to their customers, thereby creating a redistribution channel within the economy (e.g., Molina & Preve, 2009). Jackson and Liu (2010) suggest that the size of the allowance for doubtful receivables is likely to be affected by the company’s liquidity and solvency. Following Esilä (2015), we expect these leverage and liquidity variables to be positively related to both the trade receivables and the doubtful trade credit. Leverage is measured as the ratio between total debts and total assets (Cheung & Pok, 2019; Chen et al., 2020; Esilä, 2015; Molina & Preve, 2009). Liquidity is proxied by the current assets and current liabilities ratio (Esilä, 2015).
从而在经济体内形成一个再分配渠道（如 Molina 和 Preve，2009 年）。Jackson 和 Liu（2010 年）认为，可疑应收账款备抵的规模可能会受到公司流动性和偿付能力的影响。根据 Esilä（2015 年），我们预计这些杠杆和流动性变量与应收账款和可疑贸易信贷均呈正相关。杠杆率用总债务与总资产的比率来衡量（Cheung & Pok，2019；Chen et al.，2020；Esilä，2015；Molina & Preve，2009）。流动性用流动资产和流动负债比率表示（Esilä，2015）。

Profitability. Petersen and Rajan (1997) state that firms in trouble may use the extension of credit to attempt to maintain their sales. In a similar vein, [temporarily] unprofitable firms may resort to an extension of trade credit to risky clients in an attempt to restore their sales and profits. Thus, we expect a negative relationship between profitability and trade credit granted, as well as with doubtful trade credit. We use profit margin (Ebit/sales) and return on assets (ROA) (Ebit/total assets) for trade receivables and doubtful trade credit, respectively. Several authors have used this variable to explain trade receivables (e.g., García-Teruel & Martínez-Solano, 2010a, 2010b; Molina & Preve, 2009; Petersen & Rajan, 1997). Likewise, the few studies that have analysed doubtful receivables have also considered these variables (Cheung & Pok, 2019; Chen et al., 2020; Esilä, 2015; Nguyen & Nguyen, 2022).
盈利能力。Petersen 和 Rajan（1997 年）指出，陷入困境的公司可能会通过扩大信贷来维持销售。同样，[暂时]无利可图的公司可能会向风险客户发放贸易信贷，以试图恢复销售和利润。因此，我们预计盈利能力与发放的贸易信贷以及可疑贸易信贷之间存在负相关关系。对于应收账款和可疑贸易信贷，我们分别使用利润率（Ebit/销售额）和资产回报率（ROA）（Ebit/总资产）。有几位作者曾使用这一变量来解释应收账款（例如，García-Teruel & Martínez-Solano, 2010a, 2010b；Molina & Preve, 2009；Petersen & Rajan, 1997）。同样，少数分析可疑应收账款的研究也考虑了这些变量（Cheung & Pok, 2019; Chen et al., 2020; Esilä, 2015; Nguyen & Nguyen, 2022）。

Sales growth. Firms may use their trade credit policy in order to stimulate their sales. On the other hand, when sales grow, it is likely that companies will try to reduce their accounts receivable. Following García-Teruel and Martínez-Solano (2010b), we would expect a negative relationship between sales growth, trade credit granted and doubtful trade credit. The variable Sales growth is computed as the variation rate in sales between two consecutive years (Abdulla et al., 2020; García-Teruel & Martínez-Solano, 2010a).
销售增长。企业可能会利用贸易信贷政策来刺激销售。另一方面，当销售额增长时，企业很可能会试图减少应收账款。根据 García-Teruel 和 Martínez-Solano（2010b）的研究，我们认为销售增长、贸易信贷发放和可疑贸易信贷之间存在负相关关系。销售增长变量的计算方法是连续两年的销售变化率（Abdulla 等人，2020 年；García-Teruel 和 Martínez-Solano, 2010a）。

