Which countries pay more or less for their long term debt? A CART approach

González-Fernández, Marcos; González-Velasco, Carmen Article Which countries pay more or less for their long term debt? A CART approach Revista de Métodos Cuantitativos para la Economía y la Empresa Provided in Cooperation with: Universidad Pablo de Olavide, Sevilla Suggested Citation: González-Fernández, Marcos; González-Velasco, Carmen (2016) : Which countries pay more or less for their long term debt? A CART approach, Revista de Métodos Cuantitativos para la Economía y la Empresa, ISSN 1886-516X, Universidad Pablo de Olavide, Sevilla, Vol. 21, pp. 103-116 This Version is available at: https://hdl.handle.net/10419/174238 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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URL: http://www.upo.es/RevMetCuant/art.php?id=118 Which countries pay more or less for their long term debt? A CART approach Gonz´ alez-Fern´ andez, Marcos Department of Business Economics and Management Faculty of Economics and Business, University of Le´on (Spain) E-mail: [email protected] Gonz´ alez-Velasco, Carmen Department of Business Economics and Management Faculty of Economics and Business, University of Le´on (Spain) E-mail: [email protected] ABSTRACT The objective of this paper is to classify a group of EMU countries according to the main determinants of long-term sovereign bond yields. We apply the Classification and Regression Tree method (CART). According to the findings, countries with lower inflation, a lower debt to GDP ratio, a lower average income tax rate, higher public debt maturity and higher IPI growth are placed in classification groups that have lower bond yields. These results confirm the hypothesis that countries with better macroeconomic and fiscal indicators have lower sovereign bond yields. Keywords: long-term yields; sovereign yields; classification trees; decision trees. JEL classification: G12; G15; H63; C38. MSC2010: 05C05; 62G99; 62H30. Art´ıculo recibido el 05 de noviembre de 2015 y aceptado el 24 de junio de 2016. 103 ¿Qu´e pa´ıses pagan m´as o menos por su deuda a largo plazo? Una aproximaci´on a trav´es de la metodolog´ıa CART RESUMEN El objetivo de este art´ıculo es clasificar un grupo de pa´ıses de la UME teniendo en cuenta los principales determinantes de los tipos a largo plazo de la deuda soberana. Se aplica la metodolog´ıa basada en ´arboles de decisi´on. Seg´un los resultados, los grupos de pa´ıses que tienen menor inflaci´on, deuda p´ublica, tipo impositivo medio y mayor vencimiento de la deuda p´ublica y crecimiento econ´omico pagan menos por su deuda soberana a largo plazo. Se confirma la hip´otesis de que los pa´ıses que tienen los mejores indicadores macroecon´omicos y fiscales son los que presentan menores costes en su deuda soberana. Palabras claves: tipos a largo plazo; rendimientos soberanos; ´arboles de clasificaci´on; ´arboles de decisi´on. Clasificaci´on JEL: G12; G15; H63; C38. MSC2010: 05C05; 62G99; 62H30. 104 105 1. INTRODUCTION One of the Maastricht Treaty’s convergence criteria that are used for valuing countries that are in the process of entering the European Monetary Union (EMU) is the long-term interest rate. The increased harmonization of monetary and fiscal policies and the adoption of a common currency contributed to the convergence of long-term government bond yields in the EMU. This period of convergence lasted until the collapse of Lehman Brothers in September 2008. The effects of the global financial crisis moved into the real economy, and macroeconomic indicators worsened in many EMU countries, leading to an increase in long-term sovereign bond yields, especially in those countries with high deficits or with a banking sector weakened by the global financial crisis (Greece, Ireland, Portugal, Spain and Italy). Most studies on advanced economies find empirical support for the theoretical prediction that sovereign debt and other macroeconomic fundamentals have an impact on government bond yields (Caporale and Williams, 2002; Rault and Afonso, 2011; Poghosyan, 2012; Bernoth and Erdogan, 2012). The main aim of this paper is to classify a group of EMU countries by considering the main determinants of long-term sovereign bond yields to determine which countries pay more or less to borrow in the long run. For this purpose, we apply the Classification and Regression Tree (CART) methodology. This approach allows classifying individuals according to a set of variables of different nature. This methodology, which is commonly applied in other fields such as medicine or biology, is not usually employed in the economic field. Only a few papers deal with this technique. Oral et al. (1992) use CART procedure to analyze the determinants of country risk for a set of countries during the 80’s. They find evidence that the variables that mainly affect ratings are GDP per capita and the investments to GDP ratio. A more recent example is the analysis of Manasse and Roubini (2009) of sovereign debt crises through CART. They find that high debt and high inflation, along with illiquidity factors driven by large stocks of short debt are the factors that better explain the presence of debt crises. Following this line of research, this paper contributes to the literature with a new perspective in the analysis of sovereign bond determinants applying CART procedure. This technique allows us to predict the value of long