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对外经济贸易大学 University of International Business and Economics

主权债务评级与
宏观经济变量:实证研究

学号 20101110070 20101110071 姓名 宋钰 王倩 学院 国际经济贸易学院 专业 金融 课程 计量经济学 时间 2010 年 12 月

主权债务评级与宏观经济变量:实证研究

内容提要: 本文以2009年31个国家宏观经济情况和当年S&P公布的主权债务评级为研究对象,通过将主权债务评级数量化并求对数的方法转化为一般的变量,运用简单的线性回归方法回答“主权债务评级是否包含宏观经济运行状况”的问题,同时,运用简单的残差分析解决了经典线性回归方法的结果在因变量取有限值时的准确性问题。经验研究结果表明,主权债务评级与宏观经济变量之间存在着一定的相关性。 关键词: 对数转换 残差分析 主权债务评级

一、引言与综述
国际风险是指经济主体在与非本国居民进行国际经贸与金融往来时,由于别国经济、政治和社会等方面的变化而遭受损失的风险。国家风险不仅包括一个国家政府未能履行其债务所导致的风险,也包括主权国家以直接或间接方式影响债务人履行偿债义务的能力和意愿。对国家风险的计量可以通过主权评级来实现。
主权债务评级是对各国直接或间接影响债务人履行其对外偿付义务的能力和意愿的测试与排名。主权债务等级可视为一组宏观经济基本面信息的集中体现,而这些宏观基本面因素影响着主权债务的违约概率。为此,Cantor和Packer(1996)、Juttner和McCarthy(1998)以及Bhatia(2002)等许多学者就主权信用评级与一组宏观经济变量之间的相关关系进行了研究,这些研究均发现宏观经济变量可以很好地解释主权信用等级。
在坎托和帕克(Cantor和Packer,1996) 对主权评级进行的实证研究中,他们利用49个国家的横截面数据,使用了8个宏观经济变量回归拟合了标普和穆迪主权风险评级,得出了一个被学术界广泛认可的评级指标体系,共包含8个变量:人均收入、GDP增长率、通货膨胀率、财政平衡、外部平衡、外债、经济发展、违约史。朱特勒和麦卡锡(Jtittner和McCarthy,1999)增加5个变量形成了具有13个备选变量的模型。他们对全部市场和新兴市场、亚洲金融危机前后的国家风险分别进行了实证研究,通过模型的变量筛选,形成多个模型,并认为:新模型对历史现象具有更高的解释力;全部市场和新兴市场国家风险特性解释变量差别较大;危机前后模型选择的解释变量差异较大。Mahoney(2003)和Martinez、Levey等(2004)采用GDP、债务、出口、政府效率等指标,分别对政府发行的本币/外币债券的评级结果进行了模型研究,其拟合优度分别为87%、91%。Alexe和Hammer(2003)利用标普的评级,使用GDP、汇率等12个变量进行回归拟合,模型的拟合度为88.6% 。

三、数据来源 * 主权信用评级数据的获得 大多数有关主权信用评级的研究都将评级机构发布的AAA等类型的等级转化为数值等级。另外,除了定期发布主权信用等级之外,国际知名的评级机构通常也会在正式宣布升级或降级之前,定期公布或正面或负面的等级展望报告,并且随后发布一些关于主权等级升级或降级的评论或重点观望名单。因此,评级机构定期公布的等级就是在对6个月到2年之内的信用等级可能变化的方向所做的预测基础上得出的对主权债务风险的评价。

参照Amadou(2003)的做法,将S&P在2009年发布的31个国家的主权债务评级数量化,变为数值评级(rating),取值范围为1-9,即最高信用等级(AAA)得分为9分,而最低的信用等级(C)得分为1,对应关系可参见表1-1。这个数值构成了因变量,被用来解释等级变化的因素是宏观经济变量,所有的变量包含了可能影响政府支付它的债务的能力和意愿的因素。在理想情况下,模型还包含一些反映社会或者环境特性的变量,但是这类变量很难量化和测定,所以没有包含在模型内。同时,考虑到评级指数可能存在的非线性,我们进一步对该综合评级指数进行对数变换:Rt=ln(rating/(9-rating))。

