	1.0699	1.1238
Yunnan	0.9673	0.9632	0.9519
Zhejiang	0.9956	0.9971	1.0168
Chongqing	0.9944	1.0779	1.0655
Mean value	1.0154	1.0063	1.0533

Green innovation efficiency of Chinese catering industry

Region	DMU	The first stage	The second stage	Total band rate
Eastern Region	Hainan	0.9237	5.5280	2.2655
	Guangdong	2.5950	0.6817	1.3668
	Beijing	1.6487	0.8078	1.1641
	Zhejiang	0.6981	1.3203	0.9585
	Jiangsu	0.8366	1.0672	0.9666
	Shanghai	0.7217	1.0153	0.8447
	Tianjin	0.6159	0.9813	0.7566
	Fujian	0.4200	0.9737	0.6444
	Shandong	0.4116	1.0074	0.6532
	Hebei	0.3520	0.9497	0.5646
	Liaoning	0.4207	0.7360	0.5640
	Eastern Region	0.7088	1.1146
Central Region	Jilin	0.3531	1.1677	0.6277
	Henan	0.3759	1.0317	0.6208
	Hupei	0.4767	0.7756	0.6137
	Hunan	0.6669	0.5449	0.5835
	Anhui	0.8541	0.3752	0.5576
	Jiangxi	0.3172	0.7836	0.5114
	Heilongjiang	0.3583	0.7570	0.5103
	Shanxi	0.3166	0.4782	0.3978
	Central Region	0.4303	0.6997
Western region	Qinghai	0.4118	2.1140	0.9359
	Xinjiang	0.6119	0.9500	0.7748
	Chongqing	0.6226	0.7707	0.6732
	Sichuan	0.7175	0.5521	0.6285
	Ningxia	0.5294	0.6649	0.5893
	Shaanxi	0.4720	0.6843	0.5574
	Yunnan	0.623	0.4612	0.5604
	Guangxi	0.4798	0.6109	0.5438
	Inner Mongolia	0.2409	1.2080	0.5266
	Guizhou	0.7996	0.2917	0.4644
	Gansu	0.4069	0.4561	0.4319
	Western region	0.4844	0.6957

Lagrange multiplier test

Check type	Statistic	P value
Moran’s error	2.614	0.009
LM-error	6.143	0.016
Roust LM-error	0.005	0.952
Roust LM-lag	7.132	0.009
Roust LM-lag	0.973	0.319