Sovereign exposure in the euro area:
A spatial econometric analysis of financial stress transmission
MSc Thesis Eva Mulder∗ Supervisors: Prof. L.H. Hoogduin Prof. J.P. Elhorst January 2020 Abstract
This thesis studies the spillover effects of sovereign risk on real economic stress in the euro area countries during the years 2009-2018. A spatial econometric model takes into account cross-sectional dependence and can distinguish between spillover effects, which occur after a shock, and interdependence effects, which exist at all times. It is tested if and to what extent financial stress can transmit to other countries via their holdings of sovereign debt securities, using quarterly data of 18 euro zone countries. Data on sovereign debt holdings is available on a granular level from the confidential ECB securities holdings statistics (SHS). It is found that a spatial model performs better compared to a non-spatial model. Financial stress transmits via sovereign debt holdings to other countries, both in the crisis and tranquil period. Moreover, macroeconomic variables such as real GDP, public and private debt and housing prices have a different effect on the economy during crisis and non-crisis times. During crisis times, the level of public debt in one country positively affects the level of financial stress in another country.
Keywords Sovereign Debt, Financial Crisis, Spillover Effects, Spatial Panel Econometrics JEL classifications: C23, E62, F34, G21
Coursecode: EBM877A20
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1
Introduction
During the Global Financial Crisis it became clear that financial stress could spread quickly across markets and countries. Especially in the euro area, the relation between sovereigns and banks played an important role in the transmission of financial stress across countries. This so-called bank-sovereign nexus has been an important topic of the academic debate in the last decade (Reinhart and Rogoff, 2011; Schularick, 2012; Popov and Van Horen, 2013; Acharya et al., 2014; Dell’Ariccia et al., 2018; Breckenfelder and Schwaab, 2018). The European sovereign debt crisis was an example of how stress in the financial sector could transmit to the public sector, via a guarantee channel, where governments implicitly or explicitly guaranteed to bail out big banks (De Bruyckere et al., 2013). On the other hand, increased sovereign risk could in turn increase bank risk via a number of other channels, such as a collateral channel (banks use sovereign debt paper as collateral, as is allowed since Basel II), a ratings channel (the sovereign rating is often the benchmark for banks) and a sovereign exposure channel (the bank holdings of sovereign debt) (De Bruyckere et al., 2013; Acharya and Steffen, 2015; Dell’Ariccia et al., 2018; De Grauwe, 2018). The latter channel can be seen as a direct relation between sovereigns and banks.
Nevertheless, there has been only very little empirical research in the area of sovereign debt holdings on a country level and the transmission of financial stress. Acharya and Steffen (2015) analyzed how banks changed their sovereign debt holdings during the European sovereign debt crisis. They argued that there existed a carry trade, in which banks of both risky and non-risky countries invested heavily in risky debt, placing a bet on the survival of the euro zone. Other scholars examined the direction of spillovers in four markets during the global financial crisis (Diebold and Yilmaz, 2012) or between and among sovereigns and banks (Alter and Beyer, 2014) using a vector autoregression (VAR) with forecast error variance decomposition (FEVD). In both cases in/out or from/to spillovers are identified with impulse response functions that take deviations from the CDS spread (Alter and Beyer, 2014) or cross-market volatility as a shock (Diebold and Yilmaz, 2012).
holdings, which displays the average amount of public debt of one country that is held in another over the period 2009-2018. The sovereign debt securities can be held by any sector, resulting in a broader analysis of financial stress transmission than the sovereign-bank nexus. The holdings by sector are summed up to the total holdings of one country. This then results in a spatial weights matrix that interacts with the dependent and explanatory variables of other countries. Apart from macroeconomic indicators in the country itself that could explain financial stress (such as real GDP and public and private debt to GDP), a spatial model enables the country specific macro variables to interact across countries via the euro area sovereign debt holdings.
To the best of my knowledge, this is the first study that looks at a predefined cross-country sovereign holdings channel for the transmission of financial stress in the euro area. A possible reason for the absence of this research can be the previous lack of (publicly available) data on the counterparty of sovereign bonds. The publication of the Securities Holding Statistics (SHS) of the European Central Bank (ECB) in 2015 has solved this problem. Moreover, this is one of the first studies that uses a spatial econometric model rather than a VAR to analyze the cross-border transmission of risk. A spatial econometric model captures the interaction effects, either endogenous or exogenous, from one unit to the other with the use of a spatial weight matrix. Since transmission of financial stress can only occur when there is interaction among subjects, a spatial model is well equipped to analyze these transmission effects (Triki and Maktouf, 2012). A spatial model can distinguish between interdependence effects, which are links between units that always exist, and spillover effects, which are new links that arise or existing links that strengthen during turbulent times (Jing et al., 2018).
the transmission of financial stress, not necessarily sovereign stress, that affects other countries due to all their sector holdings of the other country’s government debt. The propagation of financial stress can then occur even if the sovereign is not in trouble. Thus, stress beyond what is reflected in sovereign bond spreads is also captured.
The question central in this study is whether and to what extent a sovereign debt channel explains the transmission of financial stress in the euro area during the last decade. The sovereign debt channel can have different effects during crisis and non-crisis times, which is why a two regime model with a separate crisis and non-crisis period is applied as well. The spatial model will identify the relation between the level of financial stress in one country and the others, where financial stress is captured by the country level indicator of financial stress (CLIFS) created by Peltonen et al. (2015). All the countries in the euro zone, apart from Estonia due to missing data, are analyzed for the period 2009Q1-2018Q3. As is common in the spatial econometric literature, the spatial weights matrix of sovereign debt holdings is constant over time. In this case it is likely that sovereign debt holdings change over time, especially during a crisis. However, a time-varying spatial weights matrix might lead to endogeneity problems and confidentiality issues. This is why in this thesis the spatial weights matrix is constant, following the standard spatial econometric approach.
It is found that incorporating a sovereign debt channel into the analysis of financial stress transmission improves the results significantly. The interaction between the level of financial stress in two countries is always positive and significant, which implies that an increase in financial stress of one country leads to an increase in financial stress of another country, based on the amount of sovereign debt that is held. This result holds both in crisis and tranquil times. What is more, public and private debt holdings are found to be important for the transmission of financial stress over the entire period, whereas during crisis times only public debt holdings remain significant. Conversely, an increase of public debt holdings in the domestic country during crisis lowers its own financial stress, whereas it increases the financial stress level of foreign countries. The results hold when controlling for time and country fixed effects, as well as when using a different channel or a longer time period.
sovereign risk spillovers is extensively covered. Then, the spatial model and the design of the spatial weights matrix are explained. The fourth section covers the data used in the empirical analysis. In the fifth section, the spatial regression is executed and the results are presented. After this, some robustness checks for the spatial weights matrix will be made. The last section concludes.
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Literature review
In the last decade, substantial research has been done in the field of public debt and its relation with financial stability. Some evidence points out that public debt to GDP ratios increase once a crisis nears, especially short-term debt (Reinhart and Rogoff, 2011). On the other hand, Jorda et al. (2016) argued that the surge of private credit can indicate the possible approach of a crisis, and that not public but private debt levels are the source of financial instability. However, they also admitted that higher public debt levels threaten financial stability as it amplifies the effects of private sector deleveraging (Jord`a et al., 2016). Higher sovereign debt levels reduce the ability of the government to act in case of bailout needs, which increases bank risk via a safety net or via an implicit guarantee channel increases bank risk (Dell’Ariccia et al., 2018; Acharya and Steffen, 2015; Acharya et al., 2014; De Bruyckere et al., 2013). In the case of the euro area, implicit guarantees are not so certain anymore, which decreases the tolerance of financial markets (De Grauwe, 2018). Additionally, Schularick (2012) found that after the global financial crisis, the debt ratios were significantly higher and more persistent compared to crisis episodes in the previous 140 years. This effect is especially apparent for developed countries and can be due to the larger and more integrated financial systems, as well as the higher fiscal capacity of these governments (Laeven and Valencia, 2018; Schularick, 2012). High public debt levels for a prolonged period can increase the degree of contagion between sovereigns and banks (De Bruyckere et al., 2013), impair financial stability and hamper monetary policy transmission (Hoogduin et al., 2011).
