Research on the impact of China’s free trade zone policies on urban economic development

ABSTRACT

The paper explores the impact of China’s free trade zone policies on urban economic development by way of the time-varying DID model using the annual panel data of 284 cities from 2010 to 2019. Through the study, it is found that the free trade zone policies have effectively promoted urban economic growth. Moreover, it is found that: (1) the pilot cities implementing free trade zone policies have registered economic growth via the mediating effect of foreign trade; (2) the free trade zone policies exert more obvious influential effect on eastern and coastal cities; (3) the relatively loose scope of free trade zones can more effectively promote the local urban economic development.

KEYWORDS:

• Free trade zone policy
• economic growth
• difference-in-difference method

JEL CLASSIFICATION:

• F741.2

1. Introduction

The global economy received a severe blow following the financial crisis of 2008, and the recovery was sluggish. Forces opposed to globalization and trade protectionism started to gain ground. The China Pilot Free Trade Zone (hereafter referred to as the ‘FTZ’) formed in this situation when the need arose, becoming a significant mechanism for China to advance supply-side structural reform, create a new open economy system, and implement the development strategy of new areas (Sheng 2017). Since the Shanghai Free Trade Zone was established in September 2013, its main goal has been to gather a collection of ‘replicable and promotable’ experiences (A. Z. Chen and Liu 2014). With the deepening reform and continuous promotion of the government’s free trade zone policies, as of 2022, a total of 21 provinces and cities in China have established 54 free trade zones in six batches, forming a preliminary development pattern of free trade zones from coastal to inland areas, as well as from eastern to western regions. The rapid development of free trade zones to some extent demonstrates the effectiveness of their policies, and many scholars have also demonstrated their promoting effects on the regional economy from various perspectives (Ye 2018; Zhang et al. 2018; Zhang and Yu 2020). However, due to time constraints and policy lag, most of the existing research focuses on the previous two batches of free trade zones, and the data used is primarily at the provincial level (Ye 2018; Yin and Gao 2017). Looking back at the development pattern of China’s free trade zones, the first two batches of free trade zones were established in the eastern coastal areas of China. As the third batch of free trade zones revolved around the central and western inland regions of China, the geographical location of free trade zones began to differ. In addition, although the total area of the free trade zones established by various provinces and cities is around 120 square kilometers, the number and size of the free trade zones established in each region vary depending on the local conditions. It might become more challenging to accurately depict their distinct development if provincial-level statistics are still used as research samples. Will the emergence of new elements in the creation of free trade zones have an impact on the efficacy of free trade zone policies? How does the free trade zone policy support the expansion of the local economy? And does it have urban-level heterogeneity? It might be worthwhile to look at these issues more.

Difference-in-Difference (DID) is the most widely used method in social science research. According to the different implementation timing of policies, DID can generally be divided into Staggered DID and Time-varying DID. Staggered DID is a statistical method used in policy evaluation, where policy effectiveness is evaluated by comparing the changes between treatment group and control group at different time points. While time-varying DID method is also used in policy evaluation, especially in evaluating effectiveness of progressive policy reform. It compares the changes between treatment group and control group before and after policy implementation to evaluate the net effect of policies. By utilizing observational data, it calculates the difference in incremental effects between the ‘experimental group’ and the ‘control group’ in natural experiments, enabling relatively straightforward detection of causal effects. It has been favored by domestic and foreign scholars in policy evaluation (Baker, Larcker, and Wang 2022; Huang, Zhang, and Liu 2022). According to research conducted between 2010 and 2019, the average GDP growth rate of the 262 ‘control group’ cities, which did not create free trade zones in the same province or region, was 9.83%, compared to 11.1% for the ‘experimental group’ cities, which are the first three batches of the 22 cities with free trade zones. This initially indicates that the average economic growth rate of free trade zone cities is higher than that of non-free-trade zone cities. Is this the result of the free trade zone policy? This needs further verification.

Therefore, this study takes the 22 cities that established free trade zones policy from 2010 to 2019 as the experiment group and the corresponding 262 cities that did not establish free trade zones policy as the control group. Using a time-varying DID model, it comprehensively explores the impact of China’s free trade zone strategy on the economic growth of free trade zone cities and conducts an analysis of its impact mechanisms and heterogeneity. The aim is to verify the actual impact of free trade zone policy on the economic growth of free trade zone cities and provide decision-making references for subsequent free trade zone construction.

The rest of the paper includes five sections: Section 2 is literature review; Section 3 explains research design; Section 4 presents results and discussion; Section 5 is mechanism test and heterogeneity analysis; and Section 6 makes conclusions.

2. Literature review

The development of free trade zones can be traced back to the early 1950s, when the United States proposed using manufacturing as the main target for export processing in free trade zones. The construction of free trade zones in the United States effectively formed economies of scale (Helpman and Krugman 1985), broke down market segmentation, accelerated factor mobility, and thus promoted regional economic growth (Chauffour and Maur 2011). In the late 1960s, some developing countries also utilized this form and developed it into special industrial zones, gradually becoming export processing zones. After the 2008 financial crisis, with the world economy in a downturn and trade protectionism on the rise, countries such as Europe and the United States introduced a series of free trade agreements, including the bilateral investment treaty (BIT) and the Transatlantic Trade and Investment Partnership (TTIP), to reestablish new global trade rules. In response to this challenge, China’s free trade zones emerged. This is not only the ‘second season’ of China’s open economy but also an important measure to promote the high-end development of China’s economy (A. Z. Chen and Liu 2014).

