Export Cutoff Productivity, Uncertainty and Duration of Waiting for Exporting

1 Introduction

With the rise and development of new-new trade theory represented by Melitz (2003), the dynamics of enterprises’ export entry and exit have gradually become a hot topic in the field of empirical research of international economics. At present, there are two main directions for the research on the dynamics of enterprises’ export entry and exit. The first one is the research on the decision-making of enterprises’ export entry and exit. The second one is the research on the duration related to enterprises’ export behavior. The research on the decision-making of enterprises’ export entry and exit has been very mature. The existing literature have discussed it from various perspectives. However, the research on the duration related to enterprises’ export behavior is still a relatively new direction. Further, this new direction can be divided into two sub-directions. The first one is the research on the duration required for enterprises to enter the export market, i.e. the duration of enterprises’ waiting for exporting. The second one is the research on the duration of enterprises’ export. In the existing literature, more studies are about the duration of enterprises’ export. The representative papers include Albornoz et al. (2016), Brenton et al. (2010), Esteve-Pérez et al. (2013), Peterson et al. (2018), Sui and Baum (2014), Straume (2017), Zhou et al. (2019), etc. But the studies on the duration of enterprises’ waiting for exporting are relatively rare. Ilmakunnas and Nurmi (2010) and Lemessa et al. (2018) are the two representatives of a few papers focusing on this issue. However, only in few papers focusing on the duration of enterprises’ waiting for exporting, there is still a lack of discussion from the perspective of export cutoff productivity. According to Melitz (2003), the exporting of micro-enterprises shows the “productivity threshold effect.” Specifically, only those enterprises whose productivity is above the export cutoff productivity can engage in export trade, while those whose productivity is between the domestic cutoff productivity and the export cutoff productivity can only engage in the domestic sales, and those with lower productivity will have to be eliminated by the market. Obviously, the core idea of new-new trade theory means that the level of export cutoff productivity (i.e. productivity threshold) plays an important role in deciding the export entry of enterprises and then the duration of their waiting for exporting. Therefore, discussing the duration of enterprises’ waiting for exporting from this perspective will enrich and perfect the research on the dynamics of enterprises’ export entry. In addition, the Sino-US trade war has lasted for more than 4 years since March 2018. Obviously, in this context, it is also necessary to discuss the impact of export threshold on the export behavior of micro-enterprises.

In fact, the main reason why the perspective of productivity threshold has been lacking for a long time is the lack of effective methods to estimate enterprises’ export cutoff productivity. Specifically, none of the main methods for estimating the threshold, such as those reported by Chan (1993), Caner and Hansen (2004), Gao et al. (2013), Hansen (1999, 2000), Seo and Linton (2007), etc., is applicable to the case where the dependent variable is a dummy one. However, fortunately, receiver operating characteristic (ROC) method provides us with an effective way to estimate the productivity threshold. At present, ROC method is widely applied in medicine, machine learning, and natural science. Its application in economics and management is very limited. The application is basically limited to the performance evaluation of classification models, such as those reported by Banasik and Crook (2007), Blanco et al. (2013), Buckinx and Van den Poel (2005), Crook and Banasik (2004), Cubiles-De-La-Vega et al. (2013), Chen et al. (2012), Verbeke et al. (2012), etc. Therefore, this study also contributes to the extended application of ROC method.

However, when the Non-Parametric ROC method is used for estimating enterprises’ export cutoff productivity, a problem that should be noticed is the performance loss caused by the possible productivity paradox. Many empirical studies by authors, such as Dai et al. (2016), Gao and Yin (2013), Lu (2010), Lu et al. (2010), Yang and He (2014), etc., all show that the productivity of China’s export enterprises is lower than that of its domestic-oriented enterprises. This means that there is a productivity paradox. At present, the preponderant explanation for productivity paradox is that China has a large number of enterprises engaged in processing trade (Dai et al., 2016; Gao & Yin, 2013). Yu (2015) argues that processing trade is China’s most important export mode. The generally low productivity of processing trade enterprises lowers the average productivity level of China’s export enterprises, which thus makes the productivity of export enterprises be lower than that of domestic-oriented enterprises. Thus, the productivity paradox arises. As is known to all, the export of processing trade enterprises mainly depends on the low wage of China’s labor force, rather than their productivity level. Hence, it is meaningless to measure the export cutoff productivity of this part of the enterprises. At the same time, the classification performance of export cutoff productivity under the whole sample will be reduced if these enterprises are included. In view of this, this study excludes the pure processing trade enterprises from the sample.

