Empirical Analysis of Sustainable Trade Effects of FTAs Based on Augmented Gravity Model: A Case Study of China

: China has developed many strategies to promote sustainable trade, including accelerating the signing of free-trade agreements (FTAs). However, there is a lack of studies examining the impact of FTAs on the sustainable growth of foreign trade from a holistic perspective. This paper applies an augmented gravity model to verify the trade creation and diversion effects of China’s FTAs that are currently in effect. A panel data analysis over the period of 1995–2019 is conducted on 34 countries and regions, including China, and Poisson pseudo-maximum likelihood (PPML) is employed to test three different ﬁxed-effects models. The results show that the trade effects differ across FTAs, with nine FTAs generally making positive contributions to China’s trade and social welfare growth, and the remaining ﬁve FTAs exhibiting varying degrees of trade diversion or contraction effects. Empirically, it is clear that participation in FTAs has contributed to the sustainable trade of China, but China still needs to take prudent action to pursue further trade liberalization in order to counter the potential threat of trade diversion.


Introduction
Sustainable international trade is an important aspect of economic development, and free-trade agreements (FTAs) play a key role in sustainable international trade activities.The Chinese government has promoted the processes for negotiating and signing FTAs, treating FTAs as a new path to further opening up the country, accelerating the process of deepening reform, and promoting economic development.By the end of 2021, China had signed a total of 19 FTAs with 26 countries and regions.With the rapid growth of regional trade activities since the 21st century, it is particularly important to recognize and analyze the impact of trade agreements on the sustainable international trade of China.This paper constructs an augmented gravity model that encompasses as many FTAs as possible to verify the impact of China's currently effective FTAs on sustainable trade.The main contributions of this paper are reflected in the following two aspects: First, this paper fills a gap in the research on the impact of China's FTAs on sustainable trade, while most related studies have focused on China's mega FTAs, such as the China-ASEAN FTA (ACFTA).Second, this paper provides a new holistic perspective, examining all of China's FTAs as of 2019, considering the interaction of the FTAs, and determining the main contribution of the FTAs to sustainable trade.
An FTA is an agreement between two or more economies to establish a free-trade area in which each economy's goods can be shipped to the other with few or no tariffs but where the economies impose tariffs on extra-bloc goods [1].Issues such as the contribution of FTAs to the sustainable growth of bilateral and multilateral trade, whether the increase in intraregional trade has come at the cost of extra-bloc trade diversion, and the possible export or importer trade effects of FTAs have become important concerns for the sustainability of free trade.Concerning the economic and trade benefits gained from FTAs, international trade economists have concentrated on the net social welfare changes caused by FTAs since Viner (1950) [2].Tinbergen (1962) was the first to introduce the gravity model into studies of international trade [3].Since his seminal work, the gravity model of trade has been widely used in the study of the trade and economic effects of regional trade agreements (RTAs).However, as stated by Magee (2008), many studies examining the trade changes induced by an FTA have only shown the growth of welfare because of the difficulties in acquiring data and in measuring welfare changes [4].Some of the previous empirical studies of FTAs have demonstrated the trade effects of a particular FTA on trade [5][6][7][8], while other scholars have introduced multi-FTAs in their studies.Magee (2008) improved the gravity model and examined the expected and lagged trade effects of RTAs using panel data for 133 countries from 1980 to 1998 [4].Despite the regression results, Magee's research explored the role of trade agreements as comprehensively as possible.In a study of the factors influencing exports within the ASEAN FTA (AFTA), Kien (2009) introduced dummy variables of AFTA but also of EU, MERCOSUR, and NAFTA [9].Kahouli and Maktouf (2015) introduced dummy variables of the EU-15, EMU, AMU, and AGADIR agreements into the gravity model within a Viner analysis specification when examining trade creation and diversion effects in the Mediterranean region [10].Parra et al. (2016) introduced ten FTAs to determine the creation effect of MENA trade on agricultural and industrial products in their study [11].Jagdambe and Kannan (2020) added EU-15, MERCOSUR, NAFTA, and SAFTA dummies to the gravity model in order to estimate the effects of the ASEAN-India FTA on agricultural trade [12].
For the empirical research of China FTAs, Roberts (2004) conducted an ex ante analysis of the potential of the proposed China-ASEAN FTA and argued that no potential trade creations or diversions will occur [13].Bhattacharya and Bhattacharyay (2007) stated that opening up trade cooperation between China and India can promote intra-regional trade and benefit the Asian economy and even worldwide sustainable development [14].Sun and Reed (2010) conducted OLS and PPML regressions on six regional agreements, including ACFTA and the North American Free Trade Agreement (NAFTA), applying a time and bilateral country-pair fixed-effects model, and they found that ACFTA had a significant trade creation effect on agricultural exports [15].Sheng et al. (2014) studied the impact of ACFTA on components trade using an extended gravity model [16].Yang and Martinez-Zarzoso (2014) examined the impact of ACFTA on total trade, agricultural trade, manufactured goods trade, chemical products trade, and machinery and transport equipment trade using an augmented gravity model, and they found that ACFTA had a significant trade creation effect [17].Shepherd (2019) conducted a counterfactual analysis using the structural gravity model GEPPML, which indicated that the implementation of RCEP will lead to an increase in total exports and real GDP for China, while CPTPP will be harmful to China's trade [18].Alleyne, Zhang, and Mu (2020) empirically estimated the impact of ACFTA on the efficiency of ASEAN exports to the Chinese market by using a structural gravity model, noting that ACFTA has made ASEAN members' trade with China more sustainable [19].Harada and Nishitateno (2021) examined the impact of preferential tariff reductions under FTAs on the wine trade in China, Japan, and South Korea [20].Lyu et al. (2021) found that China tends to gain economic benefits from large trading partners and non-economic benefits from concessions to smaller trading partners in FTA negotiations [21].Haq et al. (2021) and Shah et al. (2022) analyzed the China-Pakistan FTA (CPFTA) in terms of RCA and the advantages and disadvantages brought about by the FTA, and they found that the CPFTA has generally had a positive effect on China-Pakistan trade [22,23].
The review of the previous literature shows that the gravity model has been widely applied to the study of FTAs.The model has covered various forms of estimating the impact of FTAs on trade, ranging from the initial three dummies of a single FTA to the current multi-FTA model [5][6][7][8][9][10][11][12].Regarding the research on China's FTAs, most of the studies appear to focus on ACFTA.In the multi-FTA model, it is common to introduce regional mega FTAs among countries and areas with different states of development [9][10][11][12].
However, there is a lack of studies examining the impact of FTAs on the sustainable growth of foreign trade from a holistic perspective.Considering only one of China's FTAs and ignoring the impacts of the other FTAs on trade may lead to biases in the results.Therefore, in addition to filling the gap of FTA research in China, the perspective of this paper provides a major difference to that presented in the previous literature.