In 2013, when China’s Shanghai Free Trade Zone was established, numerous scholars qualitatively discussed issues related to trade facilitation, laws and regulations, and development prospects of free trade zones (Gong 2013; G. F. Wang and Guo 2014; X. S. Wang, Zhang, and Zhou 2014). Wang and Guo believed that the overall situation of China’s (Shanghai) free trade pilot zone was liberalization and facilitation of trade and investment, but more importantly, facilitation of trade. Trade facilitation lowers enterprise transaction costs and creates efficiency. Yang (2014) believed that the Shanghai Free Trade Zone has economic and political effects, which are interrelated and can help promote the legislative demonstration effect of the Shanghai Free Trade Zone. X. S. Wang, Zhang, and Zhou (2014) believed that the Shanghai Free Trade Zone is a major measure to deepen reform and expand opening up, which can bring multiple benefits to Shanghai and even China’s economy and lead to China’s transformational development.

As the Shanghai Free Trade Zone began to play its unique economic role, scholars began to focus on quantitatively evaluating the economic effects of free trade zones as another major strategy for promoting China’s economic development. Tan, Zhou, and Lin (2015) evaluated the economic growth effects of the establishment of the Shanghai Free Trade Zone based on provincial monthly panel data from 2005 to 2014 using counterfactual analysis. The results showed that the establishment of the Shanghai Free Trade Zone had significant positive effects on the economic growth of Shanghai, respectively increasing the month-on-month growth rate of Shanghai’s industrial value-added and import and export total by 2.69 and 6.73% points. L. H. Wang and Liu (2017) used synthetic control methods to compare the actual values of economic variables before and after the establishment of the Shanghai Free Trade Zone with ‘counterfactual’ values based on provincial quarterly panel data from 2006 to 2015, to evaluate the economic effects of the free trade zone policy. The study found that the impact of the free trade zone on local economies was significantly positive and passed robustness tests.

With the establishment of more free trade zones, the expansion of sample and data sizes has led to the use of more models for evaluating their economic impact, making it possible to conduct heterogeneous evaluations of free trade zone policies in various provinces and cities. Liu and Lv (2018) used synthetic control methods to compare and analyze the first two batches of four free trade zones with other provinces and cities using monthly panel data from 2010 to 2017. The results show that although the functional positioning of these four provinces varies, the free trade zone policy has a positive promoting effect on the economic performance of these four provinces. A. Zhang and Yu (2020) used PSM-DID natural experiment method to examine the economic growth effects of the first two batches of seven free trade zone pilot areas in 2009–2016. The study shows that free trade zones have a significant positive impact on the economic growth of these cities, with an increase of 0.849 units in per capita GDP compared to cities without free trade zones. Qiu, Cao, and Gan (2022) analyzed the heterogeneity of the economic growth effects of free trade zone policies on different regions using annual panel data from 2011 to 2020 and employing difference-in-difference and counterfactual analysis methods. The study found that free trade zone policies have a significant promoting effect on regional economies, but their economic impact varies across different regions. Li (2008) carves the index system of the economy, and the data of Jiangsu to carry out empirical measurement and of Jiangsu’s economy, and based on this, the scope of the extension to the Yangtze River Delta region.

Through the analysis and review of existing literature, it was found that previous studies on the relationship between FTZ policies and regional economic growth have mainly focused on the first two batches of free trade zones, and also lacked the mechanism of their impact Therefore, this study uses annual panel data from 284 cities between 2010 and 2019 and employs a time-varying DID method to empirically investigate the promotion effect of free trade zone policies on urban economies by taking the cities where the first three batches of free trade zones are located as the experimental group and other cities without free trade zones as the control group. Compared with staggered DID, time-varying DID has more flexibility, accuracy and wider applicability in dealing with time changes and differences in policy implementation modes. It can estimate policy effects more accurately, reduce bias, and improve estimation accuracy.The study also analyzes the impact mechanisms and heterogeneity of the policies, aiming to verify the actual impact of free trade zone policies on the economic growth of free trade zone cities and provide decision-making references for future free trade zone construction in China. The possible marginal contributions of the paper mainly lie in three aspects:

Firstly, the paper uses annual panel data from 284 cities between 2010 and 2019 to investigate the impact of free trade zone policies on urban economic growth. Studying the economic spillover of free trade zone policies from more specific research objects can increases the accuracy of research conclusions.

Secondly, the paper incorporates the free trade zone policies as an open element into the C-D production function on the basis of Krugman’s open economy model, while strictly selecting other control variables according to the factors in trade theory. Additionally, the paper employs a well-designed quasi-natural experiment, uses a time-varying DID model, and conducts robustness tests from multiple perspectives.

Thirdly, the paper analyzes the impact mechanism of free trade zone policies on urban economic growth from the perspective of foreign trade and conducts regional heterogeneity analysis and scope heterogeneity analysis of the relationship between free trade zone policies and urban economic growth.