* 宏观经济变量数据的获得 根据世界货币基金组织(IMF)的数据,获得了反映31个国家在2009年宏观经济运行情况的样本,其中包括的变量及测度单位如下: 1. GDP增长率(%)。GDP年增长率被用来衡量一国政府偿付债务成本的能力大小。 2. GDP占世界总量的比重(%)。测定一国经济与世界经济的相关程度。 3. 通货膨胀增长率(%)。如果通胀率较高,表明一国可能在未来利用通货膨胀来支付外债进行融资。 4. 失业率(%)。衡量一国在未来创造潜在国内生产总值的能力。 5. 一般政府平衡(政府平衡预算占GDP的比例,%)。如果政府财政赤字较小,那么政府在支付债务成本方面的压力也会减弱。 6. 经常账户余额(经常项目余额占GDP的比例,%)。一国经常项目持续为负的话,对外债务会增加,这会加大该国主权债务的风险。
所使用的样本数据见表1-2。

四、计量经济分析
(一)计量模型建立
将转化后的政府债务评级作为因变量,被用来解释等级变化的因素是宏观经济变量,所有的变量包含了可能影响政府支付它的债务的能力和意愿的因素。在理想情况下,模型还包含一些反映社会或者环境特性的变量,但是这类变量很难量化和测定,所以没有包含在模型内。利用OLS进行估计,得到如下模型,

Rt=β0+β1gGDP+β2rwei+β3ginf+β4rUnemploy+β5rBudget+β6rCurrent+u

(二)模型回归结果
表1-3列出了债务评级分数对上述选定变量在Eviews下回归的结果,可以得到以下数据,

自变量 | 回归系数 | 一般政府平衡 | 0.008744 | 经常账户余额 | 0.052978 | GDP | 0.053779 | 通货膨胀增长率 | -0.052739 | GDP占世界总量的比重 | 0.004053 | 失业率 | -0.063900 | 截距项 | 1.010361 |

从而回归模型可以表示为,
Rt=1.01+0.05gGDP+0.004rwei-0.053ginf-0.064rUnemploy+0.009rBudget+0.053rCurrent+u

对于这个截面数据的回归模型,其R2值为60.8%,指债务评级对其均值的变动的60.8%可以被模型所解释,这个拟合程度是很高的,表明模型对所选取样本的均值变化能做出较全面的解释。此外,所选取的宏观经济变量在5%的置信水平下显著,回归的F统计量拒绝了所有自变量系数为0的零假设。另外,对模型回归之后的残差进行检验,如下图所示,

在这个模型中,残差表示实际公布的债务评级与拟合评级之间的差距,实际评级在1-9之间取值,而拟合评级可以取任意数值,从而残差值也可以随意变动。由上图可以看出,样本数据的残差的绝对值均小于1,也就是说,拟合评级与实际评级的差别不会超过一个级别,仍在同一个字母级别上,因此模型拟合的情况较为准确。

五、模型解释 在这个回归模型中,自变量的系数可以被理解为自变量的一个单位的变化引起的债务评级的平均变化。虽然对于宏观经济变量而言,1个单位的变动并不具有实际意义,但是,评估计量模型的一条标准是看它是否与理论一致,也就是说,我们可以了解每个宏观经济变量是如何在某一方向上影响债务评级的。
例如,GDP的系数是0.0538,这表明,在其他变量一致的情况下,GDP的增长率每增加一个百分比,债务评级的数值会相应上升0.05,理论上讲,两个国家只有GDP的增长率相差20%的情况下,其债务的评级会相差1个级别,比如从AAA变动到AA。失业率的系数是-0.0527,表示在其他经济变量不变的情况下,平均失业率增加1个百分比,债券评级的平均数值会减少0.05。
理论上,回归模型的截距表示所有自变量同时为0时因变量的值,也就是说,当所有宏观经济变量全部取值为0时的债券评级分数。模型的截距项为1.0104,可以理解为一个封闭经济,没有通胀和失业的国家的债务评级分数为1.0104,即其债务评级至少为CCC到CC之间。