Industry. The type of activity carried out by companies significantly affects trade credit policies due to differences in production cycles (García-Teruel & MartínezSolano, 2010a). Previous studies show that trade credit transactions are usual in industrial firms (e.g., Bastos & Pindado, 2007). Therefore, in this paper, we have considered a dummy variable equal to 1 if the company is industrial and 0 otherwise. However, this variable is time invariant, so it is not possible to include it directly in the panel models estimated with fixed effects. An alternative way of solving this problem is to create the interaction between this dummy and the dummies for the years (e.g., Álvarez-Botas & González, 2021). Thus, the industry-year interaction is equal to 1 in each year when the firm belongs to an industrial sector and zero otherwise. In addition, the dummies for the years have also been considered $(\mathrm{Li}$$(\mathrm{Li}$(Li(\mathrm{Li} et al., 2018; Nguyen & Nguyen, 2022).
行业。由于生产周期的不同，企业开展的活动类型对贸易信贷政策有很大影响（García-Teruel & Martínez-Solano，2010a）。以往的研究表明，贸易信贷交易在工业企业中很常见（如 Bastos & Pindado, 2007）。因此，在本文中，我们考虑了一个虚拟变量，如果公司是工业企业，该变量等于 1，否则等于 0。然而，该变量具有时间不变性，因此无法将其直接纳入使用固定效应估算的面板模型中。解决这一问题的另一种方法是在该虚拟变量与年份虚拟变量之间建立交互作用（例如，Álvarez-Botas & González，2021 年）。因此，当企业属于某一行业部门时，每年的行业-年份交互值等于 1，否则为 0。此外，还考虑了年份的虚拟变量 $(\mathrm{Li}$$(\mathrm{Li}$(Li(\mathrm{Li} 等人，2018；Nguyen & Nguyen，2022）。

In addition to firm-level control variables, the macroeconomic conditions may affect the use of accounts receivable, although it is not clear what the expected relationship is between the business cycle and the trade credit granted by firms (García-Teruel & Martínez-Solano, 2010a, 2010b). These authors assert that, on the one hand, a deterioration in macroeconomic conditions may reduce the ability of companies to generate cash flow and limit bank financing. On the other hand, the existence of credit restrictions can restrict the possibility of providers financing their clients. In the first case, there would be an increase in accounts receivable while, in
除了公司层面的控制变量外，宏观经济条件也可能影响应收账款的使用，尽管尚不清楚商业周期与公司发放的贸易信贷之间的预期关系（García-Teruel & Martínez-Solano, 2010a，2010b）。这些作者认为，一方面，宏观经济条件的恶化可能会降低企业产生现金流的能力，限制银行融资。另一方面，信贷限制的存在也会限制供应商为客户融资的可能性。在前一种情况下，应收账款会增加，而在后一种情况下，应收账款会减少。
the second, they would decrease. Following the cited authors, the GDP is supposed to control for the macroeconomic conditions. Specifically, we include the GDP per capita (Chen et al., 2020). Table 7 of the Appendix contains a list with the description of the variables.
第二，它们会减少。根据所引用的作者的观点，GDP 是用来控制宏观经济条件的。具体来说，我们将人均国内生产总值（Chen 等人，2020 年）包括在内。附录表 7 列出了变量说明。

We estimate the relationship between trade credit granted and judicial efficiency using a panel data model. This method allows us to control for unobservable heterogeneity as it provides more than one cross-section, data reducing bias from the presence of individual effects (Hsiao, 1985). The baseline model is as follows:
我们采用面板数据模型来估计贸易信贷发放与司法效率之间的关系。这种方法允许我们控制不可观测的异质性，因为它提供了多个横截面数据，减少了个体效应带来的偏差（Hsiao，1985 年）。基线模型如下