3. Research design

3.1. Theoretical model construction

The classical Cobb-Douglas (C-D) production function only considers three factors: labor, capital, and technology when analyzing economic growth, and openness was not initially included in the C-D production model. However, as a fundamental national policy, the reform and opening-up have played an irreplaceable role in China’s economic growth (Qiu, Peng, and Zhao 2019). The new trade theory represented by Krugman incorporates trade as a factor of openness into economic growth models. The theory shows that the higher the degree of openness of a country or region, the more advantageous it is to introduce advanced technology, absorb advanced management experience, introduce foreign funds, exchange low-level resources for high-level resources on the international market, innovate and develop related industries, and promote economic growth (Fang 1979). Under the circumstances of external trade protectionism and insufficient internal driving forces, as a significant measure to deepen reform and further open up, free trade zone policies in various designated areas contain different functions and positioning, such as bonded zones, sci-tech innovation zones, and high-end industry zones. Different functional zones have different mechanisms for promoting economic growth. For example, implementing free trade zone policies based on bonded zones can further realize trade liberalization and facilitation through preferential taxation and customs special supervision policies. Trade liberalization and facilitation can improve the efficiency of factor flow between regions and promote industrial structure optimization (Yunlong 2020), ultimately achieving the goal of promoting regional economic growth. In the long term, after institutional changes formed following the establishment of the free trade zone are solidified, they can help continuously improve the business environment, promote industrial structure upgrading, stabilize investor expectations, and may significantly affect regional economic growth. Therefore, based on the labor, capital, and technology elements covered in the classic C-D function, the paper incorporates free trade zone policies as a proxy variable of openness into the improved model.

(1) $\mathit{GD}{P}_{\mathit{it}}=\mathit{A}{t}_{\mathit{it}}^{{\beta }_1}\cdot L_{\mathit{it}}^{{\beta }_2}\cdot K_{\mathit{it}}^{{\beta }_3}\cdot D_{\mathit{it}}^{{\beta }_4}$(1)

One-order difference and the logarithm of formula (1) can be used to determine that:

(2) $\Delta \mathit{GD}{P}_{\mathit{it}}={\beta }_0+{\beta }_1\mathrm{\Delta A}{t}_{\mathit{it}}+{\beta }_2\mathrm{\Delta }{L}_{\mathit{it}}+{\beta }_3\mathrm{\Delta }{K}_{\mathit{it}}+{\beta }_4\mathrm{\Delta }{D}_{\mathit{it}}+{\epsilon }_{\mathit{it}}$(2)

In Equations (1)(1) $\mathit{GD}{P}_{\mathit{it}}=\mathit{A}{t}_{\mathit{it}}^{{\beta }_1}\cdot L_{\mathit{it}}^{{\beta }_2}\cdot K_{\mathit{it}}^{{\beta }_3}\cdot D_{\mathit{it}}^{{\beta }_4}$(1) and (2(2) $\Delta \mathit{GD}{P}_{\mathit{it}}={\beta }_0+{\beta }_1\mathrm{\Delta A}{t}_{\mathit{it}}+{\beta }_2\mathrm{\Delta }{L}_{\mathit{it}}+{\beta }_3\mathrm{\Delta }{K}_{\mathit{it}}+{\beta }_4\mathrm{\Delta }{D}_{\mathit{it}}+{\epsilon }_{\mathit{it}}$(2) ), ‘$\mathrm{A}{\mathrm{t}}_{\mathit{it}}$’, ‘${\mathrm{L}}_{\mathit{it}}$’, and ‘$K_{\mathit{it}}$’ represent the input of technology, labor, capital, and degree of openness, respectively and ‘$D_{\mathit{it}}$’ represents the degree of openness for the city i at time t. While the representation of ‘${\mathrm{D}}_{\mathit{it}}$’ is relatively complex due to various factors related to openness, this study characterizes it based on whether a free trade zone is established or not. ‘β1’, ‘β2’, ‘β3’, and ‘β4’ represent the output elasticity of technology progress, labor input, capital input, and free trade zone policy establishment, respectively.

3.2. Quasi-natural experiment design

The core of this study is to reveal the causal relationship between free trade zone policy establishment and urban economic growth. However, classical econometric methods such as OLS estimation are not sufficient to provide strong evidence for causality. In policy effect evaluation methods, the difference-in-differences (DID) method is a widely used econometric method in recent years. The basic idea of this method is to treat the implementation of a new policy as a quasi-natural experiment exogenous to the economic system (Chen and Wu 2015) (Hu and Lin 2018). To carry out empirical research scientifically and reasonably, in addition to using the Krugman open economy model to ‘endorse’ the causal relationship, this study further uses the externality of the event of free trade zone policy establishment and utilizes a time-varying DID model with two-way fixed effects. Cities that have established free trade zones are included in the experimental group, while cities without free trade zones are included in the control group for a quasi-natural experiment. The specific formula is:

(3) $Y_{\mathit{it}}={\alpha }_1+{\theta }_1{D}_{\mathit{it}}+{\omega }_1{X}_{\mathit{it}}+{\mu }_i+{\gamma }_t+{\epsilon }_{\mathit{it}}$(3)

In the formula, the subscript ‘i’ represents the city identifier, and ‘t’ represents the year. ‘$Y_{\mathit{it}}$’ is the interpreted variable representing the city’s GDP growth rate in the i-th city in the t-th year. ‘${\mathrm{D}}_{\mathit{it}}$’ is the virtual variable of the free trade zone. If the i-th city establishes or has a free trade zone (area) in the t-th year, it takes a value of 1, otherwise, it takes a value of 0. ‘$X_{\mathit{it}}$’ is the set of control variables.‘${\mu }_i$’ represents the individual fixed effects of each city, and v ‘${\gamma }_t$’ represents the time-fixed effects of each city. The estimated value of ‘${\theta }_1$’ is the key observation object, representing the net effect of free trade zone policy on urban economic growth, where its positive or negative value denotes the promotion or inhibition of free trade zone policy on urban economic growth, and the absolute value indicates the magnitude of the effect of free trade zone policy on urban economic growth.