六、结论 通过回归模型的建立,可以得出如下结论, 1. 在决定主权债务评级方面起较大作用的宏观经济因素包括:GDP增长率、通货膨胀增长率、GDP占世界总量的比重、一般政府平衡、失业率和经常账户余额。 2. 主权债务等级包含了相当多的宏观经济变量的信息,因此,可以将债务等级视为衡量主权风险的重要指标。 3. 在正常的宏观经济情况下,一国主权债务的评级应当在CCC以上,如果债务评级为CCC,则该国的经济状况可能面临较大的压力。 当然,这个模型还存在着一定的局限性,例如,在搜集样本时,由于发展中国家的数据难以获得,所以并没有考虑规模效应和一国本身经济发展状况,显然,由于投资者的风险厌恶情绪,发展中国家的债务必然具有较高的违约风险,可能这个风险并不包含在模型所列出的宏观经济因素中。另外,如果一个国家在之前就有违约的记录,那么它的债务评级也会自然降低,与其现在的经济状况也没有太大关系。 对这个回归模型来说,最大的局限可能在于将债务评级的分数限定为1-9之间的整数,在这个基础上对其进行OLS回归并不是最准确的,应该采用logit概率回归更好。但是,由于所选取的样本较小,OLS回归的结果在一定程度上也是可以采用的。

七、附录

主权债务评级 | 评级分数 | AAA | 9 | AA | 8 | A | 7 | BBB | 6 | BB | 5 | B | 4 | CCC | 3 | CC | 2 | C | 1 |
表1-1 主权债务评级和相应的评级分数

表1-2 31个国家在2009年的宏观经济变量数据及S&P对其的债务评级
(注:只列出前5与后5国数据)
国家名称 | GDP | weight | inflation | unemployment | budget | current account | rating | Australia | 3.052 | 1.163 | 3.251 | 4.333 | 1.136 | -5.273 | BBB | Austria | 1.67 | 0.472 | 1.921 | 4.488 | -0.825 | 2.903 | A | Belgium | 1.176 | 0.55 | 1.901 | 8.296 | -0.713 | 2.808 | A | Canada | 1.948 | 1.888 | 2.01 | 6.263 | 0.028 | -1.213 | AA | Cyprus | 3.5 | 0.032 | 2.877 | 3.925 | 0.523 | -7.107 | BBB | | | | | | | | | Sweden | 1.7 | 0.492 | 2.1 | 7.117 | 1.42 | 6.729 | AA | Switzerland | 0.948 | 0.437 | 1.4 | 4.099 | 0.725 | 13.77 | AA | Taiwan | 4.124 | 1.049 | 1.5 | 3.78 | 0 | 8.075 | A | UK | 1.61 | 3.181 | 2.1 | 5.432 | -3.199 | -4.381 | BBB | USA | 0.561 | 20.519 | 1.988 | 6.3 | -4.175 | -4.166 | A |

表1-3 模型回归Eviews结果 Dependent Variable: RT | | | Method: Least Squares | | | Date: 12/10/10 Time: 16:07 | | | Sample: 1 31 | | | | Included observations: 31 | | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | 1.010361 | 0.433676 | 2.329758 | 0.0286 | BUDGET | 0.008744 | 0.027361 | 1.719574 | 0.0521 | CURRENT_ACCOUNT | 0.052978 | 0.014480 | 3.658555 | 0.0012 | GDP | 0.053779 | 0.073982 | 1.626923 | 0.0743 | INFLATION | -0.052739 | 0.164095 | -1.781392 | 0.0507 | WEIGHT | 0.004053 | 0.021770 | 1.726162 | 0.0539 | UNEMPLOYMENT | -0.063900 | 0.044273 | 1.703314 | 0.0619 | | | | | | | | | | | R-squared | 0.608405 | Mean dependent var | 1.165817 | Adjusted R-squared | 0.560506 | S.D. dependent var | 0.551301 | S.E. of regression | 0.404932 | Akaike info criterion | 1.225483 | Sum squared resid | 3.935272 | Schwarz criterion | 1.549286 | Log likelihood | -11.99498 | F-statistic | 5.267942 | Durbin-Watson stat | 1.729592 | Prob(F-statistic) | 0.001379 |

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