The marginal contributions of this study are mainly as follows. First, this study explores the impact of export cutoff productivity on the duration of enterprises’ waiting for exporting, which enriches the research on dynamics of enterprises’ export entry. Second, this study examines the heterogeneity of impact of productivity threshold on duration of enterprises’ waiting for exporting. Third, this study investigates the impact of China’s accession to the World Trade Organisation (WTO) on the threshold effect that the duration of Chinese enterprises’ waiting for exporting shows. Fourth, this study discusses the influence of the rising of uncertainty on this effect. Fifth, this study provides a novel threshold estimation method, which can be used for reference by other peers.

The remainder of the study is organised as follows. Section 2 gives the data source and processing. Section 3 describes the Non-Parametric estimation of the duration of Chinese industrial enterprises’ waiting for exporting. Section 4 gives the setup of econometric model and the selection of explanatory variables. Section 5 depicts the classification performance of export cutoff productivity under the whole sample. Section 6 investigates the impact of productivity threshold on duration of enterprises’ waiting for exporting, including benchmark estimation and a variety of robustness tests. Section 7 further examines the ownership, industry, and destination heterogeneity of impact of productivity threshold on enterprises’ export entry dynamics. Section 8 explores whether China’s accession to the WTO weakens the productivity threshold effect. Section 9 discusses whether the rising of uncertainty aggravates the productivity threshold effect. Section 10 gives the conclusion.

2 Data

The duration of waiting for exporting that this study defines is how long it takes for the enterprises to start exporting. It is called “failure event” or “failure” that enterprises start to enter the export market. Before the survival analysis is carried out, the censoring problems should be dealt with, including left-censoring and right-censoring. Since the data set used in this study covers the period from 2000 to 2006, it is impossible to know whether enterprises export outside the sample period. If an enterprise exports in 2000, the year when it starts to enter the export market cannot be accurately confirmed. If this is ignored, the duration of enterprises’ waiting for exporting will be underestimated, which thus results in the left-censoring problem. If there is no failure event during a certain period, that is, an enterprise is always a non-exporter during the period, it is considered that the right-censoring problem has arisen. Since the survival analysis is still valid in the presence of right-censoring, this problem does not need to be worried about. As for the left-censoring problem, the processing of this study is that if an enterprise exports in 2000, the corresponding duration of waiting for exporting is replaced by a missing value. For example, if an enterprise exports in 2000, does not export during 2001–2004, and exports again in 2005, the corresponding processing is that the duration of waiting for exporting in 2000 is set to a missing value, and that in 2001–2004 is calculated normally, which means that the enterprise enters the export market again after 4 years. One problem that needs to be explained is that the starting year used for measuring the duration of waiting for exporting is the certain one during the sample period rather than the establishment one of an enterprise. The reason for this is that one of the databases in this article, Chinese Industrial Enterprises Database, sets a threshold for non-state-owned enterprises to enter the survey. Specifically, only the non-state-owned enterprises with annual sales of RMB 5 million or more can be included in this database. Therefore, if the establishment year of an enterprise is taken as the starting one for measuring the duration of waiting for exporting, it is very much likely to overestimate the duration of waiting for exporting. In fact, this processing is consistent with Ilmakunnas and Nurmi (2010).