(1961), where monetary independence ceases to exist when a country joins a monetary union with one common currency. Giving up monetary independence implies depending on a union-wide central authority that takes into account all regions and might target a different level of inflation than what is optimal at a national level (Mundell, 1961). This is the case for euro zone countries. De Grauwe (2018) also warned against the possibility of rollover crises in the euro area as long as there is no central government budget, i.e. a fiscal union. The euro area is therefore a very suitable region for analysis: it has an integrated financial system, the sovereigns have no monetary independence, implicit government guarantees have decreased over time and debt levels have during the period increased for many sovereigns.
2.1 The sovereign-bank nexus
The sovereign risk that arises among others from high public debt levels can affect the financial sector via banks, which is known as the sovereign-bank nexus. Dell’Ariccia et al. (2018) defined the sovereign-bank nexus as the intertwined health of banks and sovereigns. This two-way relation is also often referred to as a feedback loop or a deadly embrace between bank and sovereign risk. Sovereigns and banks interact via a number of channels. Many scholars have identified several channels, some with different names for the same channel. The ones that are most referred to in the literature are mentioned here.
First of all, the sovereign exposure channel implies that risk transfers from sovereigns to banks that hold their own or other countries’ debt (Buch et al., 2016; Dell’Ariccia et al., 2018). Banks are one of the main holders of sovereign debt, especially of their own sovereign (Breckenfelder and Schwaab, 2018) and of debt issued in the same currency, such as in the euro area (Popov and Van Horen, 2013). When sovereign risk increases, the value of the assets on the bank’s balance sheet decreases. It is found by Acharya and Steffen (2015) and Popov and Van Horen (2013) that some banks deliberately increased their holdings of risky sovereign debt during the European debt crisis, which they call a carry-trade where banks put a bet on the survival of the euro zone. This subsequently increased the risk of these banks and led to the bankruptcy of some of them (Acharya and Steffen, 2015).
De Marco, 2019). Under the Basel framework (both II and III) banks can invest in sovereign debt without raising their level of capital. That is, sovereign debt is favoured to other asset classes because it is assigned a zero-risk weight (Basel Committee on Banking Supervision, 2017). According to Acharya and Steffen (2015), this leads to regulatory arbitrage: in particular large, risky and weakly capitalized banks increase their holdings of risky sovereign debt because it is regarded as a zero-risk weighted asset, yet has higher returns than other riskless assets.
Thirdly, a guarantee or safety net channel leads to increased bank risk when the sovereign is not fiscally capable of bailing out the banks (De Bruyckere et al., 2013; Acharya et al., 2014). This can be due to already high debt ratios. Dell’Ariccia et al. (2018) argued that banks hold sovereign bonds as a potential guarantee for future bailouts. This can also be an additional reason for risky and under-capitalized banks to hold on to government debt (De Marco, 2019). Especially large banks are sensitive to this implicit bailout guarantee (Acharya and Steffen, 2015). Next to many of the works mentioned above, Schularick (2012) pointed towards the problem of government guarantees in general, as the financial sector has not only been subject to deregulation, but has also increased in size after the guarantees were put in place (which was during the reforms after the Great Depression). When a sovereign is still capable of bailing out a bank, the effects on the government’s balance sheet are such that the sovereign health deteriorates significantly.
Finally, the credit ratings channel, where the sovereign is often the benchmark for credit ratings and a downgrade of the sovereign can lead to lower ratings for domestic banks as well (Popov and Van Horen, 2013; Albertazzi et al., 2014; De Grauwe, 2018). Reinhart and Rogoff (2011) call this the sovereign ceiling, implying that banks are often not rated better than their government.
2.2 Cross-border sovereign risk spillovers
Often, previous studies examined the feedback loop in a domestic setting. Nevertheless, a cross-border relation between sovereigns and banks exists as well and should thus be taken into account. Cross-border relations (aside from foreign debt holdings) can exist because of the ECB’s monetary policy transmission mechanism and risk sharing policies of the European Financial Stability Facility (EFSF) and the European Stability Mechanism (ESM) (Alter and Beyer, 2014; Breckenfelder and Schwaab, 2018). The latter analyzed the effect of the information release of the ECB comprehensive assessment in 2014 (which was the analysis of the financial health of the 130 largest banks in the euro zone). They found that due to the risk sharing mechanisms above, bank risk in one country can affect sovereign risk in a country that was not risky ex ante via a so-called cross-border risk-sharing channel (Breckenfelder and Schwaab, 2018). The relation between sovereigns and banks, for instance, can be amplified during crisis times, due to spillover effects. Acharya and Steffen (2015) found that sovereign risk can have spillover effects to other countries as non-domestic banks decide to invest in risky foreign sovereign debt. De Bruyckere et al.(2013) presented evidence for a sovereign exposure channel, mostly in the domestic setting (65-73 % excess correlation between banks and sovereigns), but also across countries (55-60 % excess correlation between banks and foreign sovereigns). De Marco (2019) stated that banks not headquartered in one of the GIIPS 1 countries but exposed to risky sovereign debt were still affected during the European sovereign debt crisis. Consequently, especially small and young firms were negatively affected, as they are often more financially dependent on banks, of whom the ones that had significant sovereign debt holdings were credit rationed by investors (De Marco, 2019). He shows that the cross-border feedback loop also has implications for the real economy.
Diebold and Yilmaz (2012) examined directional spillovers in the US during the global financial crisis. They used a generalized VAR (G-VAR) with forecast error variance decomposition (FEVD) to avoid the issue of ordering variables. The total spillover index, consisting of volatility shocks across stocks, bonds, foreign exchange and commodities to the total FEVD, showed that during crisis times the spillovers increase from 5 to 10 %, and that on average 12.6 % of all volatility comes from spillovers (Diebold and Yilmaz, 2012). Moreover, one can distinguish between net receivers
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and senders of spillovers. In terms of markets, it is found that the bond market is the largest receiver of spillovers, whereas the stock market is the largest net sender. This idea of directional spillovers is also adopted by Alter and Beyer (2014), who analyzed spillovers (known here as IN and OUT spillover effects) during the European sovereign debt crisis. The model is slightly adjusted as these authors use a VARX, which is a medium-sized VAR with exogenous variables, and establish generalized impulse response functions (GIRF) using spillover matrices. The GIRFs measure a shock in the corporate or sovereign CDS in one country that affects the response variables in other countries. They found that a Spanish sovereign CDS shock has the largest impact on Italian banks, whereas there are no spillover effects found from the Greece sovereign or banks to the rest of the EMU. Conversely, Greece is a net receiver of spillover effects from other countries, and the Greek sovereign is the most vulnerable to contagion (Alter and Beyer, 2014). Alter and Beyer (2014) also argued that the biggest net senders of spillovers are German, Italian and Austrian banks; the biggest net receivers are the Spanish, Italian and Greek sovereign.