Augmented Gravity Model
This article is mainly based on the tariff, regional integration, and universal gravitation theory of international trade.According to the customs union theory devised by Viner (1950), the net social effect of an RTA could be ambiguous [2].When two or more economies establish free-trade agreements to reduce or eliminate tariff and non-tariff barriers, reductions in the entry barriers of goods and factors for production in each other's markets facilitate the process of market integration and enhance multilateral communication and cooperation.As a result of regional integration, an economy shifts its production and trade activities, progressing from a costly and inefficient extra-bloc member to an economically efficient intra-bloc member; the generic term 'trade creation (TC)' refers to this act of increasing trade and social welfare via cost saving and the redistribution of resources, while the notion of 'trade diversion (TD)' refers to the social welfare loss caused by trade transfer from efficient extra-bloc members to inefficient and high-cost intra-bloc members.An ex post trade effects analysis of an FTA is generally based on the abovementioned concept and on a counterfactual comparison between the actual trade volume after the implementation of the FTA and the trade volume in the absence of the FTA; then, the trade effects of the FTA are assessed by calculating the average treatment effect (ATE).Therefore, the net change in social welfare brought about by an FTA is always the combination of trade creation and diversion effects.The gravity model, which is derived from Newton's law of gravitation, considers bilateral trade proportional to the respective economic volume (GDP) and negative to the geographical distance between two economies.The distance factor is often regarded as the key to distinguishing the gravity model from any other model, and the distance variable is used to represent the transportation cost.The introduction of dummy variables has been the most common approach in previous gravity studies.However, the choice of the research specification and the correct setting of FTA dummies are the key issues that haunted such studies.Carrere (2006) and Martinez-Zarzoso, Felicitas, and Horsewood (2009) argue that a proper ex post analysis of trade effects under the Vinerian specification should include three FTA dummies and that the correct introduction of dummy variables can effectively separate trade creation and diversion effects so as to distinguish between exports and imports [24,25].Therefore, the empirical models described below are used in the Vinerian specification with three FTA dummies to avoid inaccuracies and to introduce all FTAs of China in the multi-FTA model in order to estimate the joint effect.The logarithmic augmented gravity model is given below: where X ijt represents the export volume from economy i to economy j in year t; FTA k ijt , FTA k it , and FTA k jt are the three FTA dummies concerning trade creation and diversion effects, capturing intra-bloc and bloc export (import) to (from) extra-bloc.FTA k ijt takes the value of 1 when both exporter i and importer j belong to the FTA 'k' in year t; otherwise, it is 0. A positive significant FTA k ijt reflects the trade creation effect, indicating that intra-bloc trade is higher than the expected 'normal' as a result of FTA implementation.However, a negative FTA k ijt indicates trade contraction.FTA k it equals 1 when only exporter i belongs to the FTA 'k' in year t; otherwise, it is 0. A significant positive coefficient of FTA k it indicates that regional integration led to an increase in exports from intra-bloc members to non-FTA members, while a negative coefficient implies a reduction in exports to extra-bloc non-members, indicating that FTA members tended to export to members rather than non-members, which is called the export diversion effect.FTA k jt takes the value of 1 when only importer j belongs to the FTA 'k' in year t; otherwise, it is 0. FTA k jt is used to capture the import diversion effect; a significant positive coefficient implies that intra-bloc members imported more from extra-bloc non-members, while a negative coefficient indicates the import diversion from extra-bloc to intra-bloc for FTA members.