According to the two hypotheses, the dependent variable (trade credit) is the trade credit granted or doubtful trade credit. Likewise, judicial efficiency is a proxy for duration or rule of law. To alleviate the effect of outliers, we ‘winsorised’ some explanatory variables, profitability, liquidity and Sales growth, at $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% and $99\mathrm{\%}$$99\mathrm{\%}$99%99 \%. Moreover, to avoid the potential endogeneity between the dependent and firm-level independent variables, they are lagged by one year. Likewise, the proxies of judicial efficiency are also lagged one year to avoid endogeneity with the GDP. In the model, ${\mu }_i$${\mu }_i$mu_(i)\mu_{i} controls for the firm’s unobservable characteristics and ${\epsilon }_{i,t}$${\epsilon }_{i,t}$epsi_(i,t)\varepsilon_{i, t} is the error term.
根据这两个假设，因变量（贸易信贷）是已发放的贸易信贷或可疑贸易信贷。同样，司法效率是期限或法治的替代变量。为了减轻异常值的影响，我们将一些解释变量（盈利能力、流动性和销售增长）"胜选 "为 $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% 和 $99\mathrm{\%}$$99\mathrm{\%}$99%99 \% 。此外，为了避免因变量和公司层面的自变量之间可能存在的内生性，我们将它们滞后一年。同样，司法效率的代理变量也滞后一年，以避免与国内生产总值之间的内生性。在模型中， ${\mu }_i$${\mu }_i$mu_(i)\mu_{i} 控制公司的不可观测特征， ${\epsilon }_{i,t}$${\epsilon }_{i,t}$epsi_(i,t)\varepsilon_{i, t} 是误差项。

In order to use the most suitable model, we employed the Hausman (1978) test, which differentiates between fixed effects models and random effects models in a panel data analysis. The results suggest that it is appropriate to use a fixed effects model. To control for the possible problems of endogeneity, we estimated parameters through the Generalized Method of Moments (GMM). We use an extension of the Arellano and Bond (1991), proposed by Arellano and Bover (1995) and Blundell and Bond (1998), in the robustness analysis. All estimation is computed with the Stata14 econometric package.
为了使用最合适的模型，我们采用了 Hausman（1978 年）检验法，该检验法对面板数据分析中的固定效应模型和随机效应模型进行了区分。结果表明，使用固定效应模型是合适的。为了控制可能存在的内生性问题，我们采用广义矩法（GMM）估计参数。在稳健性分析中，我们使用了由 Arellano 和 Bover（1995 年）以及 Blundell 和 Bond（1998 年）提出的对 Arellano 和 Bond（1991 年）的扩展。所有估计均使用 Stata14 计量经济学软件包进行计算。

The sample distribution presented in Table 1 differs by country, with the predominance of French and German firms (nearly 51%), followed by those from Italy, Greece, Finland, Belgium, Spain and the Netherlands, which all account for about $36\mathrm{\%}$$36\mathrm{\%}$36%36 \% of the sample. The eight remaining countries jointly represent less than $13\mathrm{\%}$$13\mathrm{\%}$13%13 \%. Given that the sample is composed of listed firms, the distribution may be affected by size and development in the stock exchange. Regarding the sectorial distribution of the sample, in Table 1, we can see the importance of industrial firms, which account for $47\mathrm{\%}$$47\mathrm{\%}$47%47 \% of all of the observations, followed by firms from the information
表 1 所示的样本分布因国家而异，法国和德国的公司占绝大多数（近 51%），其次是意大利、希腊、芬兰、比利时、西班牙和荷兰的公司，它们都占样本的 $36\mathrm{\%}$$36\mathrm{\%}$36%36 \% 左右。其余 8 个国家的企业加起来还不到 $13\mathrm{\%}$$13\mathrm{\%}$13%13 \% 。由于样本由上市公司组成，其分布可能受到证券交易所的规模和发展情况的影响。关于样本的行业分布，我们可以从表 1 中看出工业企业的重要性，它们占所有观测值的 $47\mathrm{\%}$$47\mathrm{\%}$47%47 \% ，其次是信息行业的企业。

Table 1 Sample distribution by country and sector. 2011-2021
表 1 按国家和部门分列的样本分布情况。2011-2021

and communication sector ( $15\mathrm{\%}$$15\mathrm{\%}$15%15 \% ). The lowest number of observations belong to the hospitality ( $1.74\mathrm{\%}$$1.74\mathrm{\%}$1.74%1.74 \% ) and agriculture ( $3.22\mathrm{\%}$$3.22\mathrm{\%}$3.22%3.22 \% ) sectors.
和通信部门（ $15\mathrm{\%}$$15\mathrm{\%}$15%15 \% ）。最少的观测数据属于酒店业（ $1.74\mathrm{\%}$$1.74\mathrm{\%}$1.74%1.74 \% ）和农业（ $3.22\mathrm{\%}$$3.22\mathrm{\%}$3.22%3.22 \% ）。