3.3. Research object

Considering that the establishment time of the first, second, and third batches of free trade zones was September 2013, April 2015, and March 2017, respectively, with China Hainan Pilot Free Trade Zone established in October 2018 as the fourth batch, and the fifth batch of free trade zones established in August 2019. To satisfy the prerequisite for using the time-varying DID model, it is necessary to verify that the cities have similar economic growth trends before the implementation of the free trade zone policy while avoiding possible lagged effects (Zhang, Duan, and Yan 2020) and significant economic form changes caused by the establishment of free trade zones, as shown in Figure 1. This study appropriately expands the time range and selects the first three batches of free trade zones as research objects. After removing severely missing data samples, annual panel data from 284 cities between 2010 and 2019 were finally selected. Among them, 22 cities that established free trade zones from the first three batches were selected as the experimental group, including Tianjin, Shenyang, Dalian, Yingkou, Shanghai, Zhoushan, Fuzhou, Xiamen, Zhengzhou, Kaifeng, Luoyang, Wuhan, Yibin, Xiangyang, Guangzhou, Shenzhen, Zhuhai, Chongqing, Chengdu, Luzhou, Xi’an, and Xianyang. The other 262 cities without free trade zones were taken as the control group.¹

Figure 1. Graphical illustration of study sample selection.

3.4. Variable selection

3.4.1. Dependent variable

Using the GDP growth rate of each city, the economic growth rate ‘${\mathrm{Y}}_{\mathrm{it}}$’ is calculated. The specific calculation formula is: ${\mathrm{Y}}_{\mathrm{it}}=(\mathrm{GD}{\mathrm{P}}_{\mathrm{i},\mathrm{t}}-\mathrm{GD}{\mathrm{P}}_{\mathrm{i},\mathrm{t}-1})/\mathrm{GD}{\mathrm{P}}_{\mathrm{i},\mathrm{t}-1}$. Here, ‘${\mathrm{Y}}_{\mathrm{it}}$’ represents the GDP growth rate of city i in the t-th year, and ‘$\mathrm{GD}{\mathrm{P}}_{\mathrm{it}}$’ represents the GDP of city i in the t-th year.

3.4.2. Explanatory variable

Policy virtual variable ‘${\mathrm{D}}_{\mathit{it}}$’, which takes a value of 1 for cities approved with free trade zones, and 0 otherwise. It should be noted that the establishment time of the first three free trade zones was September 2013, April 2015, and March 2017, respectively. To ensure accuracy, the value of Dit for the current year when a free trade zone is established in the first half of the year is assigned as 1; while the value of Dit for the current year when a free trade zone is established in the second half of the year is assigned as 0, and then assigned as 1 in the following year.

3.4.3. Control variables

Production factors variables are selected as control variables. When examining the relationship between free trade zone policy establishment and urban economic growth, factors affecting economic growth other than the free trade zone strategy need to be added to clarify the causal relationship in the econometric experiment. Referring to the handling methods of most scholars, the Cobb-Douglas production function is selected as the basic framework for selecting control variables. It should be noted that according to the new factor theory of international trade, two types of factors, information and land, have been added to the classic C-D production model based on capital, labor, and technology factors. For the capital factor (K), the fixed asset investment rate indicator is selected. In China, fixed asset investment is approved first, followed by funding allocation and project construction. The economic performance of the prior year is mostly taken into account when investing in fixed assets in the current year. Therefore, this paper defines the fixed asset investment rate as the ratio of fixed asset investment in the current year to GDP in the previous year (Zhang, Duan, and Yan 2020). For the labor factor (L), the urban resident population growth rate is used. For the technology factor (At), the scientific expenditure-to-fiscal expenditure ratio is selected. For the information factor (M), the broadband access user growth rate is chosen. For the land factor (T), the ratio of the free trade zone establishment area to the city area is selected.

The data mainly comes from the ‘China City Statistical Yearbook’, annual statistical bulletins of various cities, and the National Bureau of Statistics of China. The specific variables are shown in Table 1.

Table 1. Model variable description.

Variables type	Variable Name	Calculation Method
Dependent Variable	Urban GDP growth rate ($Y_{\mathit{it}}$)	Growth rate of urban gross domestic product compared to the previous year
Explanatory Variable	Free Trade Zone policy ($D_{\mathit{it}}$)	Dummy variable, set as 1 after the establishment of the free trade zone, and 0 if not established
Controlled Variables	Capital (K)	The ratio of urban total fixed asset investment to GDP in the previous year
	Labor (L)	Urban population growth rate calculated at the end of the year
	Technology (At)	The ratio of scientific expenditures to fiscal expenditures
	Information (M)	The growth rate of broadband internet access users
	Land (T)	The ratio of the area of the FTZs to the city’s total area

4. Results and discussion

4.1. Descriptive statistical analysis

A descriptive statistical analysis is presented in Table 2. The average GDP growth rate of the sample cities is 9.93% (with an average GDP growth rate of 11.1% for the experimental group and 9.83% for the control group). The minimum value is −46.86% for Songyuan City in 2019, and the maximum value is 28.67% for Jinchang City in 2019. The average value of the virtual variable for the establishment of free trade zones is 0.0285, indicating that 2.85% of the sample data is after the establishment of a free trade zone. It is also found that there are significant differences among variables in the total sample, indicating significant differences in the development of different cities.