term bond yields according to a set of variables and classify the countries in groups with certain confidence intervals according to their expected values. The CART captures nonlinearity in the data and better handle missing data than regression techniques (Morrison, 1998). Thus, economic authorities can know what factors 106 drive sovereign bond yields, and they can have an estimation of their expected values. In addition, they can predict in which group their country will be whether the conditions or the values of those variables change. To be exhaustive in the analysis, we consider the most used variables in the literature as influential factors on long-term government bond yields: macroeconomic fundamentals (Hodgson et al., 1998; Hardouvelis, 1998; Kiani, 2009; Gruber and Kamin, 2012), fiscal variables (Ardagna et al., 2007; Laubach, 2009; Maltritz, 2012) and financial indicators (Schuknecht et al., 2009; Afonso et al., 2011; Bernoth and Erdogan, 2012). 2. DATA AND METHODOLOGY We consider 12 EMU countries: Austria, Belgium, Finland, France, Greece, Germany, Ireland, Italy, Luxembourg, Netherlands, Portugal, and Spain. To classify the countries analyzed1, we consider the following variables:  Dependent variable: 10-year government bond yields of each country. The data are obtained from Eurostat.  Explanatory variables: from the existing literature, we identify a set of variables that may determine long-term sovereign bond yields, aggregated into the following groups: (i) macroeconomic fundamentals (Industrial Production Index (IPI), Consumer Price Index (CPI) inflation, and unemployment rate), (ii) fiscal variables (deficit-to-GDP ratio, public debt-to-GDP ratio, debt growth-to-GDP ratio, private debt-to-GDP ratio, and average income tax rate) and (iii) financial indicators (public debt maturity, and sovereign rating). All data are obtained from Eurostat and Organization for Economic Co-operation and Development (OECD) statistics except the sovereign rating. This variable has been compiled from the score that the three main rating agencies, Fitch, Moody's, and Standard & Poor's, made on the credit quality of each country. We transform this score into a quantitative variable according to Remolona et al. (2007), whereby we are able to test its impact on sovereign spreads. We apply the CART methodology, a computer-intensive data-mining technique that selects explanatory variables, their critical values, and their interactions to classify different countries according to the main determinants of long-term sovereign bond yields. This 1 The data considered are the average values of the variables in the period 2000-2010. For this reason the countries that joined the EMU since 2007 (Slovenia, Cyprus, Malta, Slovakia, Estonia) are not included in the analysis. 107 technique was developed by Breiman et al. (1984). The CART methodology’s main field of application is the experimental sciences, especially medicine. In the economic sphere, CART is a more recent application method (Manasse and Roubini, 2009). This method uses a binary and recursive procedure, whereby parent nodes are split into two child nodes using splitting rules based on predictor variables; the process is repeated to reduce the conditional variation in the response variable. The CART method is used to search for the characteristics that are most closely associated with group membership. The key elements of a CART analysis are a set of rules for 1. Splitting a parent node into two child nodes with questions that have a “yes” or “no” answer. For example, if we use CPI inflation as an explanatory variable, the question could be: “is X country´s CPI inflation higher than 2 percentage points?” The CART method analyzes all possible splits for all included variables and selects the one that best separates the dependent variable; in our case, this variable is long-term sovereign bond yields. In practice, the CART obtains two groups according to the explanatory variables, and the process is repeated within these sub-groups. The CART method calculates an error, and selects the split that minimizes the error with the Gini criterion. 2. Deciding when to stop growing the tree when the reduction in the misclassification rate falls below the penalty associated whether we obtain more nodes. 3. Assigning each terminal node to a group. In our case, the CART algorithm creates groups based on the level of yields in each country and assigns each country to one of the groups. 3. RESULTS To perform the analysis, we first select long-term sovereign bond yields as the dependent variable2, and we select the following explanatory variables: unemployment, deficit, public debt-to-GDP ratio, debt growth-to-GDP ratio, CPI inflation, private debt-to-GDP ratio, average income tax rate, IPI, public debt maturity and the rating (Table 1). 2 We employ the XLSTAT statistical software from Microsoft Excel. 