Table 2 shows descriptive statistics of trade credit granted and doubtful trade credit, by country.
表 2 显示了按国家分列的已发放贸易信贷和可疑贸易信贷的描述性统计。

An average level of trade credit granted in the eurozone is about $18\mathrm{\%}$$18\mathrm{\%}$18%18 \%, although it differs between countries. A certain geographical pattern can be observed. Credit granted to customers is highest in Southern European countries, including Greece (28%), Italy ( $26\mathrm{\%}$$26\mathrm{\%}$26%26 \% ), Portugal ( $21\mathrm{\%}$$21\mathrm{\%}$21%21 \% ) and Spain (22%), and lowest in Estonia (7%), Malta (9%), Luxembourg (11%), Austria and the Netherlands (13%). Regarding doubtful trade credit, the average for the whole sample is close to $5\mathrm{\%}$$5\mathrm{\%}$5%5 \%, although it ranges from the $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% in Finland to $15\mathrm{\%}$$15\mathrm{\%}$15%15 \% in Greece. The countries with the highest rate of doubtful receivables are Greece (15%), Portugal (12%) and Cyprus (10%).
欧元区发放的贸易信贷平均水平约为 $18\mathrm{\%}$$18\mathrm{\%}$18%18 \% ，但各国之间有所不同。可以观察到一定的地理格局。给予客户的信贷在南欧国家最高，包括希腊（28%）、意大利（ $26\mathrm{\%}$$26\mathrm{\%}$26%26 \% ）、葡萄牙（ $21\mathrm{\%}$$21\mathrm{\%}$21%21 \% ）和西班牙（22%），在爱沙尼亚（7%）、马耳他（9%）、卢森堡（11%）、奥地利和荷兰（13%）最低。在可疑贸易信贷方面，整个样本的平均值接近 $5\mathrm{\%}$$5\mathrm{\%}$5%5 \% ，但从芬兰的 $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% 到希腊的 $15\mathrm{\%}$$15\mathrm{\%}$15%15 \% 不等。应收账款可疑率最高的国家是希腊（15%）、葡萄牙（12%）和塞浦路斯（10%）。

Table 3 shows descriptive statistics of the judicial efficiency variables by country. The overall average length (Duration) of judicial proceedings is 1.84 years and ranges from 0.88 years in Luxembourg to 3.84 years in Greece. This shows that the functioning of the courts in Europe varies significantly between countries.
表 3 显示了各国司法效率变量的描述性统计。司法程序的总体平均长度（持续时间）为 1.84 年，从卢森堡的 0.88 年到希腊的 3.84 年不等。这表明欧洲各国法院的运作情况差异很大。

Regarding the rule of law index, the national average for all periods and countries is 1.29 , and the values range from 0.32 for Greece to 2.03 for Finland (followed by Austria with 1.85). Moreover, the standard deviation and the minimum/maximum values in Table 3 reveal that there is limited inter-annual variation in both measures of judicial proceedings at the ‘country’ level. Concerning rule of law, more time variations are observed, while duration is time-invariant in some countries for the period analysed. This is most likely explained by the complexity and time needed for the implementation of judicial reforms.
关于法治指数，所有时期和国家的全国平均值为 1.29，数值范围从希腊的 0.32 到芬兰的 2.03（其次是奥地利的 1.85）。此外，表 3 中的标准偏差和最小/最大值显示，在 "国家 "层面，司法程序的两个衡量指标的年际变化有限。在法治方面，观察到更多的时间差异，而在分析期间，一些国家的持续时间是不 变的。这很可能是由于实施司法改革的复杂性和所需时间造成的。

Table 2 Descriptive statistics of trade credit granted and doubtful by country. 2011-2021
表 2 按国家分列的已发放和可疑贸易信贷的描述性统计。2011-2021

