How Does the COVID-19 Pandemic Impact Internal Trade? Evidence from China’s Provincial-Level Data

: The COVID-19 pandemic has threatened the goals of sustainable development through its impact on global public health and economic systems. This paper examines the impact of the COVID-19 pandemic on interprovincial trade in China. First, we estimate interprovincial trade ﬂows in China for 2018–2022 using information from different sources and use it to infer interprovin-cial trade costs. Second, we estimate the impact of COVID-19 on interprovincial trade ﬂows and interprovincial trade costs based on a trade gravity model. Finally, we construct a multiregional, multisector quantitative spatial model and introduce changes in interprovincial trade barriers in 2019–2020 to the model to analyze economic losses due to the early COVID-19 pandemic. We ﬁnd a signiﬁcant negative effect from the COVID-19 pandemic on interprovincial trade ﬂows in China, but we do not obtain robust results demonstrating that the intensiﬁcation of the pandemic signiﬁcantly affected bilateral trade costs. The results of the quantitative analysis suggest that changes in inter-provincial trade barriers reduced China’s overall GDP in 2019–2020 by 0.11%. The results are not the same at the regional and sectoral levels, but the impact is not signiﬁcant on average.


Introduction
The COVID-19 pandemic that began in late 2019 has affected the economies of many countries.Preventive and control measures against the pandemic, such as maintaining social distances, restrictions on the movement of people, and the inspection of goods, motivated by the need to limit the spread of the virus, will undoubtedly hinder the normal functioning of interregional trade and cause disruptions in supply chains.It is well known that a key feature of the organization of production in modern companies is their reliance on complex and interconnected supply chains, using a variety of intermediate inputs from different sources.Undoubtedly, the supply chain model of production means that intermediate goods play a very important role in the production process and that disruptions to this orderly flow of goods and services can be a source of macroeconomic volatility.The smooth flow of supply chains and interregional trade has, therefore, always attracted the attention of governments and economists, leading to a large number of studies on the impact of pandemic shocks on trade (e.g., Barbero et al., 2021;Pei et al., 2022 [1,2]).However, most of these studies have focused on international trade, and little is known about the impact of a pandemic on interregional trade within a country.In fact, data on domestic interregional trade are rather scarce compared with more complete statistics on international trade, a factor that contributes to the lack of research on domestic trade.For China, although data on its interprovincial trade are not directly available, it is possible to estimate its interprovincial trade flows using various sources of information (national input-output tables, provincial input-output tables, etc.).Using estimated interprovincial trade flows, we can further analyze the impact of the COVID-19 pandemic on China's domestic trade.
In this paper, we first estimate China's interprovincial trade flows for 2018-2022 using information from various sources and, on this basis, infer the interprovincial trade costs for each year using the method of Head and Ries (2001) [3].Second, we estimate the impact of COVID-19 on interprovincial trade and interprovincial trade costs.Finally, we incorporate changes in trade costs into a multiregional, multisector quantitative spatial model to explore the propagation and heterogeneous impact of the trade barrier effect of pandemic shock at the regional and sectoral levels within a country and provide evidence of this impact at a subdivisional level.
We estimated the effect of COVID-19 on interprovincial trade flows based on a trade gravity model.We found that the estimated coefficients of COVID-19 incidence status variables are all significantly negative at the 1% statistical level, controlling for gravity-type variables and individual and time-fixed effects, which suggests that the worsening of the COVID-19 pandemic significantly inhibited interprovincial trade flows.To test the robustness of the estimation results, we also made estimates by replacing the COVID-19 incidence status variable and applying the PPML estimator (which addresses the zero value of trade).To address potential endogeneity issues, we also performed 2SLS estimation using instrumental variables.All estimation results suggest that the worsening of the COVID-19 pandemic inhibited interprovincial trade flows.
We also inferred interprovincial trade barriers in China using estimated trade flow data and the methodology of Head and Ries (2001) [3].On this basis, we analyzed the impact of COVID-19 on trade costs.The estimation results show that there was a positive relationship between the increase in COVID-19 cases and the increase in trade costs, but the effect is not significant at the 10% level.To further analyze the impact of changes in interprovincial trade barriers on the Chinese economy, we introduced changes in interprovincial trade costs in 2019-2020 into a calibrated, multiregional, multisector general equilibrium model of China and quantified the impact of changes in interprovincial trade barriers at the regional and sectoral levels in China in the early years of COVID-19.We found that the relative change in interprovincial trade barriers from 2019 to 2020 resulted in a loss of 0.11% in China's aggregate GDP.The results at the regional-sectoral level show that GDP losses from rising trade costs in 2019-2020 were not the same across regions (or sectors), but the impact was not significant on average.
Our paper is unique in that it constructs a novel dataset by estimating interprovincial trade flows in China, providing evidence of the impact of COVID-19 on internal trade and its trade barriers.Furthermore, we include changes in interprovincial trade barriers before and after the COVID-19 outbreak in a quantitative spatial model to quantify the economic losses caused by changes in trade barriers.
Our paper contributes to the understanding of the impact of the COVID-19 pandemic on internal trade.The COVID-19 pandemic has generated numerous studies on the impact of pandemic shocks on international trade and global value chains.These studies have focused on the transmission pathways of pandemic economic shocks in international trade and their deeper impacts, highlighting the importance of global value chains and production networks during the spread of the COVID-19 pandemic (e.g., Baldwin et al., 2020;Baqaee and Farhi, 2022;Cakmakli et al., 2020;Kejžar et al., 2022 [4-7]).However, few studies have provided evidence of how COVID-19 affects inner trade.Indeed, COVID-19 has an equally important impact on inner trade, and how it propagates through regionalsectoral input-output linkages and leads to economic volatility remains to be further explored.Our paper analyzes the impact of COVID-19 on inner trade from the perspective of interprovincial trade in China and provides evidence of the impact of COVID-19 on inner trade.
Our paper is also relevant to the literature examining the COVID-19 pandemic in China.Following the COVID-19 pandemic outbreak, numerous studies have examined the impact of COVID-19 on the Chinese economy.For example, a number of studies have provided evidence of the impact of the COVID-19 outbreak on China's foreign trade (e.g., Cai and Hayakawa, 2022;Fang et al., 2020;Liu et al., 2022;Pei et al., 2022 [2,8-10]), and these studies have benefited from detailed data on country-specific trade customs statistics.Similar to the work in this paper are Luo and Tsang (2020) [11] and Chen et al. (2022) [12].Luo and Tsang (2020) used a production network model to estimate the output loss due to the Hubei lockdown triggered by COVID-19, and their estimates suggested that China would suffer a 4% output loss as a result, 40% of which would come from spillovers from domestic and foreign supply chains [11].Chen et al. (2022) analyzed the economic costs of a lockdown in China using intercity truck flow data and found that a full lockdown for one month would result in a 54% reduction in truck flows associated with the blockaded city and that the effects of a lockdown can spill over into other cities through trade links [12].In contrast to these earlier studies, our work first estimates interprovincial trade flows based on ex post data and analyzes the impact of COVID-19 on interprovincial trade flows and trade barriers.Furthermore, our paper uses the estimated trade flows to infer changes in COVID-19 interprovincial trade barriers for 2019-2020 and feeds them into a calibrated quantitative spatial model to analyze the regional and sectoral economic losses caused by changes in trade barriers.
The rest of this paper is organized as follows: Section 2 summarizes the basic facts on the COVID-19 pandemic in China.Section 3 presents the estimation methods and results of interprovincial trade flows and trade barriers.Section 4 presents the results of the empirical estimation of the impact of COVID-19 on interprovincial trade flows and trade costs.Section 5 presents the quantitative spatial model and its results.Section 6 is the conclusion.