Table 2. Descriptive statistics of variables.

Variable	Sample Size	Mean	Standard Deviation	Minimum Value	Maximum Value
$Y_{\mathit{it}}$	2839	0.0993	0.0841	−0.4686	0.2867
$D_{\mathit{it}}$	2839	0.0285	0.167	0	1
K	2839	0.884	0.329	0.0977	2.907
L	2839	0.00376	0.0213	−0.189	0.442
At	2839	0.0161	0.0162	0.006	0.207
M	2839	0.176	0.159	−0.766	0.931
T	2839	0.000326	0.00323	0	0.0822

4.2. Parallel trend test

The parallel trend assumption is a crucial prerequisite for the time-varying DID model, which assumes that the economic growth trends of the experimental and control groups must be the same before the implementation of the free trade zone policy. This paper uses the event study method proposed by Jacobson, LaLonde, and Sullivan (1993) to conduct a parallel trend test. The specific formula is:

(4) ${\mathrm{Y}}_{\mathrm{it}}={\mathit{\alpha }}_2+{\sum }_{\mathrm{k}=-4}^3{\mathrm{\partial }}_{\mathrm{k}}{\mathrm{W}}_{\mathrm{ik}}+{\mathit{\omega }}_2{\mathrm{X}}_{\mathrm{it}}+{\mathit{\mu }}_{\mathrm{i}}+{\mathit{\gamma }}_{\mathrm{t}}+{\mathit{\epsilon }}_{\mathrm{it}}$(4)

Where ‘${\mathrm{W}}_{\mathrm{ik}}$’ is a set of policy dummy variables, k represents the kth year of the implementation of the free trade zone policy in city i, and the value is 1 for the experimental group in the kth year of implementing the free trade zone policy, and 0 otherwise. ‘$X_{\mathit{it}}$’ is the set of control variables. ‘${\mu }_i$’ represents the individual fixed effects of each city, ‘${\gamma }_t$’ represents the time-fixed effects of each city. ‘${\mathrm{\partial }}_{\mathrm{k}}$’ is the key coefficient in the formula, reflecting the difference in GDP growth rates between the experimental and control groups in the kth year of implementing the free trade zone policy.

Considering the limited data for the 5 years before and 3 years after policy implementation, this paper follows the method proposed by Wang and Ge (2022) and aggregates the data of the 5 years before policy implementation to the −4th period and the data of the 3 years after policy implementation to the 3rd period. The results of the parallel trend test are shown in Figure 2. The coefficient estimates for each period before the implementation of the free trade zone policy are not significant, indicating no significant difference in GDP growth rates between the experimental and control groups before policy implementation, passing the parallel trend test. At the same time, the significant positive coefficient estimates after the implementation of the free trade zone policy further verify the promoting effect of the free trade zone policy on urban economic growth.

Figure 2. Parallel trend test.

Solid dots represent the estimated coefficient ”${\mathrm{\partial }}_{\mathrm{k}}$ in Equation (4)(4) ${\mathrm{Y}}_{\mathrm{it}}={\mathit{\alpha }}_2+{\sum }_{\mathrm{k}=-4}^3{\mathrm{\partial }}_{\mathrm{k}}{\mathrm{W}}_{\mathrm{ik}}+{\mathit{\omega }}_2{\mathrm{X}}_{\mathrm{it}}+{\mathit{\mu }}_{\mathrm{i}}+{\mathit{\gamma }}_{\mathrm{t}}+{\mathit{\epsilon }}_{\mathrm{it}}$(4) , and the short vertical lines represent the 95% confidence interval for the robust standard error.

4.3. Benchmark regression analysis

This section uses the formula (3) of a time-varying DID model with fixed effects in both directions to evaluate the impact of Free Trade Zone policies on urban economic growth. The estimation results are shown in Table 3, where the first column (1) is the estimation result without control variables, and the second column (2) is the estimation result with control variables. As indicated by the goodness of fit, the model with control variables has a more reliable overall performance. The estimated coefficient of the Free Trade Zone policy dummy variable is significantly positive at the 1% level, regardless of whether the control variables are added or not. According to the estimation results with control variables, the coefficient of the Free Trade Zone policy dummy variable is 0.031, indicating that considering other factors, the Free Trade Zone policy increases the GDP growth rate of the experimental group by about 3.1% compared to the average of the control group. This shows a significant positive effect of Free Trade Zone policies on the economic growth of the cities that established them in the first three rounds, which is consistent with the research results of most scholars on the relationship between the first two rounds of Free Trade Zone policies and economic growth. With the introduction of the third round of Free Trade Zones, the promotion of regional economic growth by the Free Trade Zone policy still exists, which is in line with the expected effect of the policy.

Table 3. Baseline regression result.

Variable	Urban GDP growth rate
	(1)	(2)
D	0.032*** (0.009)	0.031*** (0.011)
K		0.049*** (0.006)
L		0.249*** (0.060)
At		0.400*** (0.144)
M		−0.000 (0.008)
T		0.139 (0.515)
Constant	0.101*** (0.001)	0.048*** (0.006)
N	2,839	2,829
R-squared	0.508	0.557
Time Fixed Effect	Yes	Yes
Individual Fixed Effect	Yes	Yes

*, **, and *** indicate significance levels of 10%, 5%, and 1%, respectively; the clustered robust standard errors are shown in parentheses with the city as the clustering variable. The tables below are identical.

