Asset Price Bubbles and Systemic Risk

Transcription

1 Asset Price Bubbles and Systemic Risk [Please do not quote or circulate without permission] Markus Brunnermeier Princeton University, NBER, CESifo, and CEPR Isabel Schnabel University of Bonn, MPI Bonn, CESifo, and CEPR March 15, 2017 Simon Rother University of Bonn and GSEFM Frankfurt Abstract We assess the effects of stock market and real estate bubbles on systemic risk. Analyzing a broad sample of banks in 17 OECD countries over the period 1987 till 2015, we find support for two frequently formulated - yet largely untested - conjectures in the literature. First, asset price bubbles substantially threaten financial stability. The burst of a bubble leads to an increase in systemic risk by 12 to 17 percent, where we measure systemic risk by the change in the conditional value at risk, CoVaR. Moreover, already emerging bubbles increase systemic risk, though to a lesser extent. Second, the financing of a bubble affects the size of the effects. In addition to high loan growth, we find further bank characteristics such as a high maturity mismatch and a large bank size to drive the size of the effects. Together, these bank characteristics can raise the increasing effect of asset price bubbles on systemic risk to at most 40 percent. While stock market bubbles are more harmful than real estate bubbles at average levels of loan growth, maturity mismatch, and bank size, the ordering is reversed at elevated levels of these bank-level variables. The estimated effects are neither driven by a small group of countries nor limited to specific time periods within our sample. Keywords: Asset price bubbles, systemic risk, financial crises, credit booms, CoVaR. JEL-Classification: E32, G01, G12, G20, G32. We gratefully acknowledge financial support from the Frankfurt Institute for Risk Management and Regulation (FIRM). Princeton University, JRR-Building, 20 Washington Road, Princeton, NJ 08544, USA, markus@princeton.edu, telephone: (609) University of Bonn, Institute for Finance and Statistics, Adenauerallee 24-42, Bonn, Germany, simon.rother@uni-bonn.de, telephone: University of Bonn, Institute for Finance and Statistics, Adenauerallee 24-42, Bonn, Germany, isabel.schnabel@uni-bonn.de, telephone:

2 1 Introduction Financial crises are often accompanied by a boom-and-bust cycle of asset prices (Borio and Lowe, 2002; Kindleberger and Aliber, 2005). The effects of bursting asset price bubbles on the financial system can be considerable, yet vary widely depending on the specific circumstances and bubble characteristics (Brunnermeier and Schnabel, 2016). Therefore, policy makers are eager to understand what determines the financial system s vulnerability to asset price bubbles. However, the channels through which asset price bubbles affect systemic risk have hardly been studied in a systematic fashion. When an asset price bubbles bursts, systemic risk is likely to increase. The Global Financial Crisis has shown that sizeable disturbances can occur even if the burst of the bubble initially affects only a small market. At the time of the burst of the bubble, the US subprime mortgage market accounted for only 4 percent of the US mortgage market (Brunnermeier and Oehmke, 2013, p. 1223). The initial shock was amplified by the materialization of imbalances that had built up in the financial sector and ultimately depressed growth worldwide (Brunnermeier, 2009). However, asset price bubbles may not only trigger the materialization of financial imbalances. They can also cause the buildup of these imbalances. Rising prices increase the value of borrowers collateral (Bernanke and Gertler, 1989) and the liquidity of assets (Kiyotaki and Moore, 2005), causing banks to increase lending and to reduce liquidity provisions. 1 If the increases in asset prices are caused by the emergence of a bubble and if banks are unaware of this emergence, the bubble can lure banks into excessive lending and inadequate liquidity management. There is, however, no systematic empirical evidence which factors determine the extent of imbalances building up or the fallout of bursting bubbles. We fill this gap by empirically analyzing the effects of asset price bubbles on systemic risk. 2 The papers most closely related to our study are those by Schularick and Taylor (2012) and Jordà, Schularick, and Taylor (2013, 2015a,b). Using 1 Shin (2008) provides a model considering demand-side and supply side effects of asset prices on banks balance sheets and the ensuing effects on risk in the financial sector. 2 We define systemic risk as any risk threatening to impair the functioning of the financial system such that real effects are likely to occur. An asset price bubble refers to the difference between the market price of an asset and the price justified by its fundamental properties. 1