Basic Facts
The COVID-19 virus outbreak began in Wuhan in late 2019.Following the "city lockdown" of Wuhan on 23 January 2020, other provinces implemented their "First-Level Response to Major Outbreaks of Public Health Significance" strategies.In the first few months of 2020, all provinces implemented strict response measures.By the end of February 2020, the number of new confirmed cases in China decreased significantly.In the second half of 2020, small regional outbreaks occurred in Beijing, Heilongjiang, Xinjiang, Jilin, and Hebei.In these provinces, where localized outbreaks spread, the government response was strengthened.
In 2021, there were five waves of COVID-19 outbreaks in China caused by imported sources.The first wave began on 1 January 2021, with the number of new cases per day peaking on 14 January 2021.This wave was mainly characterized by regional outbreaks, with the majority of cases concentrated in Hebei and Heilongjiang.The second wave of the pandemic began on 8 July 2021 and peaked on 9 August 2021.This wave affected 12 provinces, with the most severe provinces being Jiangsu, Henan, and Yunnan.The third wave began on 10 September 2021 and peaked at 143 cases in 6 days.This wave mainly affected Fujian and Yunnan.The fourth wave began on 16 October 2021 and soon followed the previous wave, peaking at 109 newly confirmed cases on 2 November 2021 and ending on 19 November.This wave affected 14 provinces and set a new transmission peak in these provinces in 2021.The fifth wave of the pandemic began on 26 November 2021 and peaked at 209 cases per day on 27 December 2021, with this wave mainly affecting Inner Mongolia, Shaanxi, Henan, Shanghai, and Tianjin.
As the Omicron strain became more transmissible, repeated outbreaks of COVID-19 occurred in several provinces in 2022.The outbreak in Shanghai, which began in late February 2022, lasted more than two months and had a significant economic impact.This was followed by localized outbreaks in several places.After mid-December 2020, China essentially de facto liberalized the outbreak, and the economic and social impact of COVID-19 gradually diminished.In 2021 and 2022, the Chinese government implemented a "dynamic zero" control policy, the main aim of which is to break the transmission chain early and prevent the further spread of the virus.Figure 1 shows the number of newly confirmed COVID-19 cases per day in China from 2020 to 2022.gradually diminished.In 2021 and 2022, the Chinese government implemented a "dynamic zero" control policy, the main aim of which is to break the transmission chain early and prevent the further spread of the virus.Figure 1 shows the number of newly confirmed COVID-19 cases per day in China from 2020 to 2022.

Estimation of Interprovincial Trade Flows
The lack of data on interprovincial trade flows has largely limited the study of intra-China trade.There are no directly available or official statistics on interprovincial trade flows for China.Researchers have tried to use different methods to estimate interregional trade data for China.In summary, the main methods used thus far are as follows.First, the method of estimating the volume of goods transported mainly uses data from the China Transport Yearbook and the China Statistical Yearbook on railway transportation between administrative regions.However, this method cannot estimate the sectoral volume of trade because it is not disaggregated by sector, and the data are measured in units of weight rather than value, which is likely to be systematically biased when used to estimate trade flows in units of value.Second, interregional input-output tables can provide interregional trade data on a "one-to-one" subsector basis.However, there is no uniform interregional input-output table for China.Researchers have used a combination of survey and non-survey methods to compile them, but interregional input-output tables differ from researcher to researcher depending on the raw data used and the method of compilation, and their sample periods are concentrated only in years 2 or 7, with discrete sample periods leading to their limited use.The reason for this is that China's National Bureau of Statistics publishes national input-output tables every five years (e.g., 2007 and 2012 input-output tables published for that year), and provinces similarly publish provincial input-output tables every five years; these are the most basic data for compiling interregional input-output tables.Third is the gravity model estimation method.This method is based on the gravity model proposed for estimation by Leontief and Strout (1963) [13].Specifically, this method includes the transport volume distribution coefficient method, the single-point estimation method, and the cross-entropy method.The transport volume distribution coefficient method relies heavily on transport data and, therefore, has a lower accuracy in estimating value volumes.The cross-entropy method also relies on interprovincial rail transport data and is less accurate.In addition to these three methods, there is the location quotient method, the mathematical planning model estimation method, and the value-added tax (VAT) method.The location quotient method requires less data, but the accuracy of its estimates is highly questionable.The mathematical planning model estimation method suffers from a lack of transport data, which makes its classification of the trade sector cruder.VAT refers to calculations based on data recorded in China's Tax