4.4. Robustness test

4.4.1. Placebo test

To avoid the influence of unobservable omitted variables and other random factors on the estimation results, this paper follows the method of Cai et al. (2016) and Shi et al. (2017), and conducts a placebo test by randomly replacing the experimental group. Twenty-two² cities were randomly selected from the 284 sample cities as fake experimental group cities, and policy implementation time was randomly generated. The remaining cities were treated as fake control group cities. Then, the time-varying DID estimation was performed according to formula (3), and the estimated coefficients of the false Free Trade Zone policy dummy variable were obtained. Then, the experiment was repeated 500 times to obtain 500 false estimated coefficients and their corresponding p-values. The results of the placebo test are shown in Figure 3. The false estimated coefficients are close to zero and follow a normal distribution, and most regression results are not significant. The dotted vertical line represents the real estimation coefficient, and the real estimation coefficient of 0.031 is located at the high tail of the false coefficient distribution, which is a low-probability event. This indicates that there is no problem of unobservable omitted variables or random factors in the model, and the conclusion is still robust.

Figure 3. Placebo test.

4.4.2. Propensity score matching difference-in-difference (PSM-DID)

Considering the possible winner-picking behavior in selecting Free Trade Zone pilot cities, i.e. selecting cities with better economic conditions and superior geographical conditions as pilot cities, which may cause endogeneity problems due to sample selection bias, this paper chooses to use a time-varying DID model based on propensity score matching to test the robustness of the results and alleviate the endogeneity problem. The nearest neighbor matching method and kernel matching method are used to match the samples by year, and then the matched sample is estimated again using a time-varying DID estimation. The results, as shown in Table 4, indicate that the estimated coefficient of the Free Trade Zone policy dummy variable is significantly positive at the 1% level under both the nearest neighbor matching method and the kernel matching method, and the estimated coefficients are close to those obtained from formula (3), passing the robustness test.

Table 4. PSM-DID regression results.

Variable	Nearest Neighbor Matching	Nearest Neighbor Matching	Core Matching	Core Matching
	Y	Y	Y	Y
D	0.028*** (0.010)	0.032*** (0.010)	0.028*** (0.010)	0.031*** (0.010)
Control Variable	No	Yes	No	Yes
Constant	0.099*** (0.001)	0.041*** (0.008)	0.100*** (0.001)	0.044*** (0.008)
N	2,537	2,527	2,465	2,455
R-squared	0.513	0.528	0.520	0.535
Time Fixed Effect	Yes	Yes	Yes	Yes
Individual Fixed Effect	Yes	Yes	Yes	Yes

4.4.3. Dependent variable substituted

The paper replaces the urban GDP growth rate with the per capita GDP growth rate to test the impact of Free Trade Zone policies on the economic growth rate of cities using a time-varying DID regression. The results in Table 5 show that the estimated coefficient of the Free Trade Zone policy dummy variable is significantly positive at the 1% level, indicating the robustness of the conclusion.

Table 5. Regression result with substituted dependent variable.

	Per capita GDP growth rate
Variable	（1）	（2）
D	0.042*** (0.011)	0.039*** (0.013)
Constant	0.096*** (0.001)	0.048*** (0.007)
Control Variable	No	Yes
N	2,839	2,829
R-squared	0.468	0.480
Time Fixed Effect	Yes	Yes
Individual Fixed Effect	Yes	Yes

5. Mechanism test and heterogeneity analysis

5.1. Mechanism test

According to existing literature, the establishment of Free Trade Zones is beneficial for eliminating local administrative intervention and barriers, forming a transparent and open market access system, promoting foreign investment access barrier reform, reducing taxes and transaction costs, accelerating the free flow of factors, improving trade efficiency, and ultimately promoting regional economic development.

As Free Trade Zones have established different functional and positioning areas based on their own advantages, the paths of each area in playing a role may differ, but the effect of their paths will eventually be reflected in the growth of foreign trade. Therefore, in constructing the theoretical model, this paper incorporates Free Trade Zone policies as a factor of opening up to the outside world into the economic growth model, assuming that Free Trade Zone policies promote regional economic growth through the effect of foreign trade. To verify this mechanism, this paper uses the total import and export growth rate of each city to represent the city’s foreign trade situation and study the impact of Free Trade Zone policies on economic growth through the effect of foreign trade. The regression results are shown in Table 6. Column (1) of Table 6 shows the estimation results of Free Trade Zone policies on the city’s foreign trade, with an estimated coefficient of 0.339, passing the significance test at the 1% level. This indicates that under the opening-up effect of Free Trade Zone policies, pilot cities have increased their foreign trade levels. Then, the impact of foreign trade on urban economic growth is tested, and the results of column (2) of Table 6. show an estimated coefficient of 0.003, passing the significance test at the 10% level, indicating that Free Trade Zone policies promote economic growth in pilot cities through the effect of foreign trade.

Table 6. Foreign trade impact on economic growth.