This study is based on two groups of highly disaggregated firm-level data. The first group of data is the firm-level production data from Chinese Industrial Enterprises Database constructed by China’s National Bureau of Statistics. The second group of data is the transaction-level trade data from China’s General Administration of Customs. The sample used in this study is obtained from the matching of these two groups of data. When using the matching data to examine the enterprises’ export behavior, the sample period of the existing literature is usually from 2000 to 2006 (Cui & Liu, 2018; Dai et al., 2016; Fan et al. 2018; Rodriguez-Lopez & Yu, 2017; Schminke & Van Biesebroeck, 2013; Tian & Yu, 2015; Yu, 2015). In view of this and the data availability, this study also adopts the sample during the same period to carry out the research. So, the duration required for enterprises to enter the export market should be between 1 and 7 years. This study merges the two groups of data using the method of Dai et al. (2016). Finally, the sample obtained in this study covers 607,282 observations. The number of successfully matched observations is 52,206, and among them, the yearly results are 4,505, 5,573, 6,463, 8,050, 12,474, and 15,141, respectively. Furthermore, the successfully matched yearly exporters are 2,057, 2,539, 2,938, 3,716, 5,604, and 6,751, respectively.^[1] For the detailed cleaning and matching of two groups of data, refer to the study by Duan (2022).

3 Non-Parametric Estimation of Duration of Enterprises’ Waiting for Exporting

The survival and hazard functions are often used to describe the distribution characteristics of duration in survival analysis. Let T denote the duration of enterprise’s maintaining its non-export status, and take a value of t . The duration is complete if the enterprise has a transition from non-export state to export state over a period of time, which is denoted as c j = 1 . The duration is right-censoring if there is no failure event over a period of time, which is denoted as c j = 0 . The survival function of enterprise i is given as follows:

The Non-Parametric estimation of survival function can be obtained through KM product limit estimator.

where N k refers to the number of durations of waiting for exporting at risk when the length of duration is k . D k refers to the number of “failures” observed in the same duration, i.e. the number of enterprises that start to enter the export market.

The hazard function represents the probability that an enterprise changes from a non-export state in period t − 1 to an export state in period t .

The Non-Parametric estimation of hazard function can be obtained through

Based on the Non-Parametric estimators of survival and hazard functions, this study has carried out the overall estimation, the sub-ownership estimation, the sub-industry estimation, and the sub-destination estimation in turn.

3.1 Overall Results

Figure 1 shows the KM survival and hazard curves. The survival curve in Figure 1a indicates that with the prolonging of duration of waiting for exporting, the survival rate of enterprises gradually declines. The KM estimate shows that the average duration required for the enterprises to enter the export market is 4.7 years, and the median is 5 years. The proportion of enterprises that take more than 1 year to enter the export market is 92.61%, and that taking over 5 years is 68.91%. The hazard curve in Figure 1b indicates that with the prolonging of duration, the hazard rate gradually increases, that is, the possibility of enterprises’ starting to enter the export market gradually increases. Therefore, the hazard function of duration of waiting for exporting shows a significant positive duration dependence. This indicates that the enterprises will make various efforts over time to gradually cultivate their export capacities, including conducting an investigation on international market, producing high-quality products that meet the needs of international market, carrying out advertising, and so on, so as to improve the possibility of their own export participation and shorten the duration of waiting for exporting.

Figure 1

Survival and hazard curves for duration of waiting for exporting. (a) Survival curve. (b) Hazard curve.