Estimation of Interprovincial Trade Flows
The lack of data on interprovincial trade flows has largely limited the study of intra-China trade.There are no directly available or official statistics on interprovincial trade flows for China.Researchers have tried to use different methods to estimate interregional trade data for China.In summary, the main methods used thus far are as follows.First, the method of estimating the volume of goods transported mainly uses data from the China Transport Yearbook and the China Statistical Yearbook on railway transportation between administrative regions.However, this method cannot estimate the sectoral volume of trade because it is not disaggregated by sector, and the data are measured in units of weight rather than value, which is likely to be systematically biased when used to estimate trade flows in units of value.Second, interregional input-output tables can provide interregional trade data on a "one-to-one" subsector basis.However, there is no uniform interregional input-output table for China.Researchers have used a combination of survey and non-survey methods to compile them, but interregional input-output tables differ from researcher to researcher depending on the raw data used and the method of compilation, and their sample periods are concentrated only in years 2 or 7, with discrete sample periods leading to their limited use.The reason for this is that China's National Bureau of Statistics publishes national input-output tables every five years (e.g., 2007 and 2012 input-output tables published for that year), and provinces similarly publish provincial input-output tables every five years; these are the most basic data for compiling interregional input-output tables.Third is the gravity model estimation method.This method is based on the gravity model proposed for estimation by Leontief and Strout (1963) [13].Specifically, this method includes the transport volume distribution coefficient method, the single-point estimation method, and the cross-entropy method.The transport volume distribution coefficient method relies heavily on transport data and, therefore, has a lower accuracy in estimating value volumes.The cross-entropy method also relies on interprovincial rail transport data and is less accurate.In addition to these three methods, there is the location quotient method, the mathematical planning model estimation method, and the value-added tax (VAT) method.The location quotient method requires less data, but the accuracy of its estimates is highly questionable.The mathematical planning model estimation method suffers from a lack of transport data, which makes its classification of the trade sector cruder.VAT refers to calculations based on data recorded in China's Tax Administration Information System, but the accuracy of its estimates is questionable because the location of the taxpayer may not be the same as its actual location because of the problem of tax evasion.Furthermore, these data are not publicly available and are difficult to obtain.In general, the gravity model estimation method proposed by Leontief and Strout (1963) [13] is more accurate and can obtain longer subsectoral and subregional interprovincial trade flows.Therefore, following Li et al. (2022) [14], we use the gravity model to estimate interprovincial trade flows.
The gravitational model used in this paper is as follows: where t i,RS is the trade flow of sector i from province R to province S, y i,R is the total output of sector i in province R, d i,S is the total demand (equal to total output) of sector i in province S, y i is the total output of sector i nationally, and Q i,RS is the friction coefficient between provinces R and S in sector i.
The key to estimating interprovincial trade flows using the gravity model is to obtain friction coefficients.Given the availability of data, we use base-year data to calculate base-year friction coefficients and estimate trade flows using a single-point estimation method.Specifically, China Multi-Regional Input-Output Table 2017 compiled by Zheng et al. (2020) [15] provides interprovincial trade flows at the province-sector level, t i,RS ; total output, y i,R ; total demand, d i,S ; and sectoral national total output, y i .The period of interprovincial trade flows estimated in this paper is 2018-2022.China Multi-Regional Input-Output Table 2017 is the most recent year available to us and includes relatively complete data for 31 provinces and 42 sectors in China.

Estimation Method
The estimation process in this paper is as follows: 1.
Calculate the interregional friction coefficient for the base year.
From Equation (1), we have Using Equation (2) and the data provided in China Multi-Regional Input-Output Table 2017, we can calculate the friction coefficient at the sector-province-province level in 2017.

2.
Estimated total output for the target year.
In years when national input-output tables and interprovincial input-output tables are not published, data on total output by sector for each province are also not available.Therefore, it is also necessary to estimate the total output data for the target year.First, data on total output, agricultural output, and industrial output for each province for 2017 can be obtained by combining the sectors in the provincial input-output tables for 2017.
Second, data on total output, agricultural output, and industrial output for each province for the target year are estimated.China reports GDP growth rates every year, while total output is reported every five years.Therefore, we need to use these available data to extrapolate the year-by-year total output data.We assume that the growth rate of the total output of each province is positively correlated with its GDP growth rate; i.e., it obeys the following relationship: where op R is the growth rate of total output of province R every five years, Y t,R is the total output of province R in year t(base year), g t+1,R is the GDP growth rate of province R in year t + 1, and a R is the proportionality coefficient before the growth rate of total output and GDP in province R in five years (in general, a R > 0).Given op R and g t+j,R (where j = 1, 2, 3, 4, 5), the proportionality coefficient, a R , can be found by using Equation (3).
Considering data availability, we calculated the scale factor, a R , using relevant data from 2012 to 2017.
Furthermore, the total output of province R in year t (base year), Y t,R , can be used to derive the total output of province R in the target year, Y t+j,R : The agricultural and industrial output of province R for the target year can be obtained using the same method as above.The above methods may exaggerate the volatility of output data if the trend of output change does not match the trend of GDP change, and alternative methods have been used to estimate output data in this paper.
The alternative methods are . The reason for using alternative methods is that, in some provinces, the total output trend calculated using Equation ( 4) is opposite to the GDP trend.Clearly, this is not realistic.The quality issues with local statistical data largely drove this result.Our alternative methods are essentially a common linear interpolation method used in missing data handling.It is important to note that these alternative methods were only used to estimate five total output values.Specifically, the second method was used for estimating the total output of Inner Mongolia and Liaoning.The second method was used to estimate the agricultural output of Liaoning and Jilin.The first method was used for Heilongjiang, and the second method was used for Inner Mongolia and Liaoning in terms of industrial output.The total output of province R is subtracted from the agricultural and industrial output to obtain data on other industries.
Next, the sectoral output data for the target year are estimated.We decompose the output data for the target year using the output ratios of each province in China Multi-Regional Input-Output Table 2017 to finally obtain the output data of 42 sectors in 31 provinces in China for the period 2018-2022.
Through the above calculation, the friction coefficient of the base year and the total output of the target year can be obtained.Assuming that the friction coefficient remains unchanged from the base year to the target year, the interprovincial trade flow data of the target year can be estimated using Equation (1).In addition, it is necessary to divide the provincial import and export data into components in proportion to 2017 to obtain the import and export data at the provincial sector level.The data estimated in this paper are consistent with the following equilibrium relationships: Intraprovincial consumption (IC) + Interprovincial inflows (II) + International imports (IM) = Total inflows (TI)

