Can outward foreign direct investment improve China’s green economic efficiency?

Under the constraints of energy and environment, improving green economic efficiency (GEE) has become the key path to promote the sustainable economic development. Among the driving factors of GEE, the role of outward foreign direct investment (OFDI) is worth exploring. In this paper, we adopt the inter-provincial panel data of China from 2011 to 2019 and System Generalized Method of Moments (SYS-GMM) to explore the influence of OFDI on GEE. We find that OFDI significantly improves China’s GEE, and reverse technology spillover through direct investment in developed countries is an important way for OFDI to promote GEE. Regional heterogeneity test shows that OFDI significantly promotes GEE in eastern China; however, the promotion effect is not significant in midwestern China. Besides, the promoting effect of OFDI on GEE has been further improved after 2016. We further adopt panel threshold model and find that when the financial development (FD) and human capital (HUM) exceeds 2.0954 and 0.0290, respectively, the promoting effects of OFDI on GEE are greatly enhanced. We suppose that the above conclusions can provide guidance for policymakers to optimize OFDI and improve GEE.


Introduction
Energy is the key engine of economic growth. Industrialization and urbanization promote economic growth but also increase energy consumption, which exacerbates environmental degradation such as pollution discharge and carbon emission (Shah et al. 2020a;Zhang et al. 2022a). Environmental degradation in turn impedes sustainable economic development (Abbas et al. 2022), but the use of renewable energy such as biomass and the improvement of energy efficiency can help mitigate environmental degradation and improve environmental quality (Shah et al. 2020b. Therefore, in order to maintain sustainable economic growth, it is necessary to save energy and reduce pollution emissions to promote green economic development. Green economic efficiency (GEE) comprehensively considers energy consumption, economic growth, and environmental protection by adding energy input and pollution output, which is an effective indicator to measure green economic development (Hu et al. 2018;Zheng et al. 2022). The higher the GEE, the better the energy conservation and environmental improvement. Therefore, increasing the GEE has become a key way to promote sustainable economic development.
In the past four decades of reform and opening up, China has achieved long-term rapid economic growth, but at the cost of excessive energy consumption and serious environmental pollution . According to the environmental Kuznets curve (KEC), there is an inverted U-shaped relationship between economic level and environmental pollution; that is, environmental pollution will first increase and then decrease with the improvement of per capita income. However, KEC only exists in high-income countries and is not significant in low-and middle-income countries . Therefore, if China wants to maintain sustainable economic growth and cross the middleincome trap, it must focus on improving GEE and promoting comprehensive green transformation of economic and social development. In recent years, many papers analyzed the determinants of GEE from the aspects of economic agglomeration (Lin and Tan 2019), green innovation (Liao et al. 2020), manufacturing agglomeration (Yuan et al 2020), environmental regulation (Song et al. 2022), foreign direct investment (Zhao et al. 2020a, b), and so on. However, few scholars pay attention to the influence of outward foreign direct investment (OFDI) on GEE, which is also a key factor.
In the long run, technological progress can promote the efficiency of resource utilization and inhibit pollution discharges (Andreoni and Levinson 2001;Acemoglu et al. 2012), which is the key impetus for sustainable economic development (Romer 1986). While seeking advanced technology, obtaining reverse technology spillover from developed countries is one of the important motives for international OFDI (Kogut and Chang 1991;Huang and Wang 2011), and globalization further promotes OFDI flows (Bojnec and Fertő 2018). After China joined the WTO in 2001, the pace of Chinese enterprises "going global" is accelerating. The Statistical Bulletin of China's Outward Foreign Direct Investment shows that the stock of China's OFDI has grew from US $29.9 billion in 2002 to US $2580.66 billion in 2020, and the average annual growth rate reached 28.1%. Under the background of the rapid growth of OFDI and green economic development, this paper aims to explore whether OFDI is an important driving force to promote China's green economic efficiency.
Our research makes three contributions to the existing papers. First, many scholars explore the influence of OFDI on economic growth, environmental pollution, and energy efficiency respectively; however, it is difficult to fully reflect the influence of OFDI on the green economic development of the home country. Therefore, we take energy consumption, capital, and labor as inputs, GDP as expected output, and carbon dioxide emissions and pollutant discharges as negative outputs; construct a composite index that can comprehensively measure energy consumption, economic growth, and environmental pollution; and further combine with the DEA-EBM model to estimate GEE of each province in China. On this basis, our study empirically examines the impact of OFDI on GEE, which extends the scope of existing literature. Second, this paper constructs an instrumental variable (IV) from the historical perspective and adopts twostage least square (2SLS) method to overcome the interference of endogenous problems on benchmark conclusions. At the same time, we measure the R&D spillovers obtained through OFDI to inspect the influence of reverse technology spillovers on GEE. Finally, we divide the Chinese mainland region into the eastern region and the midwestern region for spatial heterogeneity analysis; further, this paper takes financial development (FD) and human capital (HUM) as threshold variables to test the nonlinear influence of OFDI on green economic efficiency, which can better play the positive impact of OFDI on GEE.