3.2 Results by Ownership

Figure 2 shows the KM survival curves by ownership, including home and foreign enterprises.^[2] This figure indicates that the survival rate of home enterprises is higher than that of foreign enterprises, which means that it is more difficult for home enterprises to enter the export market than foreign enterprises. The possible reason is that foreign enterprises usually have better international market channels and more rich export experiences. Compared with home enterprises, it is easier for foreign enterprises to enter the export market. The KM estimate shows that the average duration required for home enterprises to enter the export market is 5.13 years, while 4.63 years for foreign enterprises. In addition, the median duration for home enterprises is 6 years, which is higher than 5 years for foreign enterprises. Furthermore, 94.77% of home enterprises take more than 1 year to enter the export market and 72.79% take more than 5 years, while the corresponding proportions of foreign enterprises are 93.06 and 70.03%, respectively. Besides, it can be found that the proportion of home enterprises that take more than 6 years to enter the export market is slightly lower than that of foreign enterprises. The possible reason is that home enterprises, especially state-owned ones, can benefit from more export incentive policies than foreign enterprises, which may be conducive to shortening the duration of their waiting for exporting to no more than 6 years.

Figure 2

Survival curves by ownership.

3.3 Results by Industry

Figure 3 shows the KM survival curves by industry, including labor-intensive and capital-intensive industries.^[3] This figure shows that when the duration of waiting for exporting is less than 4 years, the survival rate of labor-intensive enterprises is almost the same as that of capital-intensive ones. However, when the duration exceeds 5 years, the survival rate of labor-intensive enterprises will be significantly lower than that of capital-intensive ones. This indicates that in the first few years, both labor-intensive and capital-intensive enterprises face almost the same difficulties in exploiting the international market, but after a period of efforts, the labor-intensive enterprises are more likely to enter the export market earlier and become exporters. The possible reason is that the labor-intensive enterprises mainly rely on the low-cost advantage based on cheap labor to participate in the export competition, while the capital-intensive enterprises mainly rely on the technological advantage based on a large amount of R&D expenditures to participate in the export competition. Generally speaking, it is much more difficult to achieve technological breakthroughs than to reduce labor costs, especially for developing countries. Hence, the labor-intensive enterprises are more likely to take the lead in entering the international market to participate in the export competition. The KM estimate shows that the proportion of labor-intensive enterprises that take more than 4 years to enter the export market is almost the same as that of capital-intensive ones. The former is 92.80%, followed by 92.43% for capital-intensive enterprises. However, 58.33% of capital-intensive enterprises need more than 6 years to enter the export market, while the proportion for labor-intensive enterprises is 54.89%, significantly lower than the former.

Figure 3

Survival curves by industry.

3.4 Results by Destination

Figure 4 shows the KM survival curves by destination, including the Unites States, the European Union, and Japan.^[4] This figure indicates that the survival rate of enterprises that export to Japan is relatively lower, while that of enterprises that export to the USA and the EU is relatively higher. Obviously, this fact is consistent with what Melitz (2003) expects. According to Melitz (2003), the transportation cost is an important component of export cutoff productivity, and has a positive correlation with it. The enterprises exporting to Japan only need to bear lower transportation costs due to short geographical distance, while those exporting to the USA and the EU have to bear relatively higher transportation costs due to long geographical distance. This means that the enterprises that export to the USA and the EU have to cross the higher productivity threshold, while those that export to Japan face the lower productivity threshold. Hence, the duration of enterprises’ waiting for exporting to Japan is relatively shorter, while that of enterprises’ waiting for exporting to the USA and the EU is relatively longer. In addition, it can be found that the survival rate of enterprises exporting to the EU is slightly higher than that of the USA. The possible reason is that EU still enjoys the retention clauses until 2004 after China’s accession to the WTO. That is to say, it can continue to impose quantitative restrictions or high tariffs on import products from China during the period. As a result, compared with enterprises exporting to the USA, those exporting to the EU will take longer to enter its market. The KM estimate shows that 79.67% of enterprises exporting to the EU take more than 3 years to enter its market, followed by 78.91% of those exporting to the USA and 76.84% of those exporting to Japan. The proportions of enterprises that take more than 5 years to enter the target market are 65.70, 64.36, and 62.76%, respectively.

Figure 4

Survival curves by destination.