µ ijt is the error term in the logarithm, and α 0 is the constant term.Control denotes a batch of control variables that could affect bilateral trade.Taking into account the characteristics of China and its FTA members, as well as those of its other major trading partners, 11 variables were added, resulting in Equation ( 2): where GDP it and GDP jt refer to the GDPs of economies i and j in year t, respectively.Dist ij is the geographical distance between the capitals of economies i and j.Pop it and Pop jt represent the populations of economy i and economy j, respectively.Bor ij takes a value of 1 when i and j share a common border; otherwise, it is 0. Lang ij takes a value of 1 when i and j have at least one common official language; otherwise, it is 0. SI M ijt refers to the similarity index that measures the similarity in economic size between economies i and j in year t, with the similarity index ranging from 0 (absolute different) to 1/2 (absolute similar).SI M ijt is expected to be positive since an increased similarity in product diversity creates more trade based on consumer demand for variety.RFE ijt reflects the difference in the relative factor endowment between i and j, and RFE follows the definition of Breuss and Egger (1999) as the absolute value of the difference in GDP per capita [26].The formulations of SIM and RFE are in accordance with Ekanayake, Mukherjee, and Veeramacheneni (2010) [27] and Kahouli and Maktouf (2015) [10], given as Equations ( 3) and (4), respectively.Considering the ongoing impact of the financial crisis on global trade and the fact that the effective years of the China-Pakistan FTA and the China-New Zealand FTA coincided with the financial crisis, the dummy variable FC is introduced to analyze its impact on China's trade, and the FC variable takes the value of 1 after 2008; otherwise, it is 0. The dummy variable TW is applied to estimate the impact of the 2018 Sino-US trade war.TW takes the value of 1 in 2018 and 2019; otherwise, it takes 0. The description of each variable is shown in Table 1.The issue of zero-value trade is inevitable when studying trade flows utilizing gravity types, where the explanatory variables are transformed into logarithmic form and zeros can only be omitted (X cannot be zero in the lnX form).However, the selective removal of zeros may lead to biased regression results.The omission of all zero trades may result in important information being missed, particularly as zero trades may be related to changes in national trade policies or other restrictive factors that may cause behavior changes in foreign trade enterprises.In the seminal work of Silva and Tenreyro (2006), they first argued that dropping zeros directly or adding a small value such as 1 to zero and Tobit regression methods are ineffective in the presence of heteroskedasticity, leading to discontinuous and biased estimates of variables such as trade policy, while the Poisson pseudo-maximum likelihood (PPML) estimation can solve the issue of zero-value trades and the common heteroskedasticity problems of trade data [28].Silva and Tenreyro (2011) confirmed that PPML estimation remains useful when there is a large proportion of zeros in the trade data [29].Westerlund and Wilhelmsson (2011) examined different estimation methods for panel data and suggested that the heteroskedasticity inherent in log-linear formulae leads to inefficient and 'deceptive' LS estimates, and the Poisson fixed-effects estimator was suggested in the gravity panel data analysis [30].Therefore, this paper applies the PPML to solve the problem of zeros and heteroskedasticity.The PPML nonlinear specification is shown below: Baier and Bergstrand (2007) argue that the average treatment effect (ATE) of an FTA calculated using cross-sectional data is unreliable and that the long-term effects are biased; the trade policy variables are not exogenous.Unbiased estimates can be obtained by controlling for endogeneity when using panel data together with country-time (timevarying) fixed-effects and pair fixed-effects models as proposed by Baldwin and Taglioni (2006) [31,32].Magee (2008) argues that time-varying factors affecting bilateral trade are difficult to test when using traditional gravity models and that the use of time-varying fixed-effects equations, while better at avoiding endogeneity, has the important disadvantage of not capturing diversion effect variables and some specific variables of interest [4].Considering the debates in the previous literature and the necessity to control the multilateral resistance terms (MRTs) argued by Anderson and Wincoop (2003), three different fixed-effects specifications are included for an analytical comparison to avoid endogeneity bias of the FTAs [33]:

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The time fixed effect (δ t ).This is used to capture macro-cyclical factors and time trends in global trade flows, as well as any shocks affecting trade in a fixed year.

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The time fixed effect (δ t ), exporter fixed effect (ϕ i ), and importer fixed effect (ϕ j ).Country fixed effects capture the effects of economy-specific factors, such as infrastructure and factor endowments.

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The time fixed effect (δ t ) and pair fixed effect (ϕ ij ).The pair fixed effect is used to control for endogeneity from trading pairs and all the unobserved dyad factors that do not vary with time, such as distance, common borders, and common languages.Therefore, such variables constant with time are omitted due to perfect multicollinearity.

Data Description
For the scope of this study, we select a total of 14 FTAs of China that are currently in force and notified by WTO as of 2019, namely, the Mainland and Hong Kong/Macau Closer Economic Partnership Arrangement (MHCEPA/MMCEPA), China-ASEAN FTA (ACFTA), China-Chile FTA (CCFTA), China-Pakistan FTA (CPFTA), China-New Zealand FTA (CNFTA), China-Singapore FTA (SCFTA), China-Peru FTA (PCFTA), China-Costa Rica FTA (CCRFTA), China-Switzerland FTA (CSFTA), China-Iceland FTA (CIFTA), China-Korea FTA (CKFTA), China-Australia FTA (CAFTA), and China-Georgia FTA (CGFTA).Information on the notification status of the FTAs is available in the WTO RTA database.Considering that the impact of COVID-19 during 2020 and 2021 will be much larger than the impact of the FTAs on bilateral trade and even global trade, the data selection in this paper does not include these two years.Therefore, the dataset of this paper contains the annual export panel data of 34 countries and regions spanning from 1995 to 2019 and 34 economies, including China and its FTA partners, as well as its top 20 trading partners in terms of exports in 2019 (the countries and regions that remain after the removal of members already on the FTA list are the US, Japan, Germany, India, the Netherlands, the UK, Taiwan, Russia, Mexico, Canada, and Brazil), for a sum of 28,050 observations (34 × 33 × 25).The annual export data are obtained from the IMF, and the GDP data are obtained from the World Bank and the UNCTAD databases.The population data are taken from the World Bank, and the distance between capitals and the dummies of common borders and official languages are drawn from the CEPII database.Since the IMF, World Bank, and other databases do not contain any foreign trade, population, or GDP data on Taiwan Province, the data on Taiwan's exports and population are taken from the Ministry of Finance of Taiwan, and the data on Taiwan's GDP are taken from UNCTAD.Information concerning the core variable FTA dummies is taken from the WTO, and the value is decided by the year in which each FTA came into effect.As the effective date of the China-Australia FTA and the China-Korea FTA was December 20, 2015, the dummies of CAFTA and CKFTA take the value of 1 starting from 2016.For the assessment of the trade effects in the mode of Carrera under the Vinerian specification, we refer to the comprehensive interpretation of the dummy variable coefficients from previous papers [8,10,15,17,25], as shown in Table 2. Trade creation in import (TCM) + Import diversion (MD) (ρ 1 > ρ 3 ) Intra-bloc import contraction (MC) + Import diversion (MD) Pure import diversion (PMD) (ρ 1 < ρ 3 ) Note: A decrease in intra-bloc exports (imports) and an increase in extra-bloc exports (imports) is considered a form of export (import)expansion (XE or ME) that FTA members tend to trade more to the rest of the world [25].