Estimation Results
Table 1 shows the aggregated results of our estimated trade flows at the country level.As shown in and total imports increased from RMB 14.13 trillion to 17.34 trillion.In terms of the share of trade flows, interprovincial outflows as a percentage of total outflows ranged from 19.23% to 19.76%, while total exports as a percentage of total outflows ranged from 9.19% to 10.36%.Interprovincial inflows as a percentage of total inflows ranged from 19.64% to 20.02%, and total imports as a percentage of total inflows ranged from 7.58% to 8.45%.Interprovincial trade as a share of total trade shows a slight decrease after 2020, while international trade as a share of total trade shows a slight increase after 2020.Tables 2-4 show our estimated total trade flows and their structural proportions at the interprovincial level in China.As shown in Tables 2-4, not only do different provinces differ significantly in terms of total trade volume, but their trade structures are also very different.The time trend shows a gradual increase in the share of import and export trade across provinces, implying an increase in international trade links.For domestic trade, however, the share of interprovincial outflows did not increase significantly across provinces and in some cases even declined.This implies that domestic trade linkages have not increased in line with the increase in total trade.

Inferred Interprovincial Trade Barriers
Based on the estimated trade flows, we measure the costs of interregional trade using the methods of Head and Ries (2001) [3], Anderson and van Wincoop (2003) [16], and many others in the international trade literature.Let X j n denote the total expenditure (or total revenue) of region n on goods from sector j.Let π j ni denote the share of region n's expenditure on the final product of sector j in region i, i.e., π . According to the gravity model of trade, the relationship between trade share and trade costs is . Furthermore, assuming that the costs of bilateral interregional trade are symmetric, the costs of bilateral trade in sector j are expressed by Using interregional trade flow data and trade elasticities, θ j , interregional trade costs can be calculated for China at the province-sector level, and this result is a matrix of J * (N * N).Table 5 shows the results of our calculations for the costs of interregional trade in China in 2020.Notes: This table shows the results aggregated at the regional level using the expenditure shares of each sector, and the trade costs at the regional-sector level are still used in the quantitative analysis in Section 5.

The Effects of COVID-19 on
Furthermore, written in logarithmic form, where trade f low ijt denotes the bilateral trade flow between province i and province j in year t.covid it is a measure of COVID-19 incidence status in province j in year t.In the baseline regression, the logarithm of the number of confirmed cases of COVID-19 is used to measure the pandemic status (labeled ln(1 + case i ) and ln(1 + case j )).dis ij and border ij are the most common control variables in the trade literature, with dis ij representing the geographical distance between the capital of province i and the capital of province j. border ij represents whether province i borders province j. δ i , δ j , and, ν t represent exporter, importer, and time-fixed effects, respectively, and are used to capture the remaining nontime-varying unobservable and time-varying unobservable at the interprovincial level to reduce omitted variable errors.ε ijt is a random disturbance term representing the remaining unobservable affecting interregional trade.We use OLS methods to estimate the above gravity model as our baseline results.
We aggregate the provincial-sector-level trade flows calculated in Section 3.1 to the provincial level to obtain trade f low ijt .The number of confirmed cases of COVID-19 was obtained from data published by the National Health Commission of China, and we collated and aggregated the daily data into annual data.The dis ij and border ij data were manually compiled by us from Chinese geographic information.dis ij denotes the geographical distance between two provincial capitals.The summary statistics of the data are shown in Table 6.