4 Econometric Model and Variables

5 Description of Export Cutoff Productivity Based on the Whole Sample

Figure 5 indicates that the export cutoff productivity under the whole sample is 6.302, the sensitivity and specificity of which are 0.685 and 0.673, respectively. When hypothesizing all the enterprises satisfying t f p i t ≥ 6.302 to be exporters, the ratio of correctly classified exporters (i.e. true positives) is 68.5%. When hypothesizing all the enterprises satisfying t f p i t < 6.302 to be non-exporters, the ratio of correctly classified non-exporters (i.e. true negatives) is 67.3%. Furthermore, the accuracy of 0.6734 means that 67.34% of total enterprises are correctly classified. In addition, the calculation shows that the quantile that corresponds to the export cutoff productivity is 65.86%. This means that the top 34.14% of total enterprises may be more likely to become exporters. However, it has to be pointed out that none of sensitivity, specificity, accuracy and AUC is very high. The possible reason is that there are many factors that could determine enterprises’ export participation. The productivity is not the only factor although it plays a major role. As a result, some enterprises with high productivity may operate only in the domestic market, while some enterprises with low productivity may engage in exports instead.

Figure 5

ROC curve based on the whole sample.

6 Impact of Export Cutoff Productivity on Duration of Enterprises’ Waiting for Exporting

6.1 Benchmark Results

In Cox regression, there are two points to be noted. First, the test of proportional hazard assumption should be implemented. Second, the tied failures should be dealt with. The partial likelihood function is independent of exact failure time, and only related to the sequence of failure events. Therefore, if the failure events of two or more individuals occur at the same time, i.e. the tied failures occur, it is not determined that which individual’s failure event first occurs. As a result, the risk set at the failure time could not be accurately identified. In addition, if the proportional hazard assumption is not satisfied, the application of Cox proportional hazard model is inappropriate. The Breslow’s (1974) method is used to deal with the tied failures and this method is an approximation of exact-marginal calculation. As for the proportional hazard assumption, this study adopts the graphic method to test it. To be specific, the fitting plot of every covariate’s Schoenfeld residual against time will be drawn to examine whether its slope is 0. The results of test of proportional hazard assumption are shown in Figure 6.

Figure 6

Test of proportional hazard assumption. (a) Cutoff, (b) TFP, (c) Scale, (d) KL ratio, (e) PS ratio, (f) New, (g) Age, (h) SOE, and (i) Foreign.

Figure 6 shows that all the slopes are very close to 0, which indicates that the correlation between each Schoenfeld residual and time is not significant after proportional adjustment. So, the proportional hazard assumption is satisfied and adopting Cox proportional hazard model for survival estimation is appropriate.

The column (1) of Table 1 reports the benchmark results. The estimated coefficient of export cutoff productivity (Cutoff) is less than 1 and statistically significant at a 1% level, which is in line with the expectation. This indicates that the improvement in export cutoff productivity does reduce the hazard rate of enterprises’ starting to enter the export market, and thus prolongs the duration of their waiting for exporting. The rising of export cutoff productivity improves the productivity level required for the enterprises to enter the export market, which means that it is more difficult for them to enter the export market. So, the hazard rate of enterprises’ starting to enter the export market will be reduced and thus the duration of their waiting for exporting will be prolonged. Obviously, this conclusion strongly supports the self-selection hypothesis proposed by the new-new trade theory. In addition, the hazard ratio of 0.8739 indicates that for every 1% increase in export cutoff productivity, the hazard rate of enterprises’ starting to enter the export market will decrease by 0.1261%.^[7]