Literature review
OFDI's economic impact on the home country has always been an important topic in academic research, and many scholars have found that OFDI significantly promoted the economic growth of the home country (Knoerich 2017;Chen 2018;Ali et al. 2018;Naresh and Nidhi;. More importantly, our study primarily focuses on the following three aspects.

The linkage between OFDI and energy
Energy consumption drives economic growth, and seeking a stable energy supply is one of OFDI's key objectives. Zhao et al. (2020a, b) find that OFDI in the energy sector does enhance China's energy security by diversifying import sources and increasing oil imports from host countries. Some scholars explore the influence of OFDI on energy density and find that the reverse technology spillovers of OFDI significantly reduce China's energy density (Zhang et al. 2022a, b, c, d). Sun et al. (2022) further reveal that high-technology-intensive firms' OFDI has a greater effect on energy intensity reduction than that of low-technologyintensive firms. Besides,  find that OFDI significantly improves China's energy efficiency. However, Liu et al. (2022) reveal that OFDI can increase total factor energy efficiency (TFEE) to a certain extent, but the effect is still weak and has a lag characteristic. In addition, the facilitating effect of OFDI on TFEE exists a threshold effect, which is influenced by some elements, such as technical ability (He et al. 2022), human capital, industrial structure, and open-up level (Pan et al. 2022). Ren et al. (2022) find that OFDI can boost the green total factor energy efficiency (GTFEE) of the home country by alleviating capital misallocation, upgrading industrial structure, and boosting innovation.

The linkage between OFDI and environment
Many scholars study the effect of OFDI on environment pollution. For example, the empirical results of Xin and Zhang (2020) show that the stock of OFDI increases by 1% and China's industrial sulfur dioxide discharge and wastewater emissions decrease by 7.76% and 4.3%, respectively. Long et al. (2020) find that OFDI can effectively improve domestic environmental performance. Besides, Zhou and Li (2021) reveal that OFDI significantly decreases two air pollutants (sulfur dioxide and particulate matter) but also increases nitrogen dioxide. With the intensification of the "greenhouse effect," more scholars pay attention to the effect of OFDI on carbon dioxide emissions. Zhang et al. (2021) find that increasing OFDI reduces the carbon footprint of Turkey and Mexico effectively. However, Zhang et al. (2022a, b, c, d) argue that China's OFDI significantly increases the carbon emissions. Hao et al. (2020) and Yang et al. (2021) further reveal that OFDI increases carbon dioxide emissions by expanding economic scale but inhabits carbon emissions through the industrial structure upgrading and reverse technology spillovers. Other papers find that the effect of OFDI on carbon emissions is affected by other factors, such as economic development degree, population size, technological level (Cai et al. 2021), environmental regulation (Zhao and Zhu 2022), and urbanization (Tan et al. 2021).