Variable	(1)	(2)
	Trade	Y
D	0.339*** (0.127)
Trade		0.003* (0.002)
Control Variable	Yes	Yes
Constant	0.094 (0.072)	0.049*** (0.006)
N	2,829	2,829
R-squared	0.125	0.556
Time Fixed Effect	Yes	Yes
Individual Fixed Effect	Yes	Yes

5.2. Regional heterogeneity analysis

The previous section conducted systematic empirical testing on the relationship between the establishment of free trade zone policy and urban economic growth. With the expansion and deepening of this policy, should cities that have not established free trade zones fully learn from or introduce this open policy with good economic driving effects? An objective issue worth noting is that the estimation results obtained from the difference-in-difference model can only describe the average effect of the establishment of free trade zone policy on urban economic growth. Therefore, there may be significant differences in policy effects among different regions, and further exploration of regional effects is needed to provide a reference for the effective promotion of free trade zone policies in the future. This article uses two strategies for analysis: first, dividing free trade zone cities into coastal and inland cities; second, dividing free trade zone cities into eastern, central, and western cities. To ensure the robustness of the estimation results, the study divides empirical testing into two parts. The first part sets regions without free trade zones in the same geographic location as the control group and the second part sets all regions without free trade zones as the control group. The estimation method still adopts a time-varying DID model with two-way fixed effects. The estimation results are shown in Tables 7 and 8.

Table 7. Heterogeneity analysis between coastal and inland cities.

Plan A Within-region Control Group
	Inland	Inland	Coastal	Coastal
Variable	Y	Y	Y	Y
D	0.021* (0.013)	0.012 (0.019)	0.038*** (0.012)	0.062*** (0.015)
Constant	0.099*** (0.001)	0.052*** (0.007)	0.095*** (0.003)	0.018 (0.013)
Control Variable	No	Yes	No	Yes
N	2,409	2,399	430	430
R-squared	0.541	0.556	0.549	0.610
Time Fixed Effect	Yes	Yes	Yes	Yes
Individual Fixed Effect	Yes	Yes	Yes	Yes
Plan B Across-region Control Group
D	0.020 (0.012)	0.011 (0.018)	0.046*** (0.013)	0.054*** (0.016)
Constant	0.099*** (0.001)	0.048*** (0.003)	0.098*** (0.001)	0.050*** (0.006)
Control Variable	No	Yes	No	Yes
N	2,739	2,729	2,719	2,709
R-squared	0.541	0.558	0.545	0.560
Time Fixed Effect	Yes	Yes	Yes	Yes
Individual Fixed Effect	Yes	Yes	Yes	Yes

Table 8. Heterogeneity analysis of East, central and west regions.

Plan A Within-region Control Group				Plan B Across-region Control Group
Variable	West	Central	East	Variable	West	Central	East
	Y	Y	Y		Y	Y	Y
D	0.008 (0.018)	0.013 (0.017)	0.054*** (0.013)	D	0.005 (0.019)	0.024 (0.018)	0.047*** (0.012)
Constant	0.110*** (0.012)	0.103*** (0.002)	0.085***(0.002)	Constant	0.099*** (0.001)	0.098*** (0.001)	0.098*** (0.001)
Control Variable	Yes	Yes	Yes	Control Variable	Yes	Yes	Yes
N	710	1,059	1,068	N	2,669	2,678	2,729
R-squared	0.593	0.551	0.529	R-squared	0.548	0.539	0.545
Time Fixed Effect	Yes	Yes	Yes	Time Fixed Effect	Yes	Yes	Yes
Individual Fixed Effect	Yes	Yes	Yes	Individual Fixed Effect	Yes	Yes	Yes

According to the report, whether the control group is within the same region or across the entire region, the economic promotion effect of the Free Trade Zone policy on inland cities is not significant, while it is very significant for coastal cities. Likewise, whether the control group is within the same region or across the entire region, the impact of FTZ policy on economic growth in central and western cities is not significant, while it is very significant for eastern cities. This further illustrates the necessity of conducting regional effect analysis. The impact of the FTZ policy on the economic growth rate of inland and cities in central and western regions is not significant, while its impact is significant for coastal and eastern cities, and the promotion effect is higher than the overall effect shown in Table 3. Possible reasons include: 1) Coastal and eastern cities are the main pilot cities for the first two batches of FTZ policy establishment. The FTZ policy has undergone long-term development and optimization locally, and it fits better with the local production and operation status, which can better promote local economic development. 2) Coastal and eastern cities have relatively better economic development, and their openness level had already reached a high level before the establishment of FTZs, with rich experience in openness, so the driving effect of FTZ policy on economic growth is more significant. 3) Inland cities have relatively weak trade resource endowments and limited structural dynamics for economic growth. The growth potential of free trade zones established in inland cities is limited. Therefore, in the subsequent promotion of FTZ policy, differences in geographical location could be taken into account, such as advancing it differently in coastal, inland, or eastern, central, and western regions.

5.3. Scope heterogeneity analysis

At the provincial level, the total area of FTZs is around 120 square kilometers. However, the number and size of Free Trade (Port) Zones established in different regions vary according to local conditions. For example, Guangdong Province has set up three free trade zones in Guangzhou, Shenzhen, and Zhuhai, with respective areas of 60, 28.8, and 28 square kilometers, totaling 116.8 square kilometers. Fujian Province has established two free trade zones in Fuzhou and Xiamen, with respective areas of 74.26 and 43.78 square kilometers, totaling 118.04 square kilometers. Liaoning Province has established three free trade zones in Shenyang, Dalian, and Yingkou, with respective areas of 29.97, 59.96, and 29.96 square kilometers, totaling 119.89 square kilometers. Thus, does the difference in the size of each free trade (port) zone affect the policy’s effectiveness? This section sorts the free trade (port) zones according to their percentage of the local urban land area into three groups to verify the relative size of each zone’s impact on the promotion effect of FTZ policies on the economy. The first group has a percentage greater than 0.5%, the second greater than 0.9%, and the third greater than 1.3%. The estimation method still uses a time-varying DID model with fixed effects in both directions. The regression results are shown in Table 9.