Table 1

Benchmark results and robustness tests based on alternative samples

	Full sample	First spell	One spell only	Gap-adjusted
Cutoff	0.8739***	0.8680***	0.8734***	0.8709***
	(−5.88)	(−5.69)	(−5.22)	(−5.76)
TFP	1.0558***	1.0415***	1.0441***	1.0470***
	(5.67)	(4.01)	(4.02)	(4.62)
Scale	1.2320***	1.1927***	1.1916***	1.2054***
	(22.23)	(17.65)	(16.82)	(19.26)
KL ratio	0.9745***	0.9589***	0.9505***	0.9652***
	(−3.78)	(−5.83)	(−6.66)	(−5.03)
PS ratio	1.0460	1.0037	0.9586	1.0314
	(1.27)	(0.11)	(−1.26)	(0.78)
New	1.0639***	1.0634***	1.0631***	1.0646***
	(25.88)	( 23.63)	(22.45)	(25.04)
Age	1.0009***	1.0008***	1.0009***	1.0009***
	(4.13)	(3.56)	(3.16)	(3.73)
SOE	1.0423	1.0068	1.0329	1.0133
	(0.65)	(0.10)	(0.41)	(0.20)
Foreign	1.0552**	1.0403*	1.0602**	1.0523**
	(2.42)	(1.69)	(2.39)	(2.23)
Year dummies	Yes	Yes	Yes	Yes
Region dummies	Yes	Yes	Yes	Yes
Log likelihood	−159634.63	−138375.97	−110238.17	−146822.76
Observations	44,248	40,948	37,632	43,011

Note: ***, **, and * denote the significance at a 1, 5, and 10% level, respectively. The z-statistics in parentheses are based on robust standard errors (corrected for clustering at firm-level).

Among control variables, the estimated coefficient of TFP is significantly greater than 1 at a 1% level, which is consistent with the expectation of this study and indicates that the higher the productivity, the higher the hazard rate of enterprises’ starting to enter the export market. Thus, the improvement in the total factor productivity could help to shorten the duration of their waiting for exporting. As expected, the estimated coefficient of enterprises’ scale is also greater than 1 and statistically significant at a 1% level. This shows that the expansion of enterprises’ scale will shorten the duration of their waiting for exporting. The estimated coefficient of capital intensity (KL ratio) is significantly less than 1 at a 1% level, which is in line with the expectation. The capital factor of China, as a country with abundant labor, is relatively more scarce and more expensive. Thus, when using more and more capitals in production, the cost of products is bound to rise and thus, the competitiveness will be weakened. So, with the increase in the capital intensity, the hazard rate of enterprises’ entering the export market will be reduced, and the duration required for their starting exporting will be prolonged. Contrary to the expectation, the regression coefficient of profit margin (PS ratio) is not statistically significant. The possible reason is that although the profit margin increases, the enterprises use a large amount of profits for shareholder’s dividend, and thus the growth of funds for exploiting the international market is limited. As expected, the regression coefficient of output value of new products (New) is greater than 1 and statistically significant at a 1% level. This shows that the increase in output value of new products could improve the hazard rate of enterprises’ entering the export market, thus helping to shorten the duration of their waiting for exporting. The estimated coefficient of enterprises’ age is significantly greater than 1 at a 1% level, which is consistent with the expectation. This indicates that the older enterprises can enter the export market earlier by virtue of more experience and better reputation accumulated over a long period. Unexpectedly, the regression coefficient of dummy for state-owned enterprises (SOE) is not statistically significant. The possible reason is that although the production and operation efficiency of state-owned enterprises is low, they can usually enjoy various preferences and subsidies from the government. The former is not conducive to the exploiting of international market, while the latter is helpful for enterprises to enter the export market early. Under the interaction of two opposite forces, it is not surprising that the regression coefficient is not statistically significant. In line with the expectation, the estimated coefficient of dummy for foreign-invested enterprises (Foreign) is significantly greater than 1 at a 5% level. The estimation results indicate that the hazard rate of foreign-invested enterprises is 5.52% higher than that of other types.

7 Heterogeneous Analysis

In order to investigate the heterogeneity of impact of productivity threshold on the duration of enterprises’ waiting for exporting, this study provides the sub-ownership results, the sub-industry results and the sub-destination results, respectively.