In both papers, the authors use FEVD and GIRFs, respectively, to determine the direction and size of the spillover effects. In this thesis, however, the relation between countries is predetermined (by their sovereign debt holdings in a spatial weights matrix) and the direction and size of spillovers to the real economy are analyzed. Both Alter and Beyer and Diebold and Yilmaz did not take into account interdependence effects, but looked only at spillovers. According to Forbes (2012), spillovers are the links between units that arise after a shock to one country, whereas interdependence effects exist also in tranquil times. Alter and Beyer (2014) defined spillovers differently, as increased interdependencies due to a large shock that result in contagion. In this paper interdependence and spillover effects are analyzed separately. Jing et al (2018) argued that distinguishing between interdependence effects and spillovers can have important policy applications, as transmission of financial stress due to links that exist at all times (i.e. interdependence effects) requires a different approach than financial stress that increases due to spillovers.
whole. To determine the direction of spillovers in the euro area, Garcia-de-Andoain and Kremer used a two-lag VAR with forecast error variance decomposition (FEVD). They found that Germany is clearly the biggest sender of sovereign stress during the last 18 years, accounting for 13.9 % of prediction error variance in each country (Garcia-de Andoain and Kremer, 2017). However, also Ireland and Belgium appeared to be important net senders, whereas Austria, France and Italy were perceived as the largest net receivers. Furthermore, the empirical results point out that 41.2 % of stress originates in the core (i.e. non-GIIPS) countries, compared to 31.5 % in the GIIPS countries. Importantly, the authors emphasized that spillovers from one country to the other do not necessarily imply structural links; Germany could have been the net sender due to the flight to safety during the European sovereign debt crisis (Garcia-de Andoain and Kremer, 2017), where the stress did originate in the periphery countries. Additionally, spillovers can also be positive, which is what could explain Germany as a net sender overall. Finally, a net sender could also be a country that is influential irrespective of the economic period, such as Germany, and reacts as the first to shocks, which then created spillovers to other countries. This would imply interdependence effects between Germany and other euro zone countries during tranquil periods which might transform to spillovers during economic turmoil. On the other hand, spillovers could also arise from different, less influential countries that are hit by a shock. This difference between interdependence and spillovers is exactly what Jing et al. (2018) and Elhorst et al. (2018) captured in their spatial econometric model. To correctly capture the magnitude of the two different effects, they have to be measured together. The right way to do this is by using a spatial model (Jing et al., 2018).
the data can now be used to identify all holders of government bonds, in terms of both sectors and countries. Therefore, this study differs from others in analyzing financial stress by all sectors’ sovereign debt holdings, using a spatial model.
Figure 1: Sectoral holdings of government debt. Source: SDW QSA, ESA2010 quarterly financial and non-financial sector accounts, author’s own calculations.
markets) and 2) real linkages (based on trade flows). The spatial weights matrix consists of these two components: 80 % information channel and 20 % trade channel. The spatial econometric model used is a spatial autoregressive model (SAR), which captures endogenous interaction effects. For this specific case, it implies that the effects of sovereign bond spreads in one country can affect the spreads in another. The spatial weights matrix reflects the interdependence that exists at all times. Spillover effects can also be identified with the use of a spatial weights matrix: when the coefficients of the explanatory variables (especially the indirect effects) increase after a shock, this implies that stronger links between countries exists in crisis times. It is found that advanced economies especially transfer their sovereign risk to each other, but also to emerging countries (Debarsy et al., 2018). Whereas these authors examined the transmission of sovereign risk from one country to the other, this thesis investigates the transmission of financial stress based on sovereign debt holdings of all sectors from one country to the other, solely through real linkages; that is, I analyze to what extent sovereign debt holdings can explain spillover effects.
3
Model
Spatial econometrics is a discipline that deals with interaction effects among units. Since its in-troduction in the 1970s, it has mainly focused on interaction of geographical units such as regions and countries. This usually takes the form of a distance channel, where units located closer to each other affect each other more. Consequently, the spatial weights matrix is normally constant over time. Interaction effects can also be based on units that are related in a different non-geographical way such as via trade relations, credit channels and in the case here sovereign debt channels. This type of research is still limited, even though it is growing (Elhorst, 2014b). A spatial econometric model is created by extending a standard linear econometric model (e.g. OLS) by a spatial weights matrix. The spatial weights matrix or connectivity matrix (W) then reflects how units relate to each other. The composition of this matrix is key to the results of the spatial econometric model. Small changes of W can have large implications for the results. Therefore, whenever possible, economic theory should be the guideline for creating a spatial weights matrix (Corrado and Fingleton, 2012). The sovereign debt channel is therefore in this study the most important aspect of the model. A simple example of a spatial weights matrix of country A, B and C can be seen in Equation (1):
W = 0 WAB WAC WBA 0 WBC WCA WCB 0 (1)
to one. The columns are not normalized and thus the total relative impact of each country can be derived by comparing the sums of each column. Appendix 7 contains the weights used for the econometric analysis later on. When computing the column totals, it is found that Germany, Italy and France have by far the most influence on other countries: their total average impact over the period 2009-2018 is above three, compared to the other countries ranging between 0.003 (Malta) and 1.675 (Spain). The total of the column sums equals the total of the row sums and the number of countries in this study, namely eighteen.
Linear regression models can be extended with a spatial lag or a spatial error. The former includes spatial lagged dependent and spatial lagged explanatory variables. The spatial econometric literature refers to lagged variables in the sense that they are lagged in space, rather than in time. In the case of lagged dependent variables, the dependent variable of one country can affect the dependent variable of another. This is also know as an endogenous interaction effect. In this case, the level of stress in country A at time t can influence the level of stress in country B at the same time, due to the holdings of government debt A by country B (where the holdings are captured by connectivity matrix W). Lagged explanatory variables are explanatory variables of country A that affect the dependent variable of country B. These exogenous interaction effects can be illustrated as follows: if the public debt of country A increases, this might lead to a higher level of financial stress in country B, as high or increasing debt levels might be perceived as riskier for the countries that hold government securities of country A. The relative sovereign risk has then increased. Finally, a spatial model can contain a spatially lagged error term, which implies that omitted variables are spatially autocorrelated or that unobserved shocks are common to all units. Since excluding a spatial error term only leads to a loss of efficiency and will not lead to biased and inconsistent estimators, this model will not be applied here (Elhorst, 2014c).
significantly different. The SAR model takes the following general form:2 yit= ρ N X j=1 wijyjt+ xitβ + it (2)
Whereas the general SDM model reads as:
yit= ρ N X j=1 wijyjt+ xitβ + θ N X j=1 wijxjt+ it (3)
Where y is the dependent variable, for every unit (country) i (i=1,...,N) at time (quarterly date) t (t=1,...,T), ρ is the endogenous interaction coefficient, wij is the element of the spatial weights
matrix of sovereign debt holdings, reflecting the relation between country i and j. The term PN
j=1wijyjt is then the dependence of country i on the dependent variable of all other countries j.
The row vector x represents 1 x K exogenous explanatory variables for each country at each point in time, β is the corresponding parameter to every x, and θ is the K x 1 vector of coefficients of the the exogenous interaction effect. The term PN
j=1wijxjt is a vector of all the control variables of
other countries, multiplied by the spatial weights.3 Note that the spatial weights are the same as for the dependent variable. Finally, =(1, ...N)T is the error term, assumed to be independently and
identically distributed (i.i.d.) with zero mean and variance σ2. As the models are very similar, the rest of the section uses the SDM model for further explanation. The SAR model will be displayed in brackets if the difference is relevant. All models are estimated using maximum likelihood (ML). The model in this thesis will be as follows:
F SIit= ρ N X j=1 wijF SIjt+ xitβ + θ N X j=1 wijxjt+ µi+ λt+ it (4)
Where the dependent variable is the level of the financial stress index (FSI) and the explanatory variables are real GDP growth, growth rate of public debt to GDP, growth rate of private debt to GDP, the level of credit and of short-term debt (both as percentage of GDP) and housing prices
2
All the formulas are taken from Jing et al (2018) and Elhorst (2014b). Moreover, the MATLAB program for the estimations, comparisons of different models and the calculation of direct and indirect effects is an adapted version of the programs available from prof. J.P Elhorst’s website: https://spatial-panels.com
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growth. The selection of the data will be discussed in more detail in the next section. Additionally, µ is a vector of spatial fixed effects (which are commonly known as country fixed effects) for each country, and λ reflects the time period fixed effects. Finally, note that the in the SAR model, θ = 0, which would remove the exogenous interaction effects (the third term) from the equation.