Table 2 presents descriptive statistics for dependent variables used in the analyses.
表 2 列出了分析中使用的因变量的描述性统计数字。
Variable description in Table 7 of the Appendix. Q1, Q2, Q3: quartiles 1, 2 and 3, respectively.
变量说明见附录表 7。Q1、Q2、Q3：分别为四分位数 1、2 和 3。
$KW$$KW$KWK W Kruskal Wallis. ${}^{\ast },{}^{\ast \ast },{}^{\ast \ast \ast }$${}^{\ast },{}^{\ast \ast },{}^{\ast \ast \ast }$^(**),^(****),^(******){ }^{*},{ }^{* *},{ }^{* * *} : significant at $10\mathrm{\%},5\mathrm{\%}$$10\mathrm{\%},5\mathrm{\%}$10%,5%10 \%, 5 \% y $1\mathrm{\%}$$1\mathrm{\%}$1%1 \%, respectively.
$KW$$KW$KWK W Kruskal Wallis。 ${}^{\ast },{}^{\ast \ast },{}^{\ast \ast \ast }$${}^{\ast },{}^{\ast \ast },{}^{\ast \ast \ast }$^(**),^(****),^(******){ }^{*},{ }^{* *},{ }^{* * *} ：分别在 $10\mathrm{\%},5\mathrm{\%}$$10\mathrm{\%},5\mathrm{\%}$10%,5%10 \%, 5 \% y $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% 显著。

A comparison between Tables 2 and 3 allows us to observe that countries with the lowest judicial efficiency, like Greece (the lowest), show the highest rates of doubtful receivables, but also the highest ratios of trade credit granted. In comparison, Finland, with the most judicial efficiency, shows the lowest doubtful receivables rate, although the trade credit granted ratio is below the average.
通过比较表 2 和表 3，我们可以发现，司法效率最低的国家，如希腊（最低），其可疑应收账款率最高，但发放的贸易信贷比率也最高。相比之下，司法效率最高的芬兰的可疑应收账款率最低，尽管其发放的贸易信贷比率低于平均水平。

Descriptive statistics of control variables are shown in Table 4. The sample is composed of firms with average (median) annual assets of about 6 million (363 thousand) euros and an average age of 56 years. In average terms, the sample is characterised by firms that are efficient in their business management with an average profit margin of $19.51\mathrm{\%}$$19.51\mathrm{\%}$19.51%19.51 \% and ROA of $10.89\mathrm{\%}$$10.89\mathrm{\%}$10.89%10.89 \%. The average liquidity is of 1.81. Firms in the sample are moderately indebted with average leverage of $55\mathrm{\%}$$55\mathrm{\%}$55%55 \%. The percentage of firm-year observations with positive growth of sales is high ( $61\mathrm{\%}$$61\mathrm{\%}$61%61 \% ). Average GDP per capita is about 35,200 euros.
表 4 列出了控制变量的描述性统计。样本公司的年平均资产（中位数）约为 600 万（36.3 万）欧元，平均年龄为 56 岁。从平均值来看，样本企业的经营管理效率较高，平均利润率为 $19.51\mathrm{\%}$$19.51\mathrm{\%}$19.51%19.51 \% ，投资回报率为 $10.89\mathrm{\%}$$10.89\mathrm{\%}$10.89%10.89 \% 。平均流动性为 1.81。样本企业的平均杠杆率为 $55\mathrm{\%}$$55\mathrm{\%}$55%55 \% ，属于中度负债。销售额正增长的公司年观测值所占比例较高（ $61\mathrm{\%}$$61\mathrm{\%}$61%61 \% ）。人均国内生产总值约为 35 200 欧元。

The analysis of the correlation matrix reveals a significant and negative (positive) relationship between duration (rule of law) and both dependent variables, trade credit granted and doubtful trade credit. Moreover, the correlation between the two judicial efficiency indicators is 0.87 . The only coefficient higher than
对相关矩阵的分析表明，持续时间（法治）与两个因变量（发放的贸易信贷和可疑贸易信贷）之间存在显著的负（正）相关关系。此外，两个司法效率指标之间的相关系数为 0.87。唯一高于

Table 3 Descriptive statistics of judicial efficiency by country. 2010-2020
表 3 各国司法效率的描述性统计。2010-2020