8 Does China’s Accession to the WTO Weaken the Productivity Threshold Effect?

On November 10, 2001, China finally joined the WTO after 15 years of hard work. This means that China can enjoy the same rights as other WTO members and have the fair-trade opportunity. Obviously, China’s accession to the WTO creates a convenient and fair-trade environment for Chinese enterprises. China’s exports have been growing rapidly after its accession to the WTO, and since 2009, China has jumped from the sixth largest exporter in 2001 to the largest exporter, thus playing an important role in the world trade. In order to investigate whether the accession to the WTO weakens the threshold effect of export cutoff productivity on duration of Chinese enterprises’ waiting for exporting, this section constructs the following econometric model:

where WTO n is the dummy related to accession to the WTO. If n ≥ 2002 , its value is 1, otherwise, 0. WTO n × C u t o f f j n is the product of dummy WTO n and productivity threshold C u t o f f j n , and C o n t r o l i j k n l represents some control variable. The control variables in expression (9) are the same as those in expression (5). υ n and υ k represent the year and region fixed effects, respectively. ε i j k n is the random disturbance term. i , j , k , and n denote the enterprise, industry, region, and year, respectively.

Table 7 reports the estimation results of expression (9). Considering the robustness, in addition to benchmark results based on the method reported by Ackerberg et al. (2015), Table 7 also reports the results based on the other three methods, including Levinsohn and Petrin (2003), Olley and Pakes (1996) and Wooldridge (2009). According to Table 7, the estimated coefficients of interaction term ( W T O × C u t o f f ) in the four cases are all significantly greater than 1, indicating that China’ accession to the WTO does weaken the threshold effect of export cutoff productivity on the duration of Chinese enterprises’ waiting for exporting. The accession to WTO enables Chinese enterprises to engage in export trade freely under the basic principles advocated by WTO, including non-discrimination, transparency, and fair competition. Obviously, this helps to weaken the threshold effect of export cutoff productivity on the duration of waiting for exporting.

9 Uncertainty and Productivity Threshold Effect

Since 2016, the world has entered a state of considerable uncertainty. The UK leaves the EU. Donald Trump, a businessman, is elected as the president of United States. The refugee problem is getting worse in Europe. Turkey’s foreign military expansion is escalating. Populism is emerging around the world. Coronavirus Disease 2019 (COVID-19) caused by a novel coronavirus is spreading globally. The war between Russia and Ukraine is still ongoing. The comprehensive strategic competition between China and the United States is getting more and more fierce. All of these increase the risk of the global economy. In this context, this study assumes that it is necessary to explore the impact of uncertainty on threshold effect of export cutoff productivity on the duration of enterprises’ waiting for exporting. So, this section constructs the following hazard model:

where U n c e r t a i n t y j n is the uncertainty faced by industry j in the n th year, and it is expressed by the variance of the daily closing price of listed industrial enterprises. U n c e r t a i n t y j n × C u t o f f j n is the product of uncertainty U n c e r t a i n t y j n and productivity threshold C u t o f f j n . In addition, the control variables used in expression (10) are also the same as those in expression (5). Further, the calculation of uncertainty is as follows:

where ω i j n = V ¯ i j n / V ¯ j n is the proportion of the average market value of the listed enterprise i in industry j in the n th year to the average total market value of industry j in the n th year, and is the weight used for measuring the uncertainty. Here V ¯ i j n = ∑ m = 1 M i j n V i j n m / M i j n and V ¯ j n = N j n × V ¯ i j n . V i j n m is the market value of enterprise i on the m th trading day of the n th year. M i j n is the total number of trading days of enterprise i in the n th year. N j n is the number of listed enterprises of industry j in the n th year. Furthermore, var ( p i j n m ) is the variance of daily closing price of enterprise i in the n th year, and can be obtained as follows:

where p i j n m is the closing price of enterprise i on the m th trading day of the n th year. In addition, the data used for calculating uncertainty are from China Stock Market and Accounting Research (CSMAR) Database.