3.1 Direct and indirect effects
To identify spillover effects, one should not look at the coefficients directly resulting from regression (4). This is because these coefficients display the total effect, which can be broken down into a direct effect and an indirect effect. The direct effect is what would be captured by β in a standard linear regression. As a result, interpreting the point estimates that appear after running the regression as in e.g. OLS would lead to overestimating the parameters. Moreover, the indirect effects are the most interesting in this case: this is the effect of one country i on another country j. In order to estimate the model and calculate the marginal effects, it should be rewritten in both vector and reduced form. That is, Y is a N x 1 vector of all countries at time t, and X is a N x K matrix of all explanatory variables:
Yt= (I − ρW )−1[Xtβ + XtW θ + µ + λt+ t] (5)
This then results in the following N x N matrix of countries 1 to N at time 1 to T when taking the partial derivatives of expected value of Y with respect to the k th explanatory variable X :
Where Equation (8) is in the literature referred to as the spatial multiplier matrix. In the case of the SAR model, the reduced form (8) excludes the θ term, which can then be written as:
Y = (IN − ρW )−1βk (9)
The time and spatial fixed effects, as well as the error term, drop out due to taking expectations. When the matrix W is constant over time, as is the case in the analysis below, the marginal effects are independent of time. On the diagonal, the direct effect of each unit (on itself, i.e. the marginal effect) is displayed, whereas the indirect effects of country A on B and vice versa can be found off-diagonal. The average direct effect can be calculated by taking the average of the diagonal element of the matrix in (8). In the case of average indirect effects, these can be derived from taking the average row sum of the off-diagonal elements of (8). For the SDM model, this would imply a fully flexible model where the magnitude of the direct and indirect effects of each explanatory variable is independent of the others. This is not the case for the SAR model, as the ratio between direct and indirect effects for all explanatory is fixed (and the same). The fixed ratio of direct and indirect effects is often seen as a limitation of the SAR model (Elhorst, 2014b). The performance of the two models will therefore also be compared later on.
The calculation of the direct effects accurately reflects the marginal effect of each explanatory variable and computing the indirect effects takes into account cross-sectional dependence. Indirect effects are therefore also called spillover effects. As country A can affect country B, which can in turn affect country C, the infinite series expansion of the spatial multiplier matrix can be written as follows:
in the diagonal elements of higher order terms in W (starting with the third term in Equation (10). Finally, indirect effects of a higher order than one include feedback effects for ’more distant’ neighbours, e.g. an effect of country A can affect country B, which in turn affects country C and therefore also country A again (Elhorst et al., 2018). In Figure 2 below, first and second order interaction effects between three countries are illustrated in a simple way.
Figure 2: Possible interaction effects in SDM model. Note that the blue filled arrows are direct effects, the green arrows examples of feedback effects, blue border arrows exogenous interaction effects, red arrows endogenous interaction effects and the orange arrow is an example of a second order endogenous interaction effect. In case of the green and orange arrows only one interaction is shown for simplicity. However, these effects can also exist between other countries.
In the figure above there are only three countries shown for simplicity, but the idea is the same for eighteen countries. Note that the blue filled arrows are the direct effects, which in a standard linear regression would be the parameter coefficients. The green arrows display a feedback effect (i.e. second order direct effect) between country A and B. The orange arrow is a second order indirect effects, as it shows the effect of country A on country B which in turn affects country C (if the effect in C then returns to country A, it would be a higher order direct effect). Naturally, second order indirect effects could originate from and transmit to any country.
estimates of the direct and indirect effects vary slightly. The difference is negligible, however. This approach is adopted in this thesis as well. The estimation method used here is maximum likelihood (ML) estimation (see Elhorst 2014b for a mathematical derivation of this). The software packages for estimating direct and indirect effects are available on https://spatial-panels.com.
3.2 Dynamic spatial models
The model above includes only spillovers in space. Nevertheless, spillovers can also occur in time. The model can be transformed to a dynamic SAR or SDM in order to include lags of dependent and explanatory variables as well as the endogenous and exogenous interaction effects. An example of a dynamic SDM model with the lagged dependent variable and the lagged endogenous interaction effect can be found in the reduced form below:
Y t = (I − ρW )−1[τ Yt−1+ ηW Yt−1+ Xtβ + XtW θ + µi+ λt+ t] (11)
Where τ and η are the parameters for the dependent variable lagged in time and the dependent variable lagged in both space and time, respectively. Note that a dynamic SDM does not necessarily include lagged exogenous interaction effects, which would make interpreting the effects even more complex. In the case of a dynamic model, one can distinguish between the short- and long-term effects of the explanatory variables, which is not possible in a non-dynamic setting that results in long-term effects only. The short and long-term effects can be calculated in the following way, respectively: ∂E(Yt) ∂x1t,k ... ∂E(Yt) ∂xN t,k = (I − δW )−1[β1kIN + β2kW ] (12) ∂E(Yt) ∂x1t,k ... ∂E(Yt) ∂xN t,k = [(1 − τ )I − (δ + η)])−1[β1kIN + β2kW ] (13)
Where Equation (12) displays the short-term effects and (13) the long-term effects. It can be seen from the latter that short-term indirect effects only occur if δ and β2k or both are nonzero, and
long-term indirect effects are present only if δ is unequal to η and β2kis nonzero (or both) (Elhorst,
non-dynamic model under- or overestimates the long-term effects. Therefore the non-dynamic model is taken into account in the next section as well. However, when distinguishing between spillovers and interdependence effects in a two regime setting, a non-dynamic model is used for simplicity.
3.3 Interdependence and spillover effects
As one of the questions this thesis sheds light on is whether a difference between spillovers and interdependence effects can be identified, the model should include a dummy that separates the crisis from the tranquil period. That is, the dummy equals one if the euro zone is in crisis, and zero otherwise. For simplicity it is assumed that the crisis period is the same for all countries, namely from 2009q1 until 2013q4. In Appendix 8.1 Figure 4 the evolution of financial stress over time is plotted for each country. It can be seen that after 2013 the levels of financial stress are reduced considerably. Moreover, it can be argued that 2009 was actually the start of the crisis in Europe, as Lehman brothers defaulted in the end of the third quarter of 2008, whereas economic projections and the European countries themselves only realized the impact of this event at the end of 2008. 2009 was the first year in which the European economy decreased unprecedentedly (European Comission, 2009). In the next model all the explanatory variables interact with a crisis dummy. As a result, the number of explanatory variables initially chosen will be multiplied by four (in the case of the SDM model): one explanatory variable as it is in tranquil times, one explanatory variable in crisis times, one exogenous interaction effects during tranquil times and one exogenous interaction effects during crisis times. The endogenous interaction effect (W Y ) will also interact with a time dummy. Following the concern of Jing et al. (2018) that the sample might not be large enough to include all the k-order explanatory variables simultaneously, the number of variables chosen will be limited. The general form of the model is based on Jing et al. (2018) and can be written as: F SIit= ρ N X j=1 wijF SIjt+ηdt N X j=1 wijF SIjt+xitβ +xitφdt+θ N X j=1 wijxjt+γdt N X j=1 wijxjt+µi+αdt+it (14) With dt as the dummy variable for the crisis (=1) and non-crisis period (=0). The coefficients
indicates interdependence, whereas significance of the latter points at spillover effects. The α is the parameter for the crisis dummy. Using the same steps as in Equations (5) to (8) eventually leads to the following matrix (Jing et al., 2018):
= (IN− ρW − ηDtW )−1 βk+ φkdt w12θk+ w12γkdt ... w1Nθk+ w1Nγkdt w21θk+ w21γkdt βk+ φkdt ... w2Nθk+ w2Nγkdt .. . ... . .. ... wN 1θk+ wN 1γkdt wN 2θk+ wN 2γkdt ... βk+ φkdt (15)
Note that in this case, time fixed effects are excluded. However, time is to a certain extent taken into account by using a time dummy for the crisis period. As a result, the direct and indirect effects differ for both periods and will be shown separately (the method of obtaining the effects is still the same). Finally, in order to compare all the nested models, the log-likelihood function of each model u will be tested against a more restrictive model r using a LR test (−2 ∗ [logLr− logLu]).