The spread effect of OFDI
Our paper is also closely related to the spread effect of OFDI, and the reverse technology spillover effect of OFDI has been widely discussed in academia. Based on the data of Chinese industrial enterprises from 1999 to 2007, Wang and Zhang (2018) confirm that OFDI enterprises have a learning effect; that is, enterprises improve their productivity by learning advanced technology and reverse technology spillover through OFDI. Ye et al. (2018) argue that cultural distance affects the reverse technology spillover effect of OFDI, and the more similar the cultural background of the home country and the host country is, the easier it is for firms to obtain the spillover effect. With the increasing importance of environmental issues, scholars began to pay attention to the green spillover effect of OFDI. Some papers find that OFDI to developed countries can generate reverse green technology spillover and promote parent companies' environmental innovation (Bai et al. 2020) and China's green innovation . Besides, the green spillover effect of OFDI is influenced by some factors such as home country's human capital and environmental regulation (Zhu et al. 2018;Zhou et al. 2019). Further, some papers find that China's reverse technology spillovers through OFDI significantly improve carbon productivity ) and reduce carbon emission intensity (Fang et al. 2022).
The above literatures explored the economic effects of OFDI from the dimensions of economic growth, energy, and environment and verified the spread effects of OFDI. However, the comprehensive impact of OFDI on the green development of the home country is still a research gap. In this paper, we take GEE as a measurement index to measure economic green development and test the influence of OFDI on GEE and its heterogeneity to make up for the shortcomings of existing studies.

Theoretical analysis and research hypothesis
The direct effect of OFDI on the home country's green economic efficiency The influence of OFDI on the home country's GEE can be analyzed from the following three aspects. First, in order to ensure the stability of raw material supply and cope with the negative impact of price changes in the international raw material market on their production, multinational enterprises (MNEs) make direct investment in countries with abundant natural resources. This resource-seeking OFDI can not only ensure the normal development of economic activities in the home country but also reduce environmental pollution caused by natural resource exploitation. Although China is relatively rich in natural resources, strategic resources such as iron ore, copper, natural gas, and oil are still difficult to meet the demand of its rapidly growing economy. Therefore, investing in resource-rich countries such as North Africa, Central Asia, and Latin America has become the main way for China to seek a stable supply of resources (Yao et al. 2017;Zhao et al. 2020a, b). Second, in order to reduce the restrictions of tariff, quota, and other trade barriers on the home country's export trade and solve the problems of overproduction in some domestic industries, MNEs transfer the production links of products to other countries through OFDI to create conditions for the adjustment of industrial structure and promote domestic industrial upgrading Wang et al. 2021), which helps reduce pollution emissions and improve GEE. Third, MNEs tend to adopt OFDI in developed countries to acquire advanced production technologies and strengthen the competitiveness in the international market. This technology-seeking OFDI can increase China's productivity (Zhao et al. 2010;Li et al. 2017), boost domestic employment (Jia et al. 2019), and thus promote green economic development. Accordingly, we propose hypothesis 1. H1: China's OFDI can effectively improve domestic green economic efficiency.

The impact of OFDI reverse technology spillover on green economic efficiency
By directly setting up technology-intensive subsidiaries or jointly setting up R&D centers in host countries, MNEs can obtain knowledge spillovers and feedback the R&D resources obtained by the subsidiaries to the home country's parent company (Branstetter 2006;Morck et al. 2008). Therefore, the home country can capture the reverse technology spillovers from the developed country by technologyseeking OFDI. Meanwhile, many papers have verified the existence of OFDI reverse technology spillovers, and OFDI in developed countries can significantly enhance the innovation capabilities of home countries (Zhou et al. 2018;Li et al. 2016) and MNEs Valacchi et al. 2021). The enhancement of innovation ability can significantly curb pollution emissions, promote economic growth, and thus boost green economic efficiency. In addition, multinational enterprises acquire and assimilate advanced cleaner production technologies of developed countries through "learning by doing" and other channels to promote the green technology innovation capacity of domestic firms.
For example, Zhu et al. (2018) find that OFDI for developed countries can capture reverse green technology spillovers and accelerate the progress of green technology in China. Accordingly, our study puts forward hypothesis 2.
H2: Through OFDI in developed countries, China can obtain reverse technology spillovers and improve domestic green economic efficiency.