Table 8 reports the estimation results of expression (10). It can be seen that the estimated coefficients of interaction term U n c e r t a i n t y × C u t o f f in the four cases are all significantly less than 1, showing that the increase in uncertainty will aggravate the threshold effect of export cutoff productivity on the duration of enterprises’ waiting for exporting. If the increase in productivity threshold is accompanied by the rise of uncertainty, the enterprises will encounter double obstacles in entering the export market. On one hand, the enterprises have to cross the higher export threshold. On the other hand, they have to bear the higher export risk. Compared with single export obstacle, the double export obstacles will make it more difficult for the enterprises to enter the export market. Therefore, the increase in uncertainty will aggravate the impact of productivity threshold on the duration of waiting for exporting.

10 Conclusion

In the existing literature on the duration related to enterprises’ export behavior, more studies are about the duration of export trade, while the analyses of duration of waiting for exporting are relatively rare. Even in the few articles that focus on the duration of enterprises’ waiting for exporting, there is still a lack of discussion from the perspective of export cutoff productivity. However, according to Melitz (2003), only the enterprises whose productivity is above the export cutoff productivity can engage in export trade, which indicates that the export cutoff productivity has an important impact on the duration of enterprises’ waiting for exporting. So, analyzing the duration of enterprises’ waiting for exporting from this perspective will enrich and perfect the research on dynamics of enterprises’ export entry. This study first carries out a Non-Parametric estimation of duration of Chinese industrial enterprises’ waiting for exporting. Then, based on estimation of export cutoff productivity by applying the Non-Parametric ROC method, this study uses Cox proportional hazard model to investigate the impact of productivity threshold on the duration of enterprises’ waiting for exporting. In addition, this study further examines the ownership, industry, and destination heterogeneity of impact of productivity threshold on the dynamics of export entry. Furthermore, this study explores the influences of China’s accession to the WTO and the uncertainty on threshold effect of export cutoff productivity on the duration of waiting for exporting. Specifically, the conclusions are as follows:

1. The average duration of enterprises’ waiting for exporting is 4.7 years and the median is 5 years. The proportion of enterprises whose duration of waiting for exporting exceeds 1 year is 92.61%, while it is 68.91% over 5 years. In addition, with the prolonging of duration, the hazard rate of export entry gradually increases, which indicates that the hazard function of duration of enterprises’ waiting for exporting shows a significant positive duration dependence.

2. The improvement in export cutoff productivity reduces the hazard rate of enterprises’ starting to enter the export market, and thus prolongs the duration of their waiting for exporting. Furthermore, this conclusion is supported by a variety of robustness tests, including estimations using alternative samples, those using alternative methods for estimating TFP and those using the sample consisting of newly established enterprises during the sample period. In addition, according to the estimation result of hazard ratio, it can be found that for every 1% increase in productivity threshold, the hazard rate of enterprises’ entering the export market will decrease by 0.1261%.

3. The impact of export cutoff productivity on the duration of enterprises’ waiting for exporting has the significant ownership and industry heterogeneity, but does not have the destination heterogeneity. First, the increase in productivity threshold has a stronger prolonging effect on the duration of waiting for exporting of foreign enterprises than that of home enterprises. In addition, the prolonging effect is stronger in capital-intensive industry, followed by labor-intensive industry. However, it does not have the significant destination heterogeneity.

4. China’s accession to the WTO helps to weaken the productivity threshold effect that the duration of Chinese enterprises’ waiting for exporting shows, while the rising of uncertainty will aggravate this effect. In addition, this finding is rather robust and can be supported by a variety of robustness tests using alternative methods for estimating TFP.

This study gives us some important inspirations. First, making great efforts to improve the productivity is still the basic way for enterprises to shorten the duration required for opening up the international market. In addition, considering that the threshold for entry into the US market has been raised, Chinese enterprises should actively seek other alternative markets, such as European market, Southeast Asian market, and South American market. Furthermore, it should be the focus of the government to accelerate the negotiation and establishment of various free trade zones, to construct a stable business environment and to lower the market uncertainty.