Results
The Hausman test is conducted to analyze the fixed-effects model (FM) and the random-effects model (RM), and the results suggest that Prob>chi2 = 0.0000; therefore, FM is preferred to RM.Since the estimates vary broadly among various specifications under PPML and OLS, the heteroskedasticity-robust regression specification error test (RESET) suggested by Silva and Tenreyro (2006) is carried out to examine the functional misspecification of the estimated models [28].The correct specification passes the RESET with a p-value higher than 0.01, accepting the null hypothesis that no misspecification was detected.The RESET results presented in Table 3 reveal that PPML is preferable in our model because all p-values of PPML estimations pass 0.01, while all OLS estimations fail the RESET.According to the regression results, the GDPs of the exporter and the importer are statistically significant at the 1% level, which is in line with the previous literature, and they have the expected positive effects on trade.The coefficient of the distance variable is, as expected, significantly negative at the 1% level and harms exports, which confirms that transport and distance-related costs are vital factors affecting trade.The coefficients of the population are negative in all models, and they are only significant in the time-fixed model.Howbeit, these results support the view that population is negatively related to trade flows because a larger population implies a larger domestic market, a richer resource endowment, and, hence, a diversification of output and a reduced dependence on international division, thus reducing foreign trade; the insignificant population coefficient in the typical pairfixed model must be valued in such a way that population no longer has an essential impact on China's trade.Sharing a common border affects the trade of China positively, which is in accordance with our expectations and previous gravity studies.The language variable is insignificant in all PPML estimations.The similarity index has a negative and insignificant coefficient under all PPML regressions, which contradicts our expectations.This result is similar to the finding of Kahouli and Maktouf (2015) [10], who asserted that the insignificant result was caused by the heterogeneity in the FTAs between developed and developing countries.It is expected that a higher development gap between economies implies higher inter-industry trade and that a lower gap between economic sizes means larger variety-orientated intra-industry trade.Given the range of coefficients from −0.05 to −0.005, inter-industry trade dominates China's trade, but the impact seems minimal.RFE is confirmed to be positive and significant at the 5% and 1% levels in the time-fixed model and the time-country-fixed model, respectively.As the total trade flows are the sum of inter-and intra-industry trades, increased differences in relative endowments lead to a greater growth in inter-industry trade than in intra-industry trade and enhance exports associated with technological progressiveness.The financial crisis and trade war dummy variables are both insignificant under the country or pair-fixed-effect model, indicating that the financial crisis had no persistent impact on China's free trade from a long-term perspective as expected and that the trade war did not cause significant trade disruption or diversion effects.
Of the three models estimated, the time-pair-fixed model is preferable to the other two [32].The interpretation of the FTA dummy variables thus focuses on the time-pairfixed model under the PPML, but the first two models are still kept as references.Therefore, the coefficients and the relative trade effects of the FTAs are summarized accordingly and presented in Table 4.To fill some research gaps and to perform a comparative analysis for the study, all of the 14 FTAs are examined in a separate regression analysis under the same model to ensure the consistency of the results, and these results are shown in Table 5.According to the results, the significances of the FTA dummies vary widely from Table 4 to Table 5.It is interesting to observe that, compared to the aggregated FTAs, the coefficients of the 19 dummy variables in total are overestimated for the first seven FTAs prior to 2010, except for MMCEPA it and SCFTA jt , while the coefficients of the last seven FTAs after 2010 are underestimated, except for CIFTA ijt and CIFTA it .The coefficients of the FTAs established after 2010 all increase significantly when considering multiple FTAs, which suggests that the mutual influence of multiple FTAs may result in the dilemma of simply attributing the latter construction to the former, while the enhancement in trade in the earlier period is not correctly reflected in the latter, and the deviation of the results also illustrates the significance of the multi-FTA model.The reasons for this, such as late entry into the FTA, the lack of experience, and the low utilization rate of the FTAs, could have a profound impact on the results.Note: The coefficients and corresponding trade effects of each FTA dummy variable are summarized according to the time-pair fixed-effect model, with ***, **, and * indicating that the statistics are significant at the levels of 1%, 5%, and 10%, respectively.The net trade effect is calculated by adding and subtracting at the same level of significance, the trade effects for each FTA in this paper are also classified according to the positive and negative meanings of the coefficients at the same level of significance, and the resulting trade effects are summarized and labeled at the 5% or 10% level in the absence of a 1% level of significance.The name of the trade effects are in accordance with Table 2, and PTC represents the pure creation effect (PTCX + PTCM).