3 historical data on macroeconomic variables, these studies primarily analyze the predictive power of asset price bubbles, credit, and further factors with regard to the likelihood and costliness of financial crises. In contrast, our analysis is conducted on the bank level, which has two major advantages. First, we can study the channels through which asset price bubbles affect systemic risk. We focus on the role of loan growth, maturity mismatch, leverage, and the size of a financial institution in contributing to the build-up of systemic risk. We can thus assess the importance of developments in the banking sector for its vulnerability to asset price bubbles. These developments also provide an explanation for the large heterogeneity of the effects of bursting asset price bubbles across bubble episodes. Additionally, the analysis of channels is useful for policy makers and regulators designing a more targeted regulatory framework. Second, the bank-level data allow for better identification. Rather than providing correlations on the macro level, we move closer to an analysis of causal effects. We focus on systemic risk contributions at the bank level rather than on the occurrence of financial crises, which allows us to better exploit the available information. For instance, the continuous measure of systemic risk accounts for periods of high risk in the financial sector that did not result in a crisis. A simple crisis dummy would miss such periods. Since asset price bubbles both cause the build-up of systemic risk and act as a trigger for the materialization of financial imbalances, our econometric setup allows for heterogeneous effects across bubble stages. Specifically, we analyze the effects during the emergence and during the collapse of a bubble. Jordà, Schularick, and Taylor (2015b) suggest that real estate bubbles are more harmful than stock market bubbles when accompanied by a lending boom. Brunnermeier and Schnabel (2016) emphasize the importance of the financing of a bubble rather than the asset class in which it occurs. Therefore, we analyze the role of loan growth and allow for heterogeneous effects across asset classes. Our results are in line with the common conjecture that asset price bubbles pose a threat to financial stability. Specifically, our results show that the burst of an asset price bubble leads to a 12 to 17 percent increase in systemic risk compared to non-bubble times. However, this effect is not limited to the turmoil following the burst of a bubble, but to some extent already exists during its emergence. The degree to which asset price bubbles threaten financial stability depends on 2

4 banks behavior during a bubble episode. Especially high loan growth, a large maturity mismatch, and a large bank size contribute to increasing the effect of asset price bubbles on systemic risk to up to 40 percent. Consequently, regulation does not necessarily need to target the bubble itself. Ensuring the resilience of the financial system can significantly decrease its vulnerability to asset price bubbles. While the size of the effect of bubbles differs across asset classes, it is significant for both stock market and real estate bubbles. From a financial stability perspective, a focus on the latter thus does not appear advisable. Likewise, policies aimed at preventing financial turmoil resulting from an asset price bubble should not focus solely on the bust period of the bubble. Instead, the risks building up in the financial system should ideally be counteracted early on. The key challenges for our analysis are threefold. First, bubble episodes need to be identified. It is likely that those asset price bubbles that cause deeper turmoil when bursting attract more attention and therefore are prevalent in the literature. Relying on such episodes might lead us to overestimate the effect of asset price bubbles on systemic risk. To prevent this sample selection bias, we estimate bubble episodes instead of relying on the episodes famous in the literature. We base our estimations on the Backward Sup Augmented Dickey-Fuller (BSADF) approach introduced by Phillips, Shi, and Yu (2015a,b). This approach implicitly identifies bubble episodes by systematically searching subsamples of price (or price-to-dividend/rent) data for explosive episodes. The main concern with respect to our bubble identification strategy is market fundamentals driving the booms and busts that are identified as bubble episodes. We therefore crosscheck our estimation results with bubble episodes identified based on an extensive literature search. All episodes prevalent in the literature are also identified by our estimations. Concerns regarding a wrong classification of certain episodes can thus only refer to potentially identifying too many bubble episodes. As we find asset price bubbles to be associated with increased systemic risk, falsely labeling episodes free of significant financial repercussions as bubbles would thus - if anything - lead to an underestimation of the true effect. The second challenge lies in the quantification of the concept of systemic risk. We apply the CoVaR (conditional value at risk) measure introduced by Adrian and Brunnermeier (2016). This measure estimates institution-specific contributions to systemic risk and allows us to conduct the 3