Table 9. Scope heterogeneity analysis.

Variable	Greater than 0.5%	Greater than 0.9%	Greater than 1.3%
	Y	Y	Y
D	0.040*** (0.015)	0.051*** (0.020)	0.074*** (0.027)
Control Variable	Yes	Yes	Yes
Constant	0.049*** (0.003)	0.051*** (0.003)	0.051*** (0.003)
N	2,739	2,689	2,659
R-squared	0.563	0.561	0.560
Time Fixed Effect	Yes	Yes	Yes
Individual Fixed Effect	Yes	Yes	Yes

According to the regression results in Table 9, when the ratio of free trade (port) zone area to city area exceeds 0.5%, the estimated coefficient of the FTZ policy dummy variable is significant at the 1% level and is 0.042. When the ratio exceeds 0.9%, the estimated coefficient is 0.051 at the 1% significance level. Finally, when the ratio exceeds 1.3%, the estimated coefficient is 0.074 at the 1% significance level. This indicates that a relatively loose free trade (port) zone scope can more effectively promote the development of the local economy under FTZ policies. The reason may be that a reasonable and loose FTZ area is conducive to the development of bonded areas, technological innovation, high-end industrial parks, and talent introduction. The logistics industry’s development prospects are also broader, which may promote the effectiveness of FTZ policies.

6. Conclusions

The paper takes the first three batches of free trade zone cities established by the country between 2010–2019 as the starting point to link the policy of establishing free trade zones with urban economic growth, in order to evaluate the promoting effect of free trade zone policies on urban economies. Based on Krugman’s economic theory model, the policy of establishing free trade zones is incorporated into the C-D production function as an open element for empirical analysis. Other control variables are strictly selected according to the factors included in trade theory, and a quasi-natural experiment design is used with a time-varying DID estimation. The robustness of the estimated results is checked through placebo tests, propensity score matching difference-in-difference, and replacing the interpreted variables. Finally, mechanism tests and heterogeneity analyses are conducted.

The research results show that the policy of establishing free trade zones has a significant promoting effect on urban economic growth, and the conclusion remains robust after a series of robustness tests. The mechanism test shows that the trial cities of the free trade zone policy promoted economic growth through the mediating effect of foreign trade. Since the estimation result under the difference-in-difference model is the average effect of the experimental group, further research on regional heterogeneity and area heterogeneity of the free trade zone policy is conducted. The study found that the economic growth effect of the free trade zone policy is not significant for inland cities and central and western cities, but very significant for coastal and eastern cities. Moreover, area heterogeneity analysis found that a relatively loose scope of free trade (port) zones can more effectively promote the development of the local economy under the FTZ policy.

The promoting effect of the free trade zone policy on urban economic growth demonstrates the correctness and necessity of continuing to promote the free trade zone policy. However, in view of the differentiated effects of the policy among cities, it may be better to carry out subsequent free trade zone pilot projects with planned and targeted approaches to fully reap the benefits of the policy for urban economies. The following inspirations are provided: Firstly, improve the soft environment and supporting measures construction level of the free trade (port) zones. The regional differences in the promoting effect of the free trade zone policy on urban economic growth indicate that in coastal and eastern regions with relatively high levels of soft environment and supporting measures construction, the free trade zone policy can more effectively promote urban economic development. Therefore, improving the soft environment and supporting measures construction level of the free trade (port) zones, insisting on strong support for enterprises within the free trade zone, implementing various guarantee measures for enterprises, strengthening the promotion of the free trade zone policy, increasing enterprise participation, and further promoting the promoting effect of the free trade zone policy on urban economic growth. Secondly, reasonably determine the area of the free trade (port) zones according to their own conditions. The area heterogeneity of the promoting effect of the free trade zone policy on urban economic growth shows that a relatively loose scope of free trade (port) zones can more effectively promote the development of the urban economy under the policy. Therefore, each province can reasonably increase the area of the free trade zone based on its own conditions in the subsequent establishment of free trade (port) zones. For the existing free trade (port) zones, consider expanding the area of the free trade zone appropriately when conditions permit. Thirdly, select pilot areas rationally and try to build multi-city joint pilot projects. The differentiation effect of the free trade zone policy on urban economic growth shows that the resource endowment conditions and the area size of the free trade zone both affect the effectiveness of the policy. Sufficient resource endowment resources are the source of its rapid development, and a reasonable and loose free trade zone area is the driving force for its healthy development. Trying to build multi-city joint pilot projects, realizing the multi-regional integration of the free trade zone, and promoting the complementary advantages of resources among cities, may further promote the effectiveness of the free trade zone policy.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. The control group cities are prefecture-level and municipalities directly under the central government that were established before 2010 and do not have free trade zones.

2. The experimental group consisted of 22 cities, and to ensure equal numbers, 22 cities are selected in placebo test.