For more details on this, please consult (Elhorst, 2014b).
4
Data
The data used in this thesis is mainly from the ECB Statistical Data Warehouse (SDW), with only one variable retrieved from the World Bank Global Financial Development Indicators database. One can distinguish between the publicly available data that is used in the OLS model, i.e. the macro data, and the confidential granular data from SHS, which allows for extension of the analysis to spatial econometrics.
its transparent and reproducible characteristics, and the fact that it isolates stress within single euro countries (whereas other measures, such as the CISS from Hollo and Kremer (2012), look at financial stress in the euro area as a whole).
The index is set up in a way that it captures co-movements of stress originating in different markets. The different sub-indices used in the CLIFS are 1) equity markets index, which covers the stock price index, 2) bond markets, containing the 10-year government bond yields, and 3) foreign exchange markets that include the real effective exchange rate. The creation of the index is illustrated in Figure 3 below. Each of these sub-indices contains the average of two variables. These are then transformed to one index using an empirical cumulative density function (ECDF). The former captures the volatility, whereas the latter looks at cumulative maximum loss (CMAX), cumulative difference of the maximum increase of the spread (CDIFF; the spread with respect to the German government bond, and in the case of Germany to the minimum CMIN) and the cumulative change over six months (CUMUL), respectively. The volatilities are standardized using a 10 year window that expands progressively to take into account new events. All the variables have been corrected for inflation. Then, the sub-indices are aggregated with the use of portfolio theory, where each sub-index is weighted by its cross-correlation with others. As a result, higher levels of financial stress occur when there is co-movement across the sub-indices. The CLIFS values range from 0-1 since the index is displayed in percentiles based on the values of the sub-indices during the 10 year window.
model should be tested for endogeneity.
The quarterly data of the CLIFS (transformed by SDW) is used not only as a dependent variable, but also as a spatially lagged endogenous variable. That is, the financial stress in one euro area country can at the same time affect the level of stress in another euro country.
Figure 3: Composition of CLIFS. Source: Duprey et al. (2015)
For a more detailed description of the selected variables and the set-up of the index, see Duprey et al. (2015). Financial stress does not always imply systemic stress. Real economic stress can materialize even when there is no significant financial stress (CLIFS levels below the median). Using the definition of the authors, systemic financial stress is defined as a period of financial market stress that is associated with a negative impact on the real economy in terms of both intensity and duration (Duprey et al., 2015). According to the authors, systemic risk is subject to three conditions. First of all, real economic stress should occur for at minimum of 6 months. Secondly, the economic stress should be the result of financial market stress in the same period. Thirdly, the financial market stress has to occur for at least a year(Duprey et al., 2015). When analyzing the CLIFS, they find that real economic stress occurs on average when values of the FSI are above the 70th percentile.
this indicator to other so-called expert databases on financial stress episodes and banking crises (such as Laeven and Valencia (2013) and Reinhart and Rogoff 2011), the systemic stress episodes align 84 % of the time (Duprey et al., 2015).
4.1 Indicators of financial stress
The explanatory variables used here are based on other literature suggesting the macroeconomic variables that can indicate or precede financial stress. Jing et al. (2018) used GDP growth, inflation and domestic credit growth in their baseline model, as GDP growth is often low and inflation high before the start of a crisis. Also, high credit growth is found to be a main indicator of banking crises. Reinhart and Rogoff (2011) and Jorda et al. (2016) argued that not only public debt (which is rising more during and shortly before a crisis), but especially the private debt to GDP ratio is rises significantly before the start of a downturn. Therefore these two variables are included here as well. It is often seen that short-term financing increases shortly before a banking crisis, leading to higher refinancing risk (Reinhart and Rogoff, 2011). The same development is found for the euro area before and during the sovereign debt crisis; see Figure 5 in the next section. Consequently, the level of short-term government debt securities is also taken into account as explanatory variable. Since short-term debt is for many countries only a very small percentage of total debt, only the short-term debt as percentage of total GDP will be used in the regression. Long-term debt is then reflected in the growth rate of total public debt to GDP.
Finally, in line with Jing et al. (2018), housing prices are included as an explanatory variable, since property prices were very volatile during the crisis and the unsustainable rise in housing prices before the crises was one of the main causes of the outbreak of the Great Recession. Housing prices are transformed to an index of residential property prices of new and existing houses (base year=2015).4 Then, the period-on-period growth rate of the index is computed and used as the explanatory variable representing housing prices growth.
All data for the explanatory variables used in this study is publicly available and used with quarterly frequency. In the case of real GDP and housing prices, the variables are taken in log differences to easily interpret the coefficients of the regressors. Since the other variables (public
4
debt, private debt, credit and short term debt) are all ratios to GDP, no logs are taken. Then the growth rate is calculated as the period on period percentage change.5. In Appendix Table 9, more information can be found on the sources of the data.
4.2 Securities Holdings Statistics
The Securities Holdings Statistics by sector (SHS-S or SHS in short) has been composed by the ECB since 2014 to get more insight into the holdings of securities within and outside the euro area (European Central Bank, 2015). The SHS data contains information on holdings on a security-by-security basis, where the SHS-S is broken down by sectors. The data set is still fairly new, resulting only recently in publications using SHS. Boermans and Vermeulen (2018) used the SHS-S data to analyze how QE has affected investment behaviour, by looking at the geographical location of the holders of bonds and the changing characteristics of the bonds issued over time. Boermans and Keshkov (2018) used the sectoral SHS data to examine how the concentration of sovereign bonds changes as a consequence of the public sector purchasing program (PSPP). They found that sovereign debt securities concentrated more in the euro area after the start of the program, as especially non-EU investors sold their sovereign debt holdings. Finally, Koijen et. al. (2019) used SHS to examine the effect of QE on bank lending. The SHS data allows them to differentiate between euro and non-euro area securities, as well as vulnerable and non-vulnerable countries. They found that especially in GIIPS countries, all sectors have a stronger home bias.
Data is available on debt and equity securities holdings, and the reporting period officially starts in the fourth quarter of 2013. For this period the coverage of debt securities issued by euro area residents is 92 % (European Central Bank, 2015). However, some data before this period is also available, starting the earliest in 2009. The coverage before 2013 is found to be around 50 % compared to after the official collection date. Only in the case of Greece, domestic holdings are not reported before 2013 (see Appendix 5). However, as the domestic holdings are excluded from the analysis, it is not expected to create any problems. Even though the holdings by counterparty slightly change over time, there can be no serious break detected around the first mandatory
reporting date. Finally, since this paper examines the sovereign debt holdings before, during and after the European sovereign debt crisis, the SHS data since 2009 is used. The total holdings are computed within every period (either the whole period or over the crisis and non-crisis period) and the holdings per issuer are expressed as percentages of this total.