The threshold effect of OFDI on the home country's green economic efficiency
Absorptive capacity can affect MNEs' OFDI performance (Lyles et al. 2014), and the influence of OFDI on GEE may be constrained by the home country's endowment conditions. Next, based on the human capital and financial development perspective, our research further analyzes the nonlinear influence of OFDI on GEE. On the one hand, OFDI by MNEs depends on their ability to obtain external financing, and financial constraints will impede their OFDI decisions (Yan et al. 2018). However, financial deepening can reduce MNEs' external financing cost and enhance the enthusiasm of MNEs to participate in OFDI and then help them learn advanced technologies from host countries (Jiang et al. 2020). Thus, the development of financial markets will strengthen OFDI's role in promoting GEE. On the other hand, the impact of OFDI on GEE will also be influenced by human capital, and provinces with weak human capital may struggle to fully capture and absorb technology spillovers through OFDI (Li and Liu 2012;Herzer 2011). Conversely, the improvement of human capital can promote MNEs to convert more advanced technologies of host countries into domestic productivity, thus promoting green economic efficiency. Synthesizing the above analysis, our research proposes hypothesis 3.
H3: Under the influence of financial development and human capital, the influence of OFDI on green economic efficiency shows an increasing nonlinear law.

Dynamic model
Considering the continuity of economic activities and the dynamic accumulation of GEE, we construct the following dynamic panel model to explore the direct influence of OFDI on GEE: In Formula (1), i and t represent province and time respectively, GEE it represents green economic efficiency, and OFDI it is outward foreign direct investment. X it represents control variables, i is the province effect, t is the year effect, and it is the random error term.

Panel threshold model
In order to test hypothesis 3 above, our study refers to the method of Hansen (1999), takes FD and HUM as the threshold variables to explore the nonlinear influence of OFDI on GEE, and further constructs the following single panel threshold model: In the above formula, I (·) is indicative function, q it represents threshold variable, and k is threshold value. If the (1) coefficients of 1 and 2 are significantly different, it suggests that there exists threshold effect. Besides, the multiple threshold effect model can be extended by Eq. (2), and whether to adopt the multiple threshold model or the single threshold model needs to be further examined.

Core explanatory variable
OFDI is the independent variable in our study. We adopt the proportion of OFDI stock to GDP as the measurement index to overcome the volatility of traffic data and alleviate the influence of economic scale.

Dependent variable
The dependent variable is GEE in our research. In the selection of input-output indicators for calculating GEE, Scheme 1 Estimation strategy flowchart we select total energy consumption and capital stock and employed population as input variables in reference to existing studies. We adopt the perpetual inventory system to measure the capital stock; the equation is as follows: where K it stands for capital stock, δ stands for depreciation rate, which is 9.6%, and I it stands for total investment in fixed assets. For the calculation of capital stock in 2011, the estimation formula is as follows: K i,2011 = I i,2011 ∕( + g i ) . I i,2011 is the total fixed asset investment in province i in 2011, and g i represents the geometric average growth rate of the total fixed asset investment in province i from 2011 to 2019.
At the same time, we take the real GDP as the expected output, and in accordance with the Twelfth Five-Year Plan set four major pollutants and carbon dioxide reduction targets, we select the ammonia nitrogen discharge, nitrogenoxide discharge, chemical oxygen demand, sulfur dioxide discharge, and carbon dioxide discharge as the nonexpected output. For the measurement of carbon dioxide emissions, we refer to the practice of Tan et al. (2021), adopt the carbon dioxide emission coefficient of 8 types of fossil fuels (natural gas, crude oil, kerosene, coal, coke, fuel oil, gasoline, diesel), and calculate the carbon dioxide emissions of every province in combination with the 2006 IPCC National Greenhouse Gas Inventory Guide. The calculation equation is as follows: is the ratio of carbon dioxide to carbon molecule weight (44/12), C i is the consumption of class i fossil fuels, and i is the emission coefficient of class i fossil fuels.
In the selection of measurement methods, considering the advantages of data envelopment analysis (DEA) in solving undesired outputs and multiple inputs, this paper chooses the DEA method to estimate GEE. In the case of non-desired output such as pollution emission, energy input and pollution emission usually have a "radial" relationship, while labor, capital input, and expected output usually have a "non-radial" relationship. DEA method based on SBM distance function is difficult to deal with both non-radial and radial input-output relationships. Therefore, we adopt the mixed distance function model developed by Tone and Tsutsui (2010), namely the mixed model (epsilon-based measure (EBM)) including SBM distance function and radial distance function to overcome the shortcomings of SBM model. Under the condition of variable returns to scale (VRS), the formula is as follows: In the above equation, and are different parameters, and ε means non-Archimedean infinitesimal. x is the input vector, b is the non-expected output vector, and y is the expected output vector. m stands for the number of input indicators, and q and s are the number of indicators of nonexpected output and expected output respectively. w − i is the weight coefficient of the input; w − p and w + r denote the weight coefficients of non-expected output and expected output respectively. s − i , s + r , and s b− p are the slack variables. stands for the weight vector. Based on the measurement indexes and method given above, this paper uses MAXDEA7.0 software to measure GEE of every province. Figure 1 depicts the change trend of GEE in eastern China, midwestern China, and whole China from 2011 to 2019. According to the trend of time, the mean value of GEE in every region remained basically stable from 2011 to 2015. Starting from 2016, GEE in eastern China suddenly rose sharply, which led to the increase of average GEE in whole China, it can be seen that the eastern provinces have actively implemented the green development concept put forward by the central government, and the awareness of energy conservation and emission reduction has been constantly enhanced, which has greatly reduced the emission of pollutants and promoted green economic efficiency. However, GEE in midwestern China has only slightly increased since 2018. In terms of regional differences, the average value of GEE in eastern Fig. 1 Variation trend of the mean value of GEE China was above 0.9, which was significantly greater than the mean value of 0.6312 to 0.6516 in midwestern China.