Baseline Results
Columns (1)-( 3) of Table 7 show the results of the baseline estimates using OLS methods.Column (1) shows the results of regressions controlling for geographical distance, exporter-fixed effects, importer-fixed effects, and time-fixed effects.Column (2) is the result of controlling for exporter-importer pair fixed effects and time-fixed effects.The results in this column do not include the gravitational variables of dis ij and border ij because nontimevarying factors are absorbed into the exporter-importer pair fixed effects.The results in Columns ( 1)- (2) show that the coefficients of ln(1 + case i ) and ln(1 + case j ) are significantly negative at the 1% statistical level, implying that the intensification of the pandemic on either the exporter or importer significantly affects bilateral trade flows.Columns ( 1)-( 2) analyze the separate effects of pandemic incidence status on bilateral trade flows by introducing the variables of pandemic incidence status on the importers and exporters for estimation.To analyze the combined impact of the pandemic on bilateral trade flows, we introduce the two into the baseline estimation by combining them.Specifically, the variables of the incidence status of the pandemic on the importers and exporters are replaced by the logarithm of the product of the number of confirmed cases on the importers and exporters; Equation ( 6) is introduced; and the results are shown in Column (3).The coefficient of ln((1 + case i )•(1 + case j )) is significantly negative at the 1% statistical level, implying a negative effect of COVID-19 on interprovincial trade flows from a bilateral perspective.Our findings are consistent with existing studies indicating a negative effect of COVID-19 on trade.This mechanism has been extensively validated in numerous international trade studies.Barbero et al. (2021) analyzed the impact of COVID-19 shocks on exports using monthly data for 68 countries, and their results suggest that the COVID-19 pandemic has a significant negative impact on exports across countries [1].Pei et al. (2022) examined the impact of COVID-19 on exports from Chinese cities and show that cities that implemented lockdown measures experienced a 34% decrease in the year-on-year export growth rate [2].Liu et al. (2022) found that a country's own COVID-19 deaths and lockdowns significantly reduced imports from China [10].Although this literature focuses on international trade, these results still provide support for our results.
In terms of the control variables, the coefficient of lndis is significantly negative at the 1% statistical level, suggesting that distance is also a barrier to interprovincial trade.The coefficient of border is negative but insignificant at the 10% level, suggesting that there is no strong evidence of a "border effect" in interprovincial trade.Of course, a more detailed discussion of the "border effect" on interprovincial trade depends on further research, which is not the focus of this paper.

Robustness
To test whether the baseline estimates are substantially altered by changes in the variable measures and estimation methods, we conducted a series of robustness tests.
Alternative core explanatory variables: Columns ( 4)-( 6) of Table 7 show the estimation results for replacing the explanatory variables.The variable for the occurrence status of COVID-19 was replaced by the number of confirmed COVID-19 cases as a dummy variable to determine whether a pandemic occurred in the province that year and then re-estimated using Equation ( 6).The dummy variable, covid_dum i , indicates whether there was a COVID-19 outbreak in the exporter, covid_dum j indicates whether there was a COVID-19 outbreak in the importer, and covid_dum ij variable represents whether there was a COVID-19 outbreak in either the exporter or importer.The results in Columns ( 4)- (6) show that the coefficients on the COVID-19 occurrence status variables are all statistically significant and negative at the 1% level, implying that the occurrence of a pandemic in either the importer or exporter has an impact on bilateral trade flows.
Addressing the zero value of the trade problem: Table 8 shows the results of estimating Equation ( 6) using the pseudo-Poisson maximum likelihood (PPML) estimator [20].shows that the log-linearization of the explanatory variables leads to the "artificial" removal of the zero value of the trade points, which causes sample selectivity bias, leading to biased estimates of the log-linearized gravity equations.To avoid possible estimation bias due to the logarithm of the explanatory variables, Equation ( 6) was re-estimated using the PPML estimator, which can fit the nonlinear gravity equation without the need to take logarithms of the trade zeros.As shown in Table 7, the coefficients of the PPML-estimated coefficients of COVID-19 status variables for both the importer and exporter are significantly negative at the 1% statistical level.Thus, the conclusion that COVID-19 has a dampening effect on interprovincial trade flows still holds after accounting for the zero value of the trade problem.

Address potential endogeneity problems:
There may be an endogeneity problem between COVID-19 and interprovincial trade flows.On the one hand, numerous epidemiological experiences have shown that trade is an important channel for the transmission of infectious diseases, implying a possible bidirectional causal relationship between COVID-19 and interprovincial trade flows.On the other hand, given the latent and insidious nature of the new coronavirus and the limitations of medical statistical techniques, statistics on the number of confirmed cases of the new coronavirus in each province may underestimate the actual incidence of the disease, creating measurement errors.Given the potential endogeneity problem, we attempt to construct appropriate instrumental variables for estimation using the 2SLS estimator.4)-( 6) use a dummy variable for the presence or absence of confirmed cases of COVID-19 in that year as the explanatory variable.The sample period is 2018-2022.Since PPML is a maximum likelihood estimator, the pseudo-R-squared is reported.
In their study of the impact of the COVID-19 pandemic on provincial international trade in China, Cai and Hayakawa (2022) found that the negative impact of the COVID-19 pandemic on trade was smaller in provinces with a higher number of deaths during the severe acute respiratory syndrome (SARS) outbreak [8].They also found that the prevalence of mobile phones in a province played a role in mitigating the negative impact of the COVID-19 pandemic on trade.Inspired by this, we use the logarithm of the product term (ln(net•SARS)) of SARS virus deaths in each province in 2003 and the rural broadband penetration rate of each province during the sample period as instrumental variables for the incidence status of the COVID-19 pandemic.Specifically, the rural broadband penetration rate was calculated as (the number of rural broadband subscribers)/(rural population).This product term was chosen as an instrumental variable because provinces that were more severely affected by SARS may have gained more experience from it and were thus able to respond more effectively to the impact of the COVID-19 pandemic.Both COVID-19 and SARS are caused by coronaviruses.Between November 2002 and July 2003, more than 5000 people were infected with SARS in China, resulting in 350 deaths.Zhang et al. (2021) [21] also showed that mobility restrictions during the COVID-19 pandemic were more effectively implemented in provinces affected by the 2003 SARS pandemic, in large part because strict SARS restrictions raised public health awareness.The product term of SARS virus deaths and rural broadband access rates implies that the population is more likely to have access to the experiences of the SARS pandemic because Internet media content can provide more expert advice on protection.Rural broadband access rates were chosen for this paper because urban broadband access rates may be associated with closer trade links.It is clear that SARS virus deaths are highly exogenous, satisfy the instrumental variable nonexclusivity constraint to some extent, and are unlikely to affect interprovincial trade in the present because they occurred 17 years ago.In contrast, trade is largely concentrated in cities, so rural broadband access rates are not directly related to interprovincial trade.
The results of the 2SLS estimator are presented in Table 9. Column (1) of Table 8 presents the results of the OLS regression for the sample period 2020-2022.The reason for presenting this result is that the number of SARS virus deaths is a time-invariant variable; therefore, the sample period is reduced to 2020-2022 in the 2SLS estimator (this period is the COVID-19 pandemic phase of the data), and the reduced sample size is reported here for comparison with the 2SLS results.Columns (2)-( 3) show the results of the first stage of the 2SLS estimator, and Column (4) shows the results of the second stage of the 2SLS estimator.The results of the first stage of estimation show that the instrumental variables on the importing and exporting sides are all significantly correlated with their pandemic status variables.The K-P rk LM, K-P rk Wald F, and Hansen J statistics in Table 8 indicate that there is no under, weak-, or overidentification of the instrumental variables.The 2SLS coefficients are significant at the 1% statistical level, which again confirms the conclusion that COVID-19 has a dampening effect on interprovincial trade flows.However, it is important to note that the estimated coefficients of 2SLS are significantly larger than those of OLS, suggesting that the OLS estimator underestimates the impact of COVID-19 on interprovincial trade flows because of measurement error, bidirectional causality, and other reasons.Notes: *** indicates p < 0.01.This table presents the estimated results using the 2SLS approach, with SARS mortality and rural broadband access rates as composite instrumental variables for the number of confirmed cases of COVID-19.Column (1) shows the results of the baseline OLS regression, Columns (2)-(3) show the results of the first-stage 2SLS regression, and Column (4) shows the results of the second-stage 2SLS regression.Column (5) reports the results of the second stage of the limited information maximum likelihood method (LIML) estimation.The sample period is 2020-2022.