5 analysis on the bank level. 3 Intuitively, the measure signals high systemic risk if many financial institutions simultaneously exhibit large equity return losses unexplained by general stock market and interest rate developments. The identification of causal effects constitutes the third challenge. By controlling for the relevant institution-specific and macroeconomic factors, we are confident to exclude the most obvious sources of endogeneity. Simultaneity would threaten causality if systemic risk at the bank level had an effect on asset price bubbles. Bad news about an unstable financial system might end investors optimism and thereby lead to the burst of a bubble or slow down its emergence. 4 There is no plausible scenario in which rising systemic risk would increase the size of a bubble. As we find a positive effect of asset price bubbles on systemic risk, simultaneity - if actually present - would thus lead to an underestimation of the true effect. The remainder of the paper is structured as follows. Section 2 briefly discusses how asset price bubbles can affect systemic risk. Section 3 elaborates on the identification of bubble episodes, the estimation of CoVaR, and the dataset used in the main analyses. Section 4 presents and discusses the empirical results. Section 5 contains a brief discussion of policy implications and concludes. 2 Systemic Risk and Asset Price Bubbles To be considered systemic, predominant definitions of systemic risk require a risk to threaten the functioning of large parts of the financial system. An impairment of such large parts can generally occur in two ways. First, a shock can simultaneously hit many institutions, directly limiting the functioning of the financial system. A high common exposure of financial institutions to sources of shocks due to e. g. 3 The Option-iPoD (Capuano, 2008), the DIP (Huang, Zhou, and Zhu, 2009), the measures introduced in Segoviano and Goodhart (2009) as well as in Gray and Jobst (2010), SES (Acharya, Pedersen, Philippon, and Richardson, 2010; Acharya, Engle, and Richardson, 2012), CoJPoD (Radev, 2013, 2014), realized systemic risk beta (Hautsch, Schaumburg, and Schienle, 2015), and SRISK (Acharya, Engle, and Richardson, 2012; Brownlees and Engle, 2015) also allow the estimation of systemic risk contributions. Especially SRISK appears equally appealing for our purposes. In aggregate, both CoVaR and SRISK evolve similarly over time such that we expect the effects of asset price bubbles to be robust with respect to this alternative measure. Nevertheless, we plan to assess the robustness of our results with respect to the applied measure at later stages of our work. 4 Abreu and Brunnermeier (2003) provide a model in which even news with relatively small informational content can simultaneously induce agents to sell off assets, thereby leading to a sudden collapse of a bubble. 4

6 lending to the same industries, lending to the same geographic areas or corresponding proprietary trading (Acharya, 2009) thus constitute a systemic risk. Asset price bubbles are such a source of a shock, as they will collapse at some point. If a sufficiently large share of the financial system is either directly invested into an asset exhibiting a bubble or indirectly exposed to the bubble e. g. by lending to industries exposed to it, the asset price bubble leads to increased systemic risk. Moreover, the supposedly good development in a sector subject to the emergence of a bubble can induce financial institutions to increase their corresponding exposures, thereby worsening the consequences of a subsequent shock and increasing systemic risk even further. Second, a shock can initially affect only a few institutions (or even only a single one), but then get propagated and amplified through the system. Direct contractual linkages such as interbank lending, contingent claims, and securitization are channels for such a contagion (cf. Rochet and Tirole, 1996; Allen and Gale, 2000) and thus contribute to systemic risk. As previously argued, an asset price bubble can lead to inadequate liquidity management and excessive lending. To the extent to which this excessive lending takes place on the interbank market, a bubble also contributes to systemic risk via the direct contractual linkages. Through liquidity spirals, shocks can get propagated through the financial system even in the absence of direct contractual linkages. The spirals are triggered by a shock inducing a financial institution to raise additional liquidity. Liquidity may be raised by asset sales which drive down the corresponding market prices. As a consequence, other financial institutions encounter losses on existing positions, increase margin requirements, or tighten their risk management. Through any of these three effects, further pressure on financial institutions liquidity arises, leading to fire sales and thereby completing the liquidity spiral (cf. Gârleanu and Pedersen, 2007; Brunnermeier and Pedersen, 2009; Diamond and Rajan, 2011). Asset price bubbles can set in motion liquidity spirals by causing the initial losses when bursting. Moreover, the bubbles can cause spirals into the opposite direction when emerging, leading to insufficient liquidity provision, thereby increasing systemic risk already before the burst. 5