By comparing the regression results of the FTA dummies under the three different models, the FTA dummies under the time-fixed model are generally higher and more significant than those under the other two.MHCEPA contributes the most to the welfare growth of the intra-bloc members and also to the extra-bloc partners, but its average treatment effect (ATE) is 1688.57%[exp(2.884)− 1], which implies that MHCEPA causes bilateral trade to be 16.88 times higher than that expected in its absence.When the net effect of MHCEPA is considered, a net trade creation effect of 23,980.80%[exp(5.484)− 1] is found, representing a 239 times promotion in international trade due to the establishment of MHCEPA, which is incredible and obviously beyond the range of an FTA.However, a more interesting finding is that, while ACFTA has insignificant impacts on both TC and TD in the pair-fixed model and the country-fixed model, the time-fixed model exhibits a positive and significant trade creation effect with an ATE of 212.68% [exp (1.14) − 1] and a net effect of 835.58% [exp(2.236)− 1], which is similar to previous studies on ACFTA.Taking into account the annual growth of trade between China and ASEAN-10, as well as the reasons for different samples and choices of specifications in the research, the results of ACFTA in the time-fixed model are summarized in Table 4 for reference.According to the estimates in Table 4, MHCEPA ijt is negative and significant at the 1% level, indicating that MHCEPA has a trade contraction effect, and MHCEPA jt is positive and significant at the 5% level.The contraction effect of MHCEPA can be explained by the economic transformation of Hong Kong and the increasing growth of the mainland's free trade with foreign countries.It is difficult to achieve very high trade volumes via trade agreements when the mainland and Hong Kong are engaged in a long-term, well-behaved, economic and trade cooperation.The significant and negative coefficients of MMCEPA ijt indicate a contraction effect of intrabloc trade, but the positive MMCEPA it and MMCEPA jt coefficients imply that MMCEPA has an expansion effect on extra-bloc exports and imports.The pure trade creation effect exhibited by ACFTA indicates that the agreement has contributed to the growth of the trade and social welfare of Sino-ASEAN and even extra-bloc countries.The positive CCFTA ijt and CCFTA it coefficients indicate that CCFTA has pure creation effect in terms of exports, suggesting that CCFTA has caused the growth of intro-bloc trade and social welfare, as well as the growth of the exports of China and Chile to non-FTA members outside the region.The coefficient of CPFTA ijt is positive but significant at the 10% level, which indicates an intra-bloc creation effect on exports.CNFTA displays the intra-bloc creation effect and import diversion effect while at the 10% level.The negative coefficient of SCFTA ijt indicates that SCFTA has caused an intra-bloc trade contraction effect and has decreased the welfare of members.The coefficients of SCFTA it and SCFTA jt are both negative, reflecting the diversion effect of imports and exports, but they are only significant at the 5% level.The coefficients of PCFTA ijt and PCFTA jt are positive and significant at the 1% level, indicating that PCFTA has had a pure trade creation effect on imports.CCRFTA jt is negative and significant at the 1% level, which indicates an import diversion effect and that the establishment of CCRFTA has led to reductions in imports from extra-bloc non-members.The coefficients of CSFTA ijt and CSFTA it are positive and significant at the 1% level, indicating that CSFTA has promoted trade between China and Switzerland and has increased exports to countries outside the region, which implies a pure trade creation effect on exports.Concerning CIFTA, the coefficient of CIFTA it is negative and significant at the 1% level, indicating that CIFTA has an export diversion effect.The negative CKFTA ijt coefficient is significant at the 5% level, indicating that CKFTA has a trade contraction effect.Both CAFTA ijt and CGFTA ijt are positive and significant at the 1% level, indicating that CAFTA and CGFTA have boosted intra-bloc trade.Overall, according to the results, four FTAs (MHCEPA, MMCEPA, SCFTA, and CKFTA) of China have a trade contraction effect resulting in a corresponding loss in China's social welfare when considering the average treatment effect only.ACFTA, CCFTA, CPFTA, CNFTA, PCFTA, CSFTA, CAFTA, and CGFTA, eight FTAs in total, have a trade creation effect, contributing to the growth of trade and social welfare between China and its FTA partners.Among the net trade effects, five FTAs (MHCEPA, SCFTA, CCRFTA, CIFTA, and CKFTA) exhibit a negative impact on China's foreign trade, while the remaining nine FTAs (MMCEPA, ACFTA, CCFTA, CPFTA, CNFTA, PCFTA, CSFTA, CAFTA, and CGFTA) all contribute to China's foreign trade and improvement in social welfare.These results suggest that China has benefited from its participation in FTAs and that the construction of the FTAs has made a significant contribution to the sustainable growth of China's foreign trade, but the impact of previous FTAs on trade and social welfare has been mixed.A comparative analysis of the change in results between the disaggregated FTA model and the aggregated FTA model also demonstrates the importance of the multi-FTA model.It is clear that China benefits from FTAs, but the potential trade diversion and contraction effects need to be given due attention that not every FTA is beneficial for sustainable trade.