Threshold variables
Financial development (FD) and human capital (HUM) are the threshold variables in our research. The proportion of formal financial institutions' loan balance to GDP is used to measure FD, and the ratio of college students in the permanent resident population is adopted to measure HUM (Pan et al. 2022).

Control variables
In order to alleviate the problem of missing variables, our study adds the following control variables: (1) foreign direct investment (FDI): represented by the proportion of actual utilized FDI to GDP; (2) energy structure (ES): represented by the ratio of coal consumption to total energy consumption; (3) state-owned enterprises (SOE): we use the proportion of state-owned fixed asset investment in the whole society to measure; (4) population density (POPDEN): we adopt the ratio of the permanent resident population to the administrative area (a ten thousand people per square kilometer) to measure; and (5) environmental regulation (ER): our study uses the percentage of investment in industrial pollution control to industrial added value.

Baseline regression
Considering the robustness of the two-step system GMM method in dealing with heteroscedasticity and crosssectional correlation, we adopt the two-step SYS-GMM approach to estimate the dynamic panel model. Table 2 column (1) and column (2) report the results; we find that whether to add control variables, the regression results of OFDI all passed the 1% significance test, which suggests that OFDI can improve China's GEE and promote green and low-carbon economic growth. Expanding OFDI can alleviate the serious problem of overcapacity in highly polluting industries such as steel and coal, boost the transformation and upgrading of industrial structure, and effectively reduce energy consumption and pollution emissions (Zhang et al. 2022a, b, c, d;Xin and Zhang 2020). Thus, hypothesis 1 is verified.
As a reference, our study also uses dynamic OLS and dynamic FE for estimation, and the results are reported in column (3) and column (4). By comparing the estimation results, it is not difficult to find that the coefficient of the first-order lag term of the system GMM regression results (0.7321) is between the estimation results of dynamic FE (0.5322) and dynamic OLS (0.9663), suggesting that the system GMM estimation results do not have a large deviation due to weak instrumental variables or the small number of samples (Bond 2002).
Among the control variables, the estimated results of FDI and ER both passed the statistical test of 1%. This shows that foreign direct investment can help promote market competition and improve green economic efficiency. Environmental regulation can stimulate firms to adopt clearer production technology and promote economic green development. The results of ES and POPDEN are significantly negative, suggesting that the higher the proportion of coal consumption, the more detrimental to the growth of GEE. Therefore, the government should encourage the consumption of clean energy such as biomass and hydro to promote sustainable growth (Zhang et al. 2022b). Besides, higher population density may aggravate pollution emissions and inhibit the improvement of GEE. The regression result of SOE passed the significance test of 5%, which suggests that the state-owned economy is conducive to promoting GEE. The possible explanation is that state-owned enterprises are usually large in scale, which can undertake the capital investment of production technology upgrading and pollution treatment equipment construction, so as to realize the scale effect of energy conservation and emission reduction.