108 Table 1. Descriptive statistics of variables Variable Observations Minimum Maximum Mean Standard Deviation IPI 11 -1.327 4.460 1.241 2.062 CPI inflation 11 1.683 2.908 2.277 0.391 Unemployment rate 11 3.885 12.785 7.428 2.647 Deficit-to-GDP 11 -4.650 2.867 -1.666 2.261 Public Debt-to-GDP 11 9.485 108.977 61.562 26.665 Private debt-to-GDP 11 100.425 315.960 178.297 59.747 Public debt growth-toGDP 11 -0.012 0.120 0.034 0.042 Average income tax rate 11 29.623 44.288 38.593 5.294 Public debt maturity 11 4.136 7.133 5.817 0.959 Rating 11 1.000 5.833 2.240 1.709 Source: own elaboration All variables are expressed in percentage except the public debt maturity which is in years, and the rating. The CART selects the following five variables out of the 10 countries listed in Table 2: CPI inflation, public debt/GDP, average income tax rate, IPI, and public debt maturity. Table 2. CART analysis Node Countries No. of observations Parent nodes Split variable Values 1 All 11 (100%) 2 AT, BE, FI, FR, IT, NT, GE 7 (63.64%) 1 CPI inflation [1.683;2.371) 3 SP, IR, LUX, POR 4 (36.36%) 1 CPI inflation [2.371;2.908) 4 AT, FI, FR, NT, GE 5 (45.45%) 2 Public debt/GDP [42.569;82.508) 5 BE,IT 2 (18.18% 2 Public debt/GDP [82.508;108.977) 6 NT, GE 2 (18.18%) 4 Average income tax rate [36.184; 40.667) 7 AT, FI, FR 3 (27.27%) 4 Average income tax rate [40.667; 44.04) 8 NT 1 (9.09%) 6 IPI [1.222; 1.774) 9 GE 1 (9.09%) 6 IPI [1.774;2.326) 10 FI, FR 2 (18.18% 7 IPI [-0.244; 2.142) 109 Node Countries No. of observations Parent nodes Split variable Values 11 AT 1 (9.09%) 7 IPI [2.142; 3.621) 12 FI 1 (9.09%) 10 Public debt maturity [4.136; 5.288) 13 FR 1 (9.90%) 10 Public debt maturity [5.288; 6.439) 14 IT 1 (9.09%) 5 IPI [-0.873; 1.495) 15 BE 1 (9.09%) 5 IPI [1.495; 3.863) 16 IR, POR, LUX 3 (27.27%) 3 Public debt maturity [4.285; 5.84) 17 SP 1 (9.09%) 3 Public debt maturity [5.84; 6.307) Source: own elaboration Countries: AT (Austria) ,BE (Belgium), FI (Finland), FR (France), Germany (GE), Ireland (IR), Italy (IT), Luxembourg (LUX), The Netherlands (NT), Portugal (POR), and Spain (SP). The first rule splits the sample into two child nodes when we use the variable “CPI inflation”: (i) node 2 with seven countries (63.64%) with low inflation between 1.683% and 2.371%, and (ii) node three with four countries (36.36%) with high inflation greater than 2.371% (Table 2). Countries with low inflation (node 2) are further split into two other nodes with low/high public debt/GDP ratio: (i) node 4, with five countries (45.45%) with a low public debt/GDP ratio between 42.57% and 82.51%, and (ii) node five, with two countries (18.18%) with a high private debt/GDP ratio greater than 82.51%. Additionally, countries with high inflation (node 3) are split into two terminals when we use the variable “public debt maturity”: (i) node sixteen, with three countries (27.27%) with a low public debt maturity between 4.28 and 5.84 years, and (ii) node seventeen, with one country (9.09%) with a high public debt maturity of more than 5.84 years. We repeat this process for the subsequent nodes using the following split rules (Table 3). Table 3. Split rules into nodes Node Predicted yields Split rules and critical thresholds 1 4.353 2 4.213 If CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.213% in 63.6% of cases. 3 4.597 If CPI inflation is between 2.371 and 2.908, then the long-term yield is 4.597% in 36.4% of cases. 110 Node Predicted yields Split rules and critical thresholds 4 4.114 If the public debt/GDP ratio is between 42.569 and 82.508, and CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.114% in 45.5% of cases. 5 4.460 If the public debt/GDP ratio is between 82.508 and 108.977, and CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.460% in 18.2% of cases. 6 4.029 If the average income tax rate is between 36.184 and 40.667, the public debt/GDP ratio is between 42.569 and 82.508, and CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.029% in 18.2% of cases. 7 4.171 If the average income tax rate is between 40.667 and 44.04, the public debt/GDP ratio is between 42.569 and 82.508, and CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.171% in 27.3% of cases. 8 4.111 If the IPI is between 1.222 and 1.774, the average income tax rate is between 36.184 and 40.667, the public debt/GDP ratio is between 42.569 and 82.508, and CPI inflation is between 1.683 and 2.371, then the longterm yield is 4.111% in 9.1% of cases. 9 3.948 If the IPI is between 1.774 and 2.326, the average income tax rate is between 36.184 and 40.667, the public debt/GDP ratio is between 42.569 and 82.508, and CPI inflation is between 1.683 and 2.371, then the longterm yield is 3.948% in 9.1% of cases. 10 4.146 If the IPI is between -0.244 and 2.142, the average income tax rate is between 40.667 and 44.04, the public debt/GDP ratio is between 42.569 and 82.508, and CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.146% in 18.2% of cases. 11 4.222 If the IPI is between 2.142 and 3.621, the average income tax rate is between 40.667 and 44.04, the public debt/GDP ratio is between 42.569 and 82.508, and CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.222% in 9.1% of cases. 12 4.148 If the public debt maturity is between 4.136 and 5.288, the IPI is between - 0.244 and 2.142, the average income tax rate is between 40.667 and 44.04, the public debt/GDP ratio is between 42.569 and 82.508, and CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.148% at 9.1% of cases. 13 4.143 If the debt maturity is between 5.288 and 6.439, the IPI is between -0.244 and 2.142, the average income tax rate is between 40.667 and 44.04, the public debt/GDP ratio is between 42.569 and 82.508, and CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.143% at 9.1% of cases. 14 4.584 If the IPI is between -0.873 and 1.495, the public debt/GDP ratio is between 82.508 and 108.977, and CPI inflation is between 1.683 and 2.371, then the long-term yield is 4.584% in 9.1% of cases.