This table presents descriptive statistics for the explanatory variables. Variable description in Table 7 of the appendix. $KW$$KW$KWK W : Kruskal Wallis., ${}^{\ast \ast },{}^{\ast \ast \ast }$${}^{\ast \ast },{}^{\ast \ast \ast }$^(****),^(******){ }^{* *},{ }^{* * *} : significant at $10\mathrm{\%},5\mathrm{\%}$$10\mathrm{\%},5\mathrm{\%}$10%,5%10 \%, 5 \% y $1\mathrm{\%}$$1\mathrm{\%}$1%1 \%, respectively.
本表介绍了解释性变量的描述性统计。变量说明见附录表 7。 $KW$$KW$KWK W ：Kruskal Wallis.， ${}^{\ast \ast },{}^{\ast \ast \ast }$${}^{\ast \ast },{}^{\ast \ast \ast }$^(****),^(******){ }^{* *},{ }^{* * *} ：分别在 $10\mathrm{\%},5\mathrm{\%}$$10\mathrm{\%},5\mathrm{\%}$10%,5%10 \%, 5 \% y $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% 时显著。
Source Own elaboration from World Bank’s WGI and Doing Business databases.
资料来源 根据世界银行 WGI 和 Doing Business 数据库自行编制。

Table 4 Descriptive statistics of control variables
表 4 控制变量的描述性统计

This table presents descriptive statistics for key variables used in the analyses.
本表介绍了分析中使用的主要变量的描述性统计。
Variable description in Table 7 of the appendix. Q1, Q2, Q3: quartiles 1, 2 and 3, respectively.
变量说明见附录表 7。Q1、Q2、Q3：分别为四分位数 1、2 和 3。
0.5 are between these indicators and GDP per capita ( 0.51 and 0.54 ), which is due in part to the fact that they are all obtained at the country level. All correlation coefficients between the remaining variables are lower than 0.25 . Moreover, the variance-inflation factors (VIF) for all models range between 1.08 and
这些指标与人均国内生产总值之间的相关系数为 0.5（0.51 和 0.54），部分原因是这些指标都是在国家层面获得的。其余变量之间的相关系数均低于 0.25。此外，所有模型的方差膨胀因子（VIF）都在 1.08 和 1.50 之间。

Table 5 Judicial efficiency and trade credit
表 5 司法效率与贸易信贷

This table presents the estimation results of fixed effects panel regressions.
本表显示了固定效应面板回归的估计结果。
Variable description in Table 7 of the appendix. Profitability is measured by Profit margin in models 1 and 2 and ROA in models 3 and $4.{}^{\ast },{}^{\ast \ast },{}^{\ast \ast \ast }$$4.{}^{\ast },{}^{\ast \ast },{}^{\ast \ast \ast }$4.^(**),^(****),^(******)4 .{ }^{*},{ }^{* *},{ }^{* * *} : significant at $10\mathrm{\%},5\mathrm{\%}$$10\mathrm{\%},5\mathrm{\%}$10%,5%10 \%, 5 \% and $1\mathrm{\%}$$1\mathrm{\%}$1%1 \%, respectively.
变量说明见附录表 7。盈利能力在模型 1 和 2 中用利润率衡量，在模型 3 中用投资回报率衡量， $4.{}^{\ast },{}^{\ast \ast },{}^{\ast \ast \ast }$$4.{}^{\ast },{}^{\ast \ast },{}^{\ast \ast \ast }$4.^(**),^(****),^(******)4 .{ }^{*},{ }^{* *},{ }^{* * *} ：分别在 $10\mathrm{\%},5\mathrm{\%}$$10\mathrm{\%},5\mathrm{\%}$10%,5%10 \%, 5 \% 和 $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% 时显著。
1.67, indicating that there are no problems of multi-collinearity (see Table 8 of the appendix).
1.67，表明不存在多重共线性问题（见附录表 8）。