COVID-19 and Interprovincial Trade Barriers
A large body of literature suggests that interregional market segmentation (or trade barriers) hampers economic development in China (e.g., Poncet, 2005; Tombe and Zhu, 2019 [22,23]).The COVID-19 pandemic has led local governments to implement measures such as travel restrictions, regional controls, and urban silencing for the purpose of pandemic prevention and control, which may impede the normal flow of interregional trade and thus raise barriers to interregional trade.

Empirical Frameworks
To further analyze whether the COVID-19 pandemic has increased interprovincial trade barriers in China, the following specification was constructed: where lntrade_costs ijt is the logarithm of bilateral trade costs between province i and province j in year t.covid it is a measure of COVID-19 incidence status in province i in year t.We use the logarithm of the number of outbreak cases to measure the outbreak (labeled ln(1 + case i ) and ln(1 + case j )).lndis ij and border ij are the most common control variables in the trade literature, with lndis ij representing the logarithm of the geographical distance between the capital of province i and the capital of province j and border ij indicating whether province i borders province j. home is a dummy variable for intraprovincial trade costs, with home = 1 when I = j.δ i , δ j , and ν t denote exporter, importer, and time-fixed effects, respectively, which are used to capture the potential effects of the nontime-varying unobservable and the time-varying unobservable at the interprovincial level to reduce omitted variable errors.ε ijt is a random disturbance term representing the remaining unobservables that affect interregional trade costs.We used OLS methods to estimate the above specification.
We aggregate the provincial-sector-level trade costs calculated in Section 3.2 to the provincial level to obtain tradecosts ijt .The data sources for the rest of the variables are the same as those introduced in Section 4.1.1.The summary statistics of the data are shown in Table 10.

Estimated Results
Table 11 shows the results estimated using the OLS estimator.Column (1) shows the results of regressions controlling for geographical distance, exporter-fixed effects, importerfixed effects, and time-fixed effects.Column (2) shows the results controlling for exporterimporter pair fixed effects and time-fixed effects.The results in this column do not include the gravity variables of geographical distance or bordering or not bordering because nontime-varying factors such as geographical distance and bordering or not bordering are included in the exporter-importer pair fixed effects.As shown in Columns (1)-(2) of Table 11, all coefficients are positive, and their signs are as expected.However, except for the coefficient of ln(1 + case i ) in Column (1), which is statistically significantly positive at the 10% level, the other coefficients are not significant at the 10% level.This implies that no strong results show that an increase in the pandemic significantly affects bilateral trade costs.The impact of measures such as community control and social distancing on trade barriers is foreseeable.Although the reduced-form estimates of the COVID-19 pandemic on China's interprovincial trade barriers are not statistically significant, there is still reason to believe that the COVID-19 pandemic has an impact on China's interprovincial trade barriers, even if this impact is extremely subtle.Therefore, in the next section, we incorporate changes in interprovincial trade barriers during COVID-19 into a quantitative spatial model in an attempt to quantify the economic consequences of changes in interprovincial trade barriers.

Trade Barrier Effects of COVID-19: Economic Consequences
In Section 4, we estimate the relationship between COVID-19 and interprovincial trade flows and their trade barriers using a causal inference approach.Although the causal inference approach discusses the impact of COVID-19 on interprovincial trade flows and their trade barriers, the economic consequences remain poorly understood.On the other hand, the reduced-form estimation can only identify the local equilibrium effects of exogenous shocks.However, in reality, various regions constitute input-output linkages because of trade, migration, and other factors, and exogenous shocks can generate general equilibrium effects through such production networks.Furthermore, although Section 4 does not provide significant evidence of the impact of COVID-19 on interprovincial trade costs, there is still reason to believe that COVID-19 has an impact (albeit a very subtle one) on interprovincial trade barriers.In this section, we introduce a quantitative spatial model incorporating multiple regions and sectors to quantify the economic consequences of changes in trade costs.