Discussion
This paper examined the impact of China's FTAs on sustainable trade from a holistic perspective, utilizing an extended gravity model, determining the contribution of all of China's FTAs to trade up until 2020, and providing a reference for subsequent relevant FTAs.The net trade effects demonstrate that China has gained some benefits from its participation in FTAs and that the FTAs have generally contributed to sustainable trade within the bloc.Given the good regional cooperation outcomes implied by an FTA, it will provide good policy insights for China and other countries that are looking to establish an FTA with China.
However, the estimations of the impacts of FTAs on trade are still insufficient, and as the gravity model continues to be improved, future research on FTAs under the gravity model should cover the following important aspects:

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A more detailed analysis of specific industries and commodities with disaggregated data.

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A comparative analysis of FTAs under more specific classifications (e.g., similarities, resource endowment, and differences in trade structure).

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The introduction of a time-varying fixed-effects model, which may require a certain number of FTA dummy variables to be removed, and dynamic research, which is set to become a relevant topic.

Conclusions
This paper aimed to investigate the sustainable contribution of China's current FTAs to trade by examining 14 FTAs in force as of 2019, by utilizing a holistic view of China, and by building a multi-FTA model using an augmented gravity model.The problems of zero-value trades and heteroskedasticity, which are common in the empirical analysis of trade flows, were solved by using the PPML, and it was confirmed via the RESET test that the PPML method is more appropriate than the OLS method.Comparing the estimation results of separate and multiple FTAs, it was suggested that the 14 FTAs in China were implemented by 2010, with the first 7 FTAs being overestimated in the separate analysis and the last 7 being underestimated, suggesting that a single FTA model may cause biases.The effect of China's FTAs on sustainable trade growth analyzed in this paper fills a certain research gap and provides a reference for related subsequent studies, which has both theoretical and practical significance for promoting the implementation of China's free trade and investment facilitation policies and the further development of FTAs.The empirical results reveal that increases in the sizes of the economies of the exporters and importers and a shared border boost bilateral trade, and distance had the expected negative impact on trade flows, while financial crises and trade wars did not have the expected trade contraction or disruption effects.MMCEPA, ACFTA, CCFTA, CPFTA, CNFTA, PCFTA,
ijt Dummy variable used to capture TC, equaling 1 when both i and j belong to an FTA in year t.+/−FTA itDummy variable used to capture TD in terms of export, equaling 1 when exporter i belongs to an FTA in year t.+/−FTA jtDummy variable used to capture TD in terms of import, equaling 1 when importer j belongs to an FTA in year t.+/−GDP it GDP jtThe gross domestic product of the exporter and importer (thousand USD).+

Table 2 .
Possible outcomes of trade effects.

Table 3 .
RESET of PPML and OLS.
Note: The coefficients and corresponding trade effects of each FTA dummy variable are summarized according to the time-pair fixed-effect model, with ***, **, and * indicating that the statistics are significant at the levels of 1%, 5%, and 10%, respectively.The net trade effect is calculated by adding and subtracting at the same level of significance, the trade effects for each FTA in this paper are also classified according to the positive and negative meanings of the coefficients at the same level of significance, and the resulting trade effects are summarized and labeled at the 5% or 10% level in the absence of a 1% level of significance.The name of the trade effects are in accordance with Table2.