In order to empirically assess the impact of judicial efficiency on trade credit granted to customers and the doubtful trade credit, we applied a panel regression with fixed effects model. We report the results in Table 5. The results of Model 1 indicate that the impact of the length of judicial proceedings (Duration) is negative and economically significant at $1\mathrm{\%}$$1\mathrm{\%}$1%1 \%. In Model 2, Duration is replaced by rule of law index, which is positive and significant at $1\mathrm{\%}$$1\mathrm{\%}$1%1 \%. It is important to recall that this variable has an inverse interpretation of judicial efficiency, while rule of law is a direct proxy of judicial efficiency. Therefore, a longer duration for dispute resolution represents lower efficiency, thus reducing trade credit granted. On the contrary, a higher value for rule of law represents a greater degree of efficiency, and this increases trade credit. Therefore, the results obtained are in line with the hypothesis H 1 , according to which, greater judicial efficiency will increase
为了实证评估司法效率对客户贸易信贷和可疑贸易信贷的影响，我们采用了固定效应模型的面板回归。结果见表 5。模型 1 的结果表明，司法程序时间（Duration）的影响是负的，且在 $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% 时具有经济显著性。在模型 2 中，"持续时间 "被 "法治指数 "所取代，"法治指数 "为正且在 $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% 处显著。需要指出的是，该变量对司法效率有反向解释，而法治指数则直接代表司法效率。因此，解决争端的时间越长，代表效率越低，从而减少贸易信贷的发放。相反，法治的数值越高，代表效率越高，从而增加贸易信贷。因此，得出的结果符合假设 H1，即司法效率越高，贸易信贷越多。
the amount of trade credit granted by providers to their customers. Specifically, a one-year increase in duration results in a $3.06\mathrm{\%}$$3.06\mathrm{\%}$3.06%3.06 \% reduction in the volume of granted trade credit, while an increase of one unit of rule of law increases granted trade credit by $8.49\mathrm{\%}$$8.49\mathrm{\%}$8.49%8.49 \%.
供应商给予客户的贸易信贷额度。具体而言，期限每增加一年，发放的贸易信贷量就会减少 $3.06\mathrm{\%}$$3.06\mathrm{\%}$3.06%3.06 \% ，而法治每增加一个单位，发放的贸易信贷量就会增加 $8.49\mathrm{\%}$$8.49\mathrm{\%}$8.49%8.49 \% 。

With the aim of contrasting the H2 hypothesis, in Models 3 and 4, we replaced the dependent variable for doubtful trade credit. As we can see, the results indicate that Duration in Model 3 and rule of law in Model 4 have a positive and negative sign, respectively, being significant at $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% in both models. Specifically, a oneyear increase in duration represents a $2.52\mathrm{\%}$$2.52\mathrm{\%}$2.52%2.52 \% increase in the volume of trade credit granted, while an increase of one rule-of-law unit reduces the doubtful trade credit by $4.66\mathrm{\%}$$4.66\mathrm{\%}$4.66%4.66 \%. These results may be interpreted in the sense that more judicial efficiency reduces the trade credit default rate and offers support to the H 2 hypothesis.
为了对比 H2 假设，我们在模型 3 和模型 4 中将因变量替换为可疑贸易信贷。我们可以看到，结果表明，模型 3 中的期限和模型 4 中的法治分别具有正负符号，且在两个模型中均在 $1\mathrm{\%}$$1\mathrm{\%}$1%1 \% 处显著。具体而言，期限每增加一年，贸易信贷发放量就会增加 $2.52\mathrm{\%}$$2.52\mathrm{\%}$2.52%2.52 \% ，而法治每增加一个单位，可疑贸易信贷就会减少 $4.66\mathrm{\%}$$4.66\mathrm{\%}$4.66%4.66 \% 。这些结果可以解释为，更高的司法效率降低了贸易信贷违约率，并为 H 2 假设提供了支持。