The SHS sectoral data of government debt securities can be divided into two subparts: 1) con-taining the holdings of government securities by investors residing in the euro area, e.g. households, firms, banks etc., and 2) non-euro area investor holdings. 80 % of the holdings by euro area in-vestors are securities issued by euro area residents (European Central Bank, 2015). One of the biggest non-euro area holder-area is the United States. However, the quality and coverage of the data on holdings by investors from the euro area (direct reporting) is far better than that for non-euro area residents (indirect reporting) (European Central Bank, 2015). As the focus is on the non-euro area in this thesis, the holdings of non-euro area counterparties are excluded. The non-euro area investors can be seen as the rest of the world not included in the analysis here.
To create a constant spatial weights matrix, the sovereign debt holdings per country and holder area are aggregated up over the entire period. The weights in the matrix are calculated in terms of the percentage that the holder area has of the government debt securities of another euro zone country to the total of holdings in that period. In this calculation, the country’s own holdings are excluded, as the spatial econometrics literature assumes a country cannot be interdependent with itself (Jing et al., 2018). This implies that the diagonal of the matrix is zero. The constant spatial weights matrix of sovereign debt holdings WS, which was informally illustrated in Equation 1, can
be formally written as:
wijS = Sij Si
(16) Where wij is country i ’s holdings of government bonds of country j. The constant spatial weights
matrix can be found in Appendix (7), whereas the holdings during the crisis and non-crisis period are displayed in Appendix 8 and 9, respectively. The holdings of foreign sovereign debt of country j are then a percentage of total foreign holdings of the euro zone country, excluding Estonia. Including United States as a counterparty is thus topic a for another paper.
A problem can arise with third party holdings (tph), which are holdings that are reported by residents but held by non-resident investors (Rousov and Caloca, 2015). This variable is often estimated rather than reported in the SHS data. Tph are debt securities issued by one country, held by investors outside the euro zone but reported by a euro zone resident. To avoid double counting and custodian bias (where the holder reported by the custodian is not necessarily the final holder), tph are excluded, which is in line with Boermans and Keshkov (2018) and Boermans and Vermeulen (2018).
5
Empirical results
displayed in full in the Appendix 8.5 (Figure 10 to 15), that is the effect of each explanatory variable multiplied by the spatial weights matrix for each country. Finally, the period will be divided into a crisis and tranquil period to identify interdependence and spillover effects between countries.
5.1 Base model
The panel of 18 countries spans over 39 quarters, from 2009Q1 until 2018Q3. A panel without too many missing values is obtained for the period 2006Q1-2018Q3. However, in order to compare the base model results with the spatial extensions, the periods need to align and the panel needs to be balanced. This is why all estimation results are based on the period starting in 2009. The results also hold when the period is extended to 2006 with the constant spatial weight matrix, which will be discussed in the section of robustness checks.
The variables used for the model are the log difference of real GDP and housing prices, the growth rates of public debt to GDP, and private debt to GDP, and the level of credit and short-term debt securities to GDP. Moreover, the level of short-short-term debt as a percentage of total debt is according to the public SDW data very small (see Appendix 8.2, 5 and 6). Why these ratios of short and long-term debt are so different from the SHS data can be due to: 1) SDW defines long-term debt as debt with maturity over one year or no stated maturity, 2) The counterparty of SDW debt securities is the entire world, whereas in SHS it is only the 18 euro zone countries used here, and 3) SHS might, especially before 2013, not contain all data, as reporting became mandatory in 2013. Strictly speaking, short-term debt is also included in the public debt variable. However, replacing the total public debt to GDP with long-term debt to GDP would result in only capturing debt securities. The reason for this is that public debt to GDP represents Maastricht Debt, which includes debt securities, loans and currency and deposits, whereas long-term debt is available with only debt securities. To be able to look at the effect of total general government debt, Maastricht debt to GDP is used. The level of short-term debt to GDP is still included as it often increases before a crisis (Reinhart and Rogoff, 2011; Hoogduin et al., 2011).
equal to zero. The countries do not play a big role in the spatial weights matrix (carry almost no weight to other countries) and taking an average of the years after would be misleading, as 2009 and 2010 were very turbulent years compared to the years afterwards. Using average values would then lead to inclusion of these countries into the exogenous interaction effects (when the explanatory variables are multiplied by the spatial weights matrix), whereas nothing is known about the actual values of their credit to GDP. Therefore, it is safer to just set these values to zero. As a robustness check the countries are also tested with average values. When substituting these in, the results do not change a lot. On a final note, according to the data Luxembourg never had any short-term debt in the period under analysis. The value of short-term debt to GDP of Luxembourg is thus always zero.
In Table 1 below, the summary statistics for all the variables can be found, for both the complete period as well as for the separate crisis and tranquil period. The division of the sample into these periods can be justified by examining the FSI for each country (see Appendix 1), where the tranquil period clearly starts in 2014 for almost all countries. Moreover, following the literature one can argue that the crisis period already started before 2009, with the Global Financial Crisis, and continued into the European sovereign debt crisis, where most countries had recovered by the end of 2013 (apart from Greece, who still received financial assistance in 2014 and 2015). Not surprisingly, the summary statistics table shows distinct descriptive results for the crisis and tranquil period.
Table 1: Summary statistics
Variable Mean Std. Dev. Min. Max. N
Crisis period 2009-2013
CLIFS 0.194 0.12 0.03 0.823 360
Log difference real GDP -0.001 0.016 -0.136 0.035 360 Short term debt to GDP 0.054 0.041 0 0.173 360
Credit to GDP 1.061 0.458 0.425 2.531 348
Growth rate of private debt to GDP 0.003 0.018 -0.084 0.08 360 Growth rate of public debt to GDP 0.029 0.059 -0.195 0.442 360 Log difference of housing prices -0.006 0.028 -0.224 0.08 360 Tranquil period 2014-2018
CLIFS 0.077 0.05 0.02 0.569 342
Log difference real GDP 0.008 0.015 -0.06 0.21 342 Short term debt to GDP 0.037 0.032 0 0.164 342
Credit to GDP 0.890 0.408 0.361 2.515 342
Growth rate of private debt to GDP -0.004 0.026 -0.087 0.335 342 Growth rate of public debt to GDP -0.004 0.029 -0.124 0.151 342 Log difference of housing prices 0.01 0.019 -0.122 0.078 342 Complete period 2009-2018
CLIFS 0.137 0.109 0.02 0.823 702
Log difference real GDP 0.003 0.016 -0.136 0.21 702 Short term debt to GDP 0.457 0.038 0 0.173 702
Credit to GDP 0.976 0.442 0.364 2.531 690
Growth rate of private debt to GDP -0.001 0.022 -0.087 0.335 702 Growth rate of public debt to GDP 0.013 0.05 -0.195 0.442 702 Log difference of housing prices 0.002 0.025 -0.224 0.08 702
as well: the higher coefficient of private debt in all models is in line with Reinhart and Rogoff 2011, who argue that private debt levels are a better indicator of a financial stress than public debt levels (note that these are nevertheless also significant). The negative coefficient of housing prices can be debated; an increase in housing prices would lower financial stress in the model, even though increasing housing prices often precede periods of economic downturn. As the sample starts in the middle of an economic downturn, one could argue that in this case decreasing housing prices increased financial stress even more. This reasoning can be supported once the crisis and tranquil period are separated. Credit to GDP becomes insignificant when only time fixed effects are accounted for, whereas short term debt to GDP becomes insignificant whenever time fixed effects are included. The log-likelihood of the model improves when time fixed effects are included. The significance of time fixed effects could indicate that the crisis period should be accounted for; this will be done in section 5.3.
comparing regression 4 with the others, time and spatial fixed effects might also explain to a large extent the average value of the FSI.