Replace the measurement of OFDI
Here, our research adopts the proportion of OFDI flows to GDP as a measurement index to alleviate the regression bias caused by measurement errors. The coefficients of OFDI in Table 3 column (1) and column (2) all are positive at the statistical level of 1%, which suggests that the    baseline estimation results are not affected by measurement errors.

Eliminate the influence of outliers
In order to alleviate the interference of possible outliers, we conducted 1% tail reduction for all continuous variables. Column (3) and column (4) in Table 3 show that the coefficients of OFDI still remain positive, which indicates that the baseline estimation results are not disturbed by extreme values.

Replace the sample
In order to reduce the sample selection bias, we choose 2011-2018 as the research interval for re-estimation. The coefficients of OFDI in Table 3 column (5) and column (6) are still positive at the statistical level of 1%, suggesting that the baseline results are not disturbed by sample selection bias.

Instrumental variable method
When examining the influence of OFDI on GEE, the endogenous problem should also be considered. There may be bidirectional causality between OFDI and green economic efficiency. It has been proved above that OFDI can significantly improve GEE, but provinces with higher green economic efficiency usually have higher capital level and stronger OFDI capacity. Therefore, in order to overcome the interference of endogenous, we try to select appropriate instrumental variable (IV) and use 2SLS for estimation. Effective instrumental variables should satisfy both correlation and exogenous. In our study, we select the proportion of total export-import volume to GDP (foreign trade dependency (FTD)) from 2000 to 2008 as the instrumental variable of OFDI. In terms of correlation, FTD can reflect the degree of a region's participation in the global economy; historically, provinces with higher foreign trade dependency usually have stronger OFDI tendency and ability (Zhang and Daly 2011), so as to meet the requirements of correlation. In terms of exogenous, the previous FTD has been difficult to influence the current green economic efficiency, so it meets the exogenous condition. Table 4 reports the results of IV-2SLS; the coefficients of IV are positive at the 1% level of significance in the first-stage regression results, which means it passes the correlation test between IV and the endogenous explanatory variable OFDI. At the same time, the statistical test results of Kleibergen-Paap rk LM and Kleibergen-Paap rk Wald F indicate that the instrumental variable passes the unidentifiable test and the weak instrumental variable test, which means that the IV we selected is valid. After overcoming the endogenous problem, the promoting effect of OFDI on GEE is still significantly positive, which further verifies that the benchmark results remain robust, and OFDI can become an important driving force to boost the low-carbon and green transformation of Chinese economy.

OFDI reverse technology spillover effect
Through OFDI, the home country can obtain reverse technology spillovers from developed countries. We adopt to the practice of Bitzer and Kerekes (2008) and use the following two methods to calculate OFDI reverse technology spillover: In Eqs. (4) and (5), OFDI jt stands for the stock of China's OFDI in period t of country j. K jt , RDK jt , and GDP jt represent the gross fixed capital formation, the R&D investment stock, and the gross domestic product in period t of country j respectively. For RDK jt , our study uses the approach of Potterie and Lichtenberg (2001) to measure. First, based on the GDP data from 2011 to 2019 and the percentage of R&D spending in GDP to calculate the R&D investment of each country, we adopt the perpetual inventory system as above to measure the stock of R&D investment ( RDK jt ). (4) Investment in developed countries often makes it easier to capture technology spillovers and promote domestic innovation (Panagiotis et al. 2018). Therefore, we select Germany, America, France, Canada, England, Japan, South Korea, and Italy as research objects; these eight countries have the highest levels of industrial production capacity and technological innovation, and Chinese direct investment in these countries can help capture reverse technology spillovers. Statistical Bulletin of China's Outward Foreign Direct Investment provides data on China's stock of direct investment in these eight countries, while data on GDP, R&D spending as a share of GDP, and the gross fixed capital formation for these eight countries are all from the World Bank Database (WDI).
Based on the above methods, we calculate the R&D spillovers from developed countries through OFDI and then take the percentage of R&D spillovers to GDP as the index to measure reverse technology spillovers (OFDI-Spillover). Based on the model (1), we use OFDI-Spillover to replace       (1) and (2) in Table 5 are regression results of technology spillovers calculated by Formula (4); the estimation results of technology spillovers calculated by Formula (5) are reported in columns (3) and (4). We find that the coefficients of OFDI-Spillover are all positive at the statistical level of 1%, which suggests that expanding OFDI can capture green technology spillover from developed countries, promote domestic green technology progress (Bai et al. 2020;Luo et al. 2021), and improve China's GEE. Thus, hypothesis 2 is verified.