Regarding the control variables, in models 1 and 2, we observed that size, profitability and liquidity show significant and positive signs, while age, leverage and Sales_growth are significant and negative. Thus, the larger, but less old firms extended more credit to customers. The result regarding size supports the argument that larger firms have better access to financial markets to fund receivables (Cheung & Pok, 2019; Petersen & Rajan, 1997). Profitability, liquidity and sales growth show the expected sign. The negative sign of leverage is contrary to the expected relationship with the receivables, since greater access to external financing also means that firms can and will extend more trade credit to their customers (Molina & Preve, 2009). This result indicates that firms also use other alternatives to external financing in order to grant more credit.
关于控制变量，在模型 1 和模型 2 中，我们发现规模、盈利能力和流动性显示出显著的正符号，而年龄、杠杆率和销售增长则显示出显著的负符号。因此，规模较大但年龄较小的公司向客户提供了更多信贷。有关规模的结果支持了这样一种论点，即规模较大的企业更容易进入金融市场为应收账款提供资金（Cheung & Pok，2019；Petersen & Rajan，1997）。盈利能力、流动性和销售增长显示出预期的符号。杠杆率的负号与预期的应收账款关系相反，因为更容易获得外部融资也意味着企业可以并将向客户提供更多的贸易信贷（Molina & Preve，2009）。这一结果表明，企业也会利用外部融资以外的其他方式来提供更多信贷。

In models 3 and 4, we observed that all significant control variables, show an inverse sign compared to models 1 and 2. Age and leverage are positive, while size, profitability and sales growth are negative. Contrary to our predictions, older companies have a higher rate of ‘doubtful customers’ in relation to their accounts receivable. One possible explanation for this result is that these companies place more value on long-term relationships with their customers, which leads them to keep a higher proportion of doubtful customers on their books (who are not necessarily insolvent). Leverage and sales_growth show the predicted signs. Liquidity and GDP per capita are not significant.
在模型 3 和模型 4 中，我们发现所有重要的控制变量都与模型 1 和模型 2 呈反比。年龄和杠杆率为正，而规模、盈利能力和销售增长为负。与我们的预测相反，与应收账款相比，年龄较大的公司 "可疑客户 "比例较高。对这一结果的一种可能解释是，这些公司更重视与客户的长期关系，这导致它们在账簿上保留了更高比例的可疑客户（这些客户不一定资不抵债）。杠杆率和销售增长显示出预测的迹象。流动性和人均国内生产总值不显著。

Finally, in models 1 and 2, the results regarding the year (untabulated by brevity) indicate that compared to 2011, years 2013 and 2014 are positive and significant, while in 2015 and years from 2018 to 2020 are negative and significant. The interaction industry-year is not significant for any year. In models 3 and 4, from 2016 to 2020, there is a significant and negative sign. The interaction ‘industry-year’ is positive and significant for the period 2013-2019, which indicates that industrial firms had a more doubtful trade credit rate than non-industrial firms during these years.
最后，在模型 1 和 2 中，有关年份的结果（为简洁起见未列表）表明，与 2011 年相比，2013 年和 2014 年为正且显著，而 2015 年和 2018 年至 2020 年为负且显著。行业-年份交互作用在任何年份都不显著。在模型 3 和 4 中，2016 年至 2020 年为显著负号。在 2013-2019 年期间，交互作用 "行业年份 "为正且显著，这表明在这些年份中，工业企业的贸易信贷可疑率高于非工业企业。

In this section, we provide additional estimations to demonstrate the robustness of the obtained results. The results of the main variables are reported in Table 6. In this table, in panels A and B , the dependent variable is trade credit granted and in panels C and D, doubtful trade credit. Likewise, in panels A and C, the explanatory variables are duration and in panels B and D , rule of law.
在本节中，我们将提供更多的估计结果，以证明所得结果的稳健性。主要变量的结果见表 6。在该表中，A 组和 B 组的因变量是已发放的贸易信贷，C 组和 D 组的因变量是可疑贸易信贷。同样，在面板 A 和 C 中，解释变量是期限，在面板 B 和 D 中，解释变量是法治。
Table 6 Judicial efficiency and trade credit in the eurozone. Robustness analysis. Panels A and B. Dependent variable: trade credit granted. Panels C and D. Dependent variable: doubtful trade credit
表 6 欧元区的司法效率和贸易信贷。稳健性分析。面板 A 和 B：因变量：发放的贸易信贷。面板 C 和 D：因变量：可疑贸易信贷

Panel B. Explanatory variable: Rule of Law. Re-estimation model 2
面板 B. 解释性变量：法治。重新估计模型 2

Table 6 (continued)  表 6（续）