Table 2: OLS estimation results (dependent variable: FSI) 2009Q1-2018Q3
Variable (1) (2) (3) (4) Relative
contribution(%) Coefficient t-stat Coefficient t-stat Coefficient t-stat Coefficient t-stat
Log ∆ real GDP -0.387 -1.406 -1.110*** -4.811 -0.433** -2.053 -0.513*** -2.642 11.04
Short term debt/GDP 0.481*** 4.136 0.838*** 5.021 -0.026 -0.326 0.095 0.713 4.86
Credit/GDP 0.092*** 13.952 0.097*** 4.954 0.004 0.674 0.069*** 4.346 41.02
%∆(Private debt/GDP) 0.778*** 4.242 0.956*** 6.361 0.405*** 3.044 0.491*** 4.051 14.53
%∆(Public debt/GDP) 0.754*** 8.638 0.495*** 6.753 0.262*** 4.106 0.256*** 4.423 17.22
Log ∆ housing prices -0.548*** -3.058 -0.596*** -4.073 -0.493*** -3.915 -0.337*** -2.949 11.33
Time FE N N Y Y Country FE N Y N Y No. observations 702 702 702 702 R2 0.0893 0.3829(0.4371) 0.0885 0.1237(0.6887) ¯ R2 0.0828 0.3785 0.0819 0.1174 σ2 0.0110 0.0068 0.0049 0.0038 Log-likelihood 589.991 760.077 872.881 966.781
(a) This table shows the regression results of the OLS in Matlab for country fixed effects, time fixed effects and both for 18 EU countries (excluding Estonia) over the period 2009-2018. The relative contribution is calculated as the mean of the coefficient multiplied by the standard error of the variable (=absolute contribution), weighted by the sum of absolute contributions of all variables. ***, ** and * indicate significance at 1, 5 and 10% level, respectively. The R-squared in brackets is the fixed effects (within) R-squared
5.2 Spatial models
The fact that cross-sectional dependence is present in model (4) of Table 2 indicates that an extension to a spatial model might improve results, since cross-sectional dependence can then be accounted for. Using a constant spatial weights matrix W consisting of weights of the sovereign debt holdings of the 18 euro zone countries to the total holdings, the model is transformed to a spatial econometric one. The SAR, SDM and dynamic SDM are estimated and compared to each other. The results of these regressions can be found in Table 3 below. The R-squared and log-likelihood show that all models improve in comparison with the non-spatial models. However, one should conduct a formal LR test to see whether the OLS model can be rejected against the SAR. The LR test points at significantly better performance of the spatial models compared to OLS (in the case of SAR: LR = 4.176, df = 1, p = 0.041). When comparing the two non-dynamic spatial models with each other, the SDM model outperforms the SAR model clearly ( LR = 80.986, df = 6, p = 0.000). The dynamic model can unfortunately not be compared formally as the number of observations is different from the other models. Nevertheless, it can be seen from the (adjusted) R-squared and the log-likelihood values that the dynamic model has a better fit. Other scholars have warned for using a dynamic spatial model, as it is still relatively new and more research needs to be done in order to confirm that the results of long and short-term effects make sense (Elhorst, 2014a). What is more, dynamic models possibly suffer from identification problems (Anselin et al., 2008) and over-fitting. This might explain why almost all direct and indirect effects (see Table 4) of the dynamic SDM are insignificant. For this reasons, as well as for simplicity, this study will proceed with the non-dynamic SDM model.
It can be seen that including a spatial lag (W*FSI) improves the model. In all cases the coefficient of the spatial lag (in space) is significant and positive, which implies that an increase in the FSI level of another country increases the FSI of the respective country. To correctly capture the magnitude of this effect, the coefficients resulting from the spatial regressions should substituted for ρ in the calculation of the indirect effect of the FSI (see Equation 9).6 In the case of the SAR model, this results, ceteris paribus, in an increase of the FSI of 0.5457 percentage point of the respective country, if the FSI of all other countries increases one percentage point. The effect is
Table 3: Spatial regression estimation results (dependent variable: FSI) 2009Q1-2018Q3 Variable Spatial Autoregressive Model Spatial Durbin Model Dynamic Spatial Durbin Model Coefficient t-stat Coefficient t-stat Coefficient t-stat Log ∆ real GDP -0.482** -2.422 -0.338* -1.746 -0.259* -1.775 Short term debt/GDP 0.084 0.611 0.245* 1.808 -0.042 -0.427 Credit/GDP 0.070*** 4.322 0.091*** 5.249 0.022* 1.728 %∆(Private debt/GDP) 0.473*** 3.936 0.487*** 4.014 0.207** 2.377 %∆(Public debt/GDP) 0.148** 2.558 0.147** 2.531 0.032 0.778 Log ∆ housing prices -0.332*** -2.824 -0.287** -2.409 0.006 0.061 W* FSI 0.359*** 7.185 0.353*** 7.041 0.618*** 5.064 W* real GDP growth 1.292 1.345 0.641 0.846 W* short term debt/GDP 4.722*** 7.202 1.321*** 2.592 W* credit to GDP -0.143* -1.865 -0.023 -0.408 W* growth rate private debt/GDP 2.735*** 4.745 1.035** 2.400 W* growth rate public debt/GDP 0.530** 2.336 0.367** 2.296 W* growth rate housing prices -0.622 -1.100 -1.406*** -3.028
η * FSI 0.676*** 24.887 η* W * FSI -0.447*** -3.898 No. observations 702 702 684 R2 0.6934 0.7267 0.8513 ¯ R2 0.1250 0.2218 0.5872 σ2 0.0040 0.0035 0.0015 Log-likelihood 968.905 1009.398 1239.930
slightly smaller in the SDM model (on average 0.5326 percentage point). For individual cases, the transmission of financial stress depends on the link between the two respective countries. Using appendix 8.4 Figure 7, the effect of the FSI for each country can be calculated. For instance, the effect of Germany on the Netherlands is 0.3639 (36% of the total Dutch sovereign bond holdings are issued in Germany, on average). This implies that an increase in the FSI of Germany leads to an increase in the FSI of the Netherlands of 0.199 percentage point, holding everything else constant. In this way a spatial econometric model illustrates how countries can affect each others’ stress, even when there is no change in fundamentals in the country itself.
The coefficients of the explanatory variables in the SAR and SDM (non-dynamic) maintain their significance and correct signs. However, interpreting these coefficients can be misleading, as the marginal effects can only be derived from the calculation of direct and indirect effects, using Equa-tion 9. In Table 4 below the average direct and indirect effects over the entire period are shown for all spatial models. As the W matrix does not change over time, the effects are independent of time t.
Often, the indirect effects are clearly smaller than the direct effects and slightly less significant. The coefficients of the average direct effects are sometimes bigger than the coefficients of the regression, due to feedback effects. The indirect effects should be interpreted with caution, as explained by Jing et al (2018), as they are an average. For instance, in the SAR model, the log difference of real GDP is on average -0.266, which implies that a one percentage point decrease of all countries’ real GDP growth leads to a 0.003 percentage point increase in the FSI of the respective country (dividing by hundred is necessary as the variable is in logs). This value needs to be multiplied by the weight of each country linked to the respective country, in order to estimate the individual country effect. According to the constant sovereign bond holdings matrix (Appendix 7), Austria holds 22 % of its sovereign debt holdings in German bonds. If real GDP growth decreases by one percentage point in Germany, which is one of the most influential countries, this will lead to an increase in the FSI of Austria of 0.220*0.0026 = 0.006 percentage point. This only holds when Germany is the only country experiencing declining growth rates. That is, the effect will be larger when taking into account all countries.
Table 4: Estimates of direct and indirect effects of spatial models
Variable SAR SDM Dynamic SDM
Short term Long Term Coefficient t-stat Coefficient t-stat Coefficient t-stat Coefficient t-stat Direct effects
Log ∆ real GDP -0.484*** -2.394 -0.285 -1.416 -0.270* -1.659 -0.984 -0.172
Short term debt/GDP 0.083 0.584 0.449*** 3.056 -0.016 -0.137 -0.003 -0.001
Credit to GDP 0.071*** 4.279 0.087*** 5.340 0.027* 1.667 0.117 0.122
%∆(private debt/GDP) 0.471*** 3.644 0.593*** 4.714 0.223** 2.191 0.792 0.217
%∆(public debt/GDP) 0.247*** 4.364 0.172*** 2.878 0.114 0.686 0.560 0.056
Log ∆ housing prices -0.336*** -2.878 -0.321*** -2.618 0.177 0.796 1.351 0.046
Indirect effects Log ∆ real GDP -0.266** -2.092 1.814 1.254 -0.412 -0.642 -3.715 -0.038 Short-term debt/GDP 0.046 0.566 7.309*** 6.197 0.530 0.796 2.503 0.053 Credit/GDP 0.039*** 3.108 -0.166 -1.430 0.128 0.730 0.974 0.060 %∆(private debt/GDP) 0.259*** 2.811 4.380*** 4.735 0.412 0.594 2.890 0.047 %∆(public debt/GDP) 0.135*** 3.111 0.904** 2.570 1.815 0.583 9.171 0.054
Log ∆ housing prices -0.184*** -2.439 -1.104 -1.326 3.804 1.098 25.607 0.052
by one percentage point would in one country would lead to an increase of the FSI of on average, 0.028 percentage point. In the short term, credit to GDP thus has to increase around 35 percentage points to result in a one percentage point increase of the financial stress of a country, ceteris paribus. Such movements of credit in the short term only happen very infrequently, for instance in Ireland in 2009/2010 where credit to GDP fell from 168% to 133% within one year. On the other hand, using the SAR (SDM) model, an increase in the growth of private debt of one percentage point in all countries would not only increase their own FSI by 0.471 (0.593) percentage point, but would also lead to an increase of financial stress of all the others by 0.259 (or even 4.380) percentage points. That is, when all countries have increase private debt levels, the FSI would increase by 0.73 (4.973) percentage points, ceteris paribus. The large point estimate of the indirect effect in the SDM model is possibly due to a loop of higher order indirect effects. In the case of the dynamic model, the long-term direct and both long and short-term indirect effects of the dynamic model are all insignificant.
When looking again at Table 4, especially the indirect effect of short-term debt in the SDM model attracts attention, as the coefficient is very big. This can be interpreted as follows: the spatial weights matrix W shows that Italy has a big impact on Spain (0.609), due to the relatively large Spanish holdings of Italian government debt. As a result, if the level of short-term debt to GDP in Italy increases by one percentage point, the FSI in Spain will increase by 7.309*0.609 = 4.451 percentage points. The stress level of Spain would increase four times as much as the rise of the Italian public debt level.
affected by public debt ratios of France, Germany and Spain, and Portugal is most influenced by Spain (but not the other way around). What stands out is the public debt to GDP ratio that is also very significant as an indirect effect for the non-dynamic models, meaning that an increase of the public debt to GDP ratio of one country not only increases its own stress level, but also the financial stress in another country.
5.3 Regression results with two regimes
As the period is characterized by a crisis (2009-2013) and non-crisis period (2014-2018), the coeffi-cient of the explanatory variables might vary in these periods. Moreover, dividing the sample into two regimes enables one to distinguish between interdependence effects and spillovers. As inter-dependence effects are links that exist at all times, we expect them to be present in the tranquil period as well. That is, the coefficients of the same variable are expected to have more or less the same sign, size and significance as before. Spillovers, on the other hand, arise after a shock and can only be detected in the crisis period. First, the results will be displayed with the constant spatial weights matrix W. Nevertheless, it might very well be the case that the sovereign debt holdings are significantly different in crisis and tranquil periods, which is why the period with two separate W’s should be estimated as well (this will be done later).
The two regimes can be estimated simultaneously when including a dummy for the tranquil period. That is, all the quarters after 2013q4 get a dummy equal to zero, and the quarters before 2014q1 get a dummy equal to one. As a result, the number of explanatory variables will be expanded by three (each variable multiplied by the dummy, the W and multiplied by both the dummy and W). Using the current six explanatory variables, this leads to 24 variables. The results of the two regime regression with a SDM model can be found in Table 5 above.
Table 5: Estimation results of SDM model with two regimes 2009Q1-2018Q3
Variable Coefficient t-stat Relative
contribution (%) Intercept 0.173 Crisis -0.312 -1.112 Crisis period 2009Q1-2013Q4 Log ∆ real GDP * Dt 0.096 0.571 0.25 Short-term debt/GDP * Dt -0.038*** -2.649 0.26 Credit/GDP * Dt 0.506* 1.926 37.90 %∆ (private debt/GDP) * Dt 0.256* 1.858 0.75 %∆ (public debt/GDP) * Dt -0.659*** -2.721 6.36
Log ∆ housing prices * Dt 1.528 1.169 6.70
W * log ∆ real GDP * Dt 0.243 0.353 0.28
W * short-term debt/GDP * Dt 0.228** 2.155 1.37
W * credit/GDP * Dt -0.370 -0.495 30.39
W * %∆ (private debt/GDP) * Dt 0.178 0.434 0.174
W * %∆ (public debt/GDP) * Dt 1.699** 2.079 5.38
W * log ∆ housing prices * Dt -0.176** -2.369 0.23
W * FSI * Dt 0.493*** 9.519 9.67 Tranquil period 2014Q1-2018Q3 Log ∆ real GDP 0.039 0.212 0.37 Short-term debt/GDP 0.120*** 5.291 2.38 Credit/GDP 0.145 0.877 36.07 %∆ (private debt/GDP) -0.062 -0.499 0.97 %∆ (public debt/GDP) 0.082 0.432 1.46
Log ∆ housing prices 0.400 1.027 4.63
W * log ∆ real GDP 2.277*** 3.130 10.92
W * short-term debt/GDP -0.425*** -3.288 3.74
W * credit/GDP 0.285 0.554 18.66
W * %∆ (private debt/GDP) 0.000 0.000 0.00
W * %∆ (public debt/GDP) -0.659 -1.023 8.56
W * log ∆ housing price -1.125 -0.800 7.24
W * FSI 0.164*** 3.131 5.00 Number of observations 702 R2 0.7091 ¯ R2 0.6897 σ2 0.0035 Log-likelihood 985.314
to interpret. Also the exogenous interaction effects of real GDP are positive, and in the case of the tranquil period also rather big. The only possible explanation for this is that in times of economic prosperity, increasing growth levels of other countries, ceteris paribus, are due to better technology or highly skilled workers. The respective country does not experience this increase in GDP, which then could cause the financial stress level to increase. Whether this point is valid is debatable. Eventually, the economic significance and the magnitude of real GDP is very small, so the model is not dominated by this effect.
The crisis coefficient of table 5 is negative but not statistically significant. One can see that the spatial lag is in both cases significant, but has a slightly higher coefficient during the tranquil period: this would imply that an increase in the stress of one country has more effect on others when there is not already financial stress. It can perhaps be argued that the first shock before a crisis has the most impact. What is certain is that there is evidence for interdependence effects along the sovereign debt channel, as the W*FSI is always positive and significant. The financial stress transmission link between countries is thus present at all times, which points at the existence of both interdependence effects and spillovers.
Another interesting aspect that is displayed in Table 5 is the big and significant sign for the exogenous spatial lag of the growth rate of public debt to GDP in crisis time, which can be seen as a spillover effect. That is, during crises the growth rate of public debt to GDP affects countries that are linked via the sovereign debt channel. Other countries’ debt levels affect on average the respective country even more than their own public debt level, which has now gotten a negative sign. Possibly this negative sign is due to the counter-cyclical fiscal policy that a government should ideally pursue during a crisis, i.e. lowering the debt level is in this case not very helpful in recovering an economy.