Heterogeneity of the period
In 2015, the central government put forward the vision of green development, which provides a guide for local governments to strengthen environmental conservation and promote sustainable economic growth. Combining with the change trend of GEE in Fig. 1, we can speculate that there exists a discrepancy in the promotion effect of OFDI on GEE before and after 2016. Based on this, we construct the time dummy variable T, which is set as 0 from 2011 to 2015 and 1 from 2016 to 2019, and then add the product term T × OFDI to model (1) to investigate the heterogeneity of the period. Table 6 column (1) shows that the result of OFDI remains significantly positive, and the regression coefficient of T × OFDI is also positive at the significance level of 1%, suggesting that the promoting effect of OFDI on green economic efficiency is further enhanced after 2016. The possible reason is that under the constraint of the total pollution index control target, local enterprises may transfer the heavily polluted production links and absorb the clean production technology of the host country through OFDI, so as to accelerate the green transformation development.

Heterogeneity of region
China is a vast country, and different provinces have very different resource endowments. In order to give full play to the geographical advantages of the eastern region, the State encouraged the eastern provinces to give priority to development after reform and opening up; therefore, eastern China is clearly ahead of midwestern China in terms of economic level, science and education level, etc. Besides, as of 2019, the OFDI stock of by local enterprises was US $785.55 billion, of which eastern China (Hebei, Tianjin, Beijing, Jiangsu, Shanghai, Fujian, Zhejiang, Hainan, Guangdong, Shandong) reached US $640.94 billion, accounting for 81.6%. Therefore, we speculate that there may be regional heterogeneity in the influence of OFDI on GEE. We adopt the practice of Jia et al. (2021) to test the heterogeneity of the region, when examining the impact of OFDI on GEE in eastern China, and we assign a value of 1 to the ten provinces in eastern China and a value of 0 to the midwestern provinces and construct the interaction term between regional dummy variable (eastern) and OFDI. Similarly, we also construct the cross-terms of regional dummy variable (midwestern) and OFDI to test the influence of OFDI on GEE in midwestern China.
The results of columns (2) and (3) in Table 6 show that the coefficient of eastern × OFDI is positive and passes the 1% significance level test; however, the regression coefficient After more than 30 years of rapid development and market-oriented reform, eastern provinces have accumulated relatively sufficient capital and technology, and the developed economic level has created conditions for carrying out OFDI and absorbing reverse technological spillovers. However, the marketization degree and economic level of the midwestern provinces lag behind relatively. On the one hand, the OFDI of these provinces could squeeze out their own investment (Gondim et al. 2018) and, detrimental to technological innovation, then counteract the promoting effect of OFDI on GEE; on the other hand, the technological gap between the midwestern regions and developed countries is relatively large, which is not conducive to absorbing the reverse technology spillovers through OFDI (Hong et al.). Therefore, the promoting effect of OFDI on GEE in midwestern China is not significant.

The threshold effect test of OFDI on GEE
Above, we have examined the linear influence of OFDI on GEE, but this ignores the differences in resource endowments between regions. In fact, the impact of OFDI on GEE is relatively complex, and it may be constrained by a variety of endowment characteristics and conditions. Next, we take financial development level (FD) and human capital (HUM) as threshold variables respectively to further investigate the nonlinear impact of OFDI on GEE. From Table 7, we find that the F statistical values all pass the single threshold test at the statistical level of 5%, but the double thresholds do not pass the statistical test, so there is only one threshold value in the model. 95% confidence intervals and corresponding threshold estimates are shown in Table 8.
The estimation results in the Table 9 column (1) show that, when FD is less than 2.0972, the coefficient of OFDI is 0.4771, when FD exceeds 2.0972, the coefficient of OFDI on GEE increases to 2.5459 and passes the 1% statistical level test. Suggesting that the influence of OFDI on GEE is affected by the regional financial market, with the progress of financial markets, the promoting effect of OFDI on GEE presents a nonlinear law of positive increase. This situation is not difficult to explain; financial deepening can alleviate the financing constraints of MNEs, which helps them to carry out OFDI and green innovation. Besides, FD can encourage the consumption of renewable energy and promote green growth (Pata et al. 2022). Similarly, in Table 9 column (2), we find that when the HUM is less than 0.0290, the coefficient of OFDI is 0.6822; when HUM exceeds 0.0290, the coefficient of OFDI on GEE significantly increases to 4.5920. This indicates that the growth of human capital level can strengthen the promoting effect of OFDI on GEE. Human capital can provide support for MNEs to learn and absorb technology from developed countries; the stronger human capital is, the greater the absorption effect on technology spillovers will be (Zhu et al. 2018). Thus, hypothesis 3 is verified. Unfortunately, we find that most samples are located in the first threshold range, and the financial development level and human capital of most provinces did not exceed the threshold value (except for a few regions such as Beijing and Tianjin). This indicates that most provinces can significantly enhance the motivating effect of OFDI on GEE by promoting the development of financial markets and improving the human capital. Fig. 2 The impact of OFDI on GEE On the basis of the above conclusions, we express the outcomes as follows (see Fig. 2).