Model Setup
Following Caliendo et al. (2018) [24], we introduce a multiregional, multisector quantitative spatial economic model.This framework includes J sectors in N regions, and sectors are divided into tradable and non-tradable sectors.Producers produce using two factors of production: labor and the land and structures composite factor.The specific setup is as follows: Consumers: Representative consumers in region n ∈ {1, . . . ,N} consume according to Cobb-Douglas preferences: where ∑ J j=1 α j = 1, and c j n is the consumption of final goods purchased at price P j n with a share of α j , j ∈ {1, . . . ,J}.
Intermediate goods production: Representative firms in sector j of region n produce a variety of intermediate goods on a continuum according to their idiosyncratic level of productivity, z Given the above production function, the input bundle cost of producing intermediate goods at the region-sector (n, j) level under perfect competition is (10) where . Production of final goods: Region n, sector j produces final goods by combining intermediate goods from sector j. qj n z j denotes the demand for intermediate goods of a given variety, and given that these varieties are mutually different at the level of region n, the productivity specific vector, z j = z (11) denotes the joint density function of the vector, z j .
Regional trade and prices: The producer of the final goods in each region chooses the cheapest intermediate goods for production in all regions.Denoted by p j n z j , the price of the intermediate goods chosen by sector j in region n imply that Following the method of [25] to solve for the price distribution, for tradable sector j in region n, the price of the final goods is where Γ ξ j n is a gamma function with ξ j n = 1 + 1 − η j n /θ j .For non-tradable sectors, κ j ni = ∞, ∀i = n, which can be shown to be a simplification: Furthermore, given the nature of the Fréchet distribution, the share of expenditures in intermediate goods purchased by sector j in region n from region i in the total expenditure can be solved as For the non-tradable sector, π Trade balance and market clearing: Regional labor market clearing conditions are expressed by where L j n is the quantity of labor in the region-sector (n, j), and for national labor market clearing, ∑ N n=1 L n = L.In regional equilibrium conditions, land and structures must satisfy the following: where H j n denotes the land and structures used by the region-sector (n, j).The regional market clearance of the final product can be written as Let X j n denote the total expenditure of region n on final goods in sector j.Regional market clearing implies Use Y n to denote the trade deficit.In equilibrium, for each region n, its total expenditure for purchasing intermediate goods in other regions must equal its total income from selling intermediate goods to other regions, namely, Equilibrium conditions in relative terms: Denote the change in the variable x following a change in the economic environment as x = x x .The expression of the relative change term under the following equilibrium conditions is then obtained.
The expression for the change in the cost of the input bundle is The expression for the price change is given by Pj The trade share after the exogenous change is The equilibrium condition for trade becomes ωn Ln Given the above model, our mechanism implies that the effect of trade cost changes in commodity prices reshapes the structure of comparative advantage among trading partners, which further influences regional trade shares.This is the key mechanism by which changes in trade costs impact GDP.

Calibration
Considering data availability, the benchmark economy in this paper includes 31 provinces and 27 sectors.Hong Kong, Macau, Taiwan, and the rest of the world were excluded due to a lack of intersectoral input-output data.For computational simplicity, the 42 sectors are grouped into 27 sectors in this paper, including 16 tradable sectors and 11 non-tradable sectors.The first 16 sectors listed below are tradable sectors and the last 11 sectors are non-tradable sectors.The parameters and data required for model calibration are θ j , α j , β n , ι n , γ

Economic Effects of Changes in Trade Barriers
The main economic impact of the COVID-19 pandemic is concentrated between 2020 and 2022.Given the availability of data and the fact that the pandemic may have a significant impact on the structure of the economy and estimates for longer time cycles may be biased by excessive differences between the structure of the economy and the baseline economy in this period, we only introduce changes in trade barriers in the early years of the COVID-19 pandemic to the baseline model to calculate its economic impact.Specifically, we introduce the relative change in China's interprovincial trade barriers in 2019-2020 ) to the baseline model and calculate its impact on GDP.The results of the quantitative analysis suggest that the relative change in interprovincial trade barriers from 2019 to 2020 results in a loss of 0.11% in China's aggregate GDP.Many factors could have influenced the change in interprovincial trade barriers in 2019-2020.However, we find that, on average, China's interprovincial trade barriers were on a downward trend before the COVID-19 pandemic, which is closely related to China's strengthening of its transportation infrastructure and reforms to its economic system.Therefore, it is reasonable to assume that economic losses due to rising trade costs in 2019-2020 were caused by the COVID-19 pandemic.However, it is worth noting that the loss of 0.11% in GDP is relatively small.This is broadly consistent with the results in Section 4.2, where COVID-19 is shown to have an impact on interprovincial trade barriers but is not significant.In fact, China's control of COVID-19 in 2020 was relatively good, with the main impact concentrated in the first quarter and less in the other quarters because of better control over the number of cases.As the time interval of this paper is annual, obviously, its average results will also be relatively small.
Table 12 shows the sectoral effects of interprovincial trade cost changes in 2019-2020.As mentioned above, the loss of trade cost changes in 2019-2020 is mainly due to the impact of the COVID-19 pandemic and its prevention and control measures.Overall, the impact of changes in trade costs on GDP during this period is relatively small.The tradable sector suffered more GDP losses than the non-tradable sector, and this result is understandable because the change in trade costs in our model setting occurs only in the tradable sector.Thus, the tradable sector suffers both direct shocks from interprovincial trade costs and spillovers based on input-output linkages, while the non-tradable sector suffers only from spillovers based on input-output linkages.Specifically, the largest GDP loss in the tradable sector is the machinery and equipment manufacturing industry, while the smallest loss is the food and tobacco industry.For the non-tradable sector, the largest GDP loss is transportation, storage, and communication, followed by hotels and restaurants and other services.Most unusual was the real estate sector, which was the only sector that did not suffer a GDP loss.Table 13 shows the regional effects of changes in interprovincial trade costs in 2019-2020.Overall, the GDP effect of trade cost changes is not the same across provinces.In particular, the largest GDP loss is observed in Tibet (−1.16), followed by Beijing (−0.54) and Zhejiang (−0.36).Some provinces, however, did not experience GDP losses but rather positive GDP gains because of changes in trade costs, namely, Fujian (0.11), Shandong (0.08), Hunan (0.04), Hubei (0.15), and Sichuan (0.04).The initial outbreak of the COVID-19 pandemic started in Wuhan, Hubei Province, where a strict city lockdown was imposed early in the pandemic, but the government focused heavily on ensuring the normal flow of goods in the process, and thus, it did not cause an increase in trade costs and a GDP loss for the whole of 2020.