7 3 Data We construct a dataset containing monthly observations on 1,438 financial institutions located in 17 countries, covering the period 1987 to Our results are neither driven by a specific country nor by a specific time period (cf. the robustness checks in Section 4.3). The dataset includes estimates of systemic risk contributions of financial institutions as well as data on their leverage, size, maturity mismatch and loan growth, estimates of variables indicating the emergence and bust phase of real estate and stock market bubbles on a country level respectively, and information on real GDP growth, investment-to-gdp growth, credit-to-gdp growth, inflation, and interest rates. Tables 1 and 2 provide summary statistics. The subsequent exposition provides more detailed information on the dataset. First, the construction of the bubble indicators is described. Second, the estimation of CoVaR is discussed. Third, details on the final dataset including balance sheet data and macroeconomic control variables are provided. 3.1 The Bubble Indicators We identify bubble episodes applying the BSADF approach introduced in Phillips, Shi, and Yu (2015a,b). It outperforms all comparable approaches in terms of size and power in case of multiple bubble episodes within a dataset (Breitung and Homm, 2012; Phillips, Shi, and Yu, 2015a). 6 The BSADF approach applies sequences of ADF tests to systematically changing fractions of samples of price data in order to identify episodes of explosiveness. The procedure of analyzing these subsamples accounts for the possibility of several asset price bubbles emerging in rapid succesion, which is difficult to distinguish from stationary behavior. Section A of the appendix provides a detailed description of the estimation procedure. We estimate real estate bubbles on a country level using a dataset on real house prices provided by the OECD. The dataset contains quarterly observations on real estate prices and rents over the 5 Table C.1 in Section C of the appendix provides an overview of observations per country and per year, respectively. 6 The approach is applied frequently (e. g. Gutierrez, 2013; Bohl, Kaufmann, and Stephan, 2013; Etienne, Irwin, and Garcia, 2014; Jiang, Phillips, and Yu, 2015). Comparable approaches are suggested in Kim (2000), Kim and Amador (2002), Busetti and Taylor (2004), Phillips, Shi, and Yu (2011) and Breitung and Homm (2012). More sophisticated but not necessarily more reliable approaches are suggested by Al-Anaswah and Wilfling (2011), Asako and Liu (2013), and Shi and Song (2014). 6

8 period 1976 to Stock market bubbles are estimated using monthly observations of countryspecific MSCI indices over the period 1973 to 2016 obtained from Datastream. 7 The MSCI indices used are country-specific stock market indices computed based on a single methodological framework. Each of them covers 85 percent of a country s total market capitalization. Consequently, the indices are comparable across countries and have a fairly broad coverage without containing highly illiquid values for which a reliable pricing is problematic. The available data allows us to simultaneously estimate real estate bubbles and stock market bubbles for 17 OECD countries. The choice of countries included in our sample thus is exclusively based on data availability. The BSADF approach identifies the beginning and end of each bubble episode. We use the results of the approach to construct 4 binary variables per country which indicate episodes in which a real estate or stock market bubble emerges and episodes in which it bursts. The boom and bust phases are determined based on the peak of the underlying price series during each bubble episode, respectively. Denoting the beginning of bubble episode k in country c by τe k,c, the corresponding end by τ k,c f, and the point in time at which the price series reaches its maximum by τm k,c, 1 if t [τe k,c, τm k,c ] for any k Bubble Boom c,t = 0 else 1 if t ]τm k,c, τ k,c f ] for any k Bubble Bust c,t = 0 else, (1). (2) We apply cubic spline interpolations to adjust the quarterly real estate bubble indicators to the monthly frequency used in the main analyses. Table 1 and Figure C.1 in the appendix provide an overview of the estimation results. 7 The data used to estimate the bubble episodes goes back further than the data used in the main analysis. The larger historical coverage improves the properties of the BSADF test. Its size distortions vary between 1 and 2.2 percentage points for sample lengths between 100 and 1,600 observations. The evolution of the size distortions over increasing sample lengths is U-shaped. The power of the test is reported with 0.7 for T=100, 0.9 for T=200 and approaching 1 for T=1600 (Phillips, Shi, and Yu, 2015b). We apply the approach to stock market and real estate data with sample lengths between 155 and 507 periods. 7

9 Table 1: Descriptive Statistics on Bubble Episodes The statistics are computed for the dataset used in the main analyses, which includes 17 OECD countries and covers the period 1987 to Figure C.1 in the appendix provides an overview of bubble episodes estimated per country. Differences in the number of emergences and busts of bubble episodes are due to bubbles which take place only partly during the sample period. As argued in the introduction, confusing booms and busts driven by market fundamentals with asset price bubbles would - if anything - bias our results towards zero. 8 We perform an additional robustness test by normalizing real estate data with rent data obtained from the same OECD dataset. We thus include the most important market fundamental in the estimation. While the precise start and end of identified bubble episodes varies slightly, the bubble estimation results are generally highly robust towards this alternative (cf. Figures C.1b and C.1c in the appendix). 3.2 Systemic Risk Contributions CoVaR measures the additional stress in some part of the financial system associated with another part of the financial system experiencing distress. Specifically, we quantify institution-specific contributions to the overall level of systemic risk by estimating the additional stress in the entire financial system associated with a single institution experiencing distress. The estimates rely on tail dependences between losses in the market value of equity of individual institutions and those of the entire financial system. When estimating these dependences, general risk factors are 8 We find all