Research conclusions
Chinese enterprises' "going global" is a key impetus for the green transition of the domestic economy. Our study adopts the data of 30 provinces from 2011 to 2019 to examine the influence of OFDI on China's green economic efficiency. Our findings show the following: (1) OFDI significantly boosts the improvement of GEE, a series of robustness tests still support this conclusion, and reverse technology spillover through direct investment in developed countries is an important way for OFDI to improve GEE. The above conclusions further verify that OFDI can promote energy conservation and emission reduction in the home country and can capture the green technology spillover from the host country.
(2) The OFDI in eastern China significantly improves GEE; however, the impact of OFDI on GEE in midwestern China does not pass the statistical test; this may be closely related to regional resource endowment and OFDI distribution. In addition, the promoting effect of OFDI on GEE has been further enhanced after 2016. (3) We further use the panel threshold model to test the nonlinear influence of OFDI on GEE and find that, with the enhancement of and HUM, the promoting effect of OFDI on GEE shows a nonlinear law of positive increase. This also validates the conclusion of existing studies that FD and HUM can enhance absorptive capacity and reverse technology spillovers.

Policy recommendations
According to the above conclusions, this paper puts forward the following policy recommendations: First, China should further open up to the outside world at a high level and encourage domestic multinational enterprises to carry out OFDI. The eastern region should expand technology-oriented OFDI and invest more funds in hightech industries such as high-end manufacturing, ICT industry, energy conservation, and environmental protection industry, so as to fully absorb reverse technology spillovers from developed countries and improve domestic green economic efficiency.
Second, our study shows that OFDI in the midwestern region does not significantly promote GEE, and the stock of OFDI in the midwestern region accounts for less than 20%, indicating that OFDI is not an important driving force to improve GEE in the midwestern provinces. Therefore, the midwestern region still needs to attract FDI and expand foreign trade to accumulate capital and increase the R&D investment, so as to avoid crowding out the green technology innovation investment of local enterprises due to OFDI.
Third, the state should accelerate the reform of financial liberalization, improve the credit financing capacity of all regions, optimize the credit structure, and increase the credit support for the overseas investment of MNEs, so as to reduce the financing cost of MNEs carrying out OFDI and absorbing reverse technology spillovers. At the same time, all provinces should continue to increase investment in education, provide more opportunities to receive higher education for young people, strengthen the training of scientific and technological talents, and accelerate the accumulation of human capital, so as to provide talent support for absorbing OFDI technology spillovers and improving green economic efficiency.
Finally, OFDI may be influenced by a variety of risk factors (including political, economic, and geographical) in the host country ). Therefore, China should strengthen investment cooperation with host countries and promote investment liberalization and facilitation by relying on economic and trade platforms such as the Belt and Road Initiative (BRI) and the Regional Comprehensive Economic Partnership (RCEP). At the same time, government departments should improve the policy support system for OFDI and provide MNEs with political, cultural, and legal information of host countries, so as to reduce the negative impact of OFDI caused by political or economic crisis of host countries. In future studies, when investigating the influence of OFDI on GEE in the home country, factors such as the political, economic, and cultural of the host country should also be considered.