Conclusions
Our paper examines the impact of the COVID-19 pandemic on interprovincial trade in China.Interprovincial trade flows are the most important data in our study, but there are no directly available data on interprovincial trade flows in China, so we first estimate interprovincial trade flows in China for 2018-2022 using information from different sources and infer interprovincial trade costs based on interprovincial trade flows.Second, we estimate the impact of COVID-19 on interprovincial trade flows and interprovincial trade costs based on the trade gravity model.Finally, we construct a multiregional and multisector quantitative spatial model and introduce changes in interprovincial trade barriers in 2019-2020 to the model to analyze economic losses due to the early COVID-19 pandemic.
In our study of the impact of the COVID-19 pandemic on trade flows, we found that the estimated coefficients of COVID-19 incidence status variables on both the inflow and outflow sides were significantly negative at the 1% statistical level, controlling for gravitytype variables and individual and time-fixed effects, suggesting that the intensification of the COVID-19 pandemic significantly dampens interprovincial trade flows.This result is supported by the results of robustness tests and the instrumental variable approach.
In our study of the impact of the COVID-19 pandemic on interprovincial trade barriers, we found that there is a positive relationship between the intensification of COVID-19 and the rise in trade costs, but its effect is not statistically significant at the 10% level.To further analyze the impact of changes in interprovincial trade barriers on the Chinese economy, we introduce changes in trade costs from 2019-2020 to a calibrated, multiregional, multisector general equilibrium model of China and quantify the impact of changes in interprovincial trade barriers at the regional-sectoral level in China during the early years of COVID-19.The results at the regional-sectoral level show that GDP losses from rising trade costs in 2019-2020 are not the same across regions (or sectors).However, on average, the GDP losses are not significant.
Our results imply the importance of maintaining internal trade networks in times of pandemic.Policymakers need to give internal trade the same attention as international trade.Because of the lack of observation data, our study relies on estimated interprovincial trade flows, which may be subject to the influence of estimation methods.Obtaining more observation data to improve this study will be a promising direction for future research.Additionally, COVID-19 has had a profound impact on the Chinese economy, particularly in terms of supply chain disruptions.Exploring how these impacts affect the economy through interregional trade linkages will provide insights for assessing exogenous shocks such as natural disasters, which is an important area for future research.

Figure 1 .
Figure 1.Number of newly confirmed COVID-19 cases daily in China from 2020 to 2022.

Figure 1 .
Figure 1.Number of newly confirmed COVID-19 cases daily in China from 2020 to 2022.

Trade: Causal Inferences 4 . 1 .
COVID-19 and Interprovincial Trade Flows 4.1.1.Empirical Frameworks In the broader trade literature, bilateral trade gravity models are the main method used to analyze the causal impact of specific variables on trade (e.g., Allen et al., 2020; Evenett and Keller, 2002; Head and Mayer, 2014 [17-19]).Based on the estimated trade flows, a bilateral trade gravity model is introduced to estimate the impact of COVID-19 on bilateral trade flows.Bilateral trade flows are determined by a number of geographical, economic, and institutional factors, and to examine the impact of the COVID-19 pandemic on interprovincial trade in China, we use the following form of the trade gravity model: demand for structures and labor, respectively; M jk n is the demand for materials from sector k by sector j; γ j n is the share of value added in total output; and γ jk n is the share of the materials from sector k used by sector j.The production function fixes returns to scale so that∑ J k=1 γ jk n = 1 − γ j nis the average level of productivity of firms at the region and sector (n, j) level.
unit cost of transporting the intermediate goods of sector j from region i to region n, κ j ni ≥ 1, and κ j nn = 1.For the non-tradable sector, κ j ni = ∞.

,
and I n , L n , Y n , π α j , β n , ι n , and data, I n , L n , Y n , π j ni N,N,J n=1,i=1,j=1 , are available based on China Multi-Regional Input-Output Tables 2017 provided by the CEADS database, as well as China Economic Census Yearbook 2018 and China Statistical Yearbook 2018.Trade elasticities, θ j , are from Che et al., (2022) [26].

Table 1 ,
China's domestic outflows rose from RMB 161.21 trillion to 193.36 trillion, and interprovincial outflows rose from RMB 35.11 trillion to 40.96 trillion between 2018 and 2022.Total exports increased from RMB 16.46 trillion to 21.70 trillion,

Table 1 .
Estimated total and proportion of China's domestic trade and international trade: 2018-2022.
Notes: The Chinese National Bureau of Statistics has not yet published the import and export data for 2022, so no other items are reported for 2022 except for domestic outflows and interprovincial outflows.Same as below.

Table 5 .
Interprovincial trade costs in China in 2020.
Notes: *** indicates p < 0.01.Columns (1)-(3) use the log of the number of confirmed new cases of COVID-19 in each province as the explanatory variable.Columns (

Table 12 .
Sectoral effects of interprovincial trade cost changes in 2019-2020.

Table 13 .
Regional effects of interprovincial trade cost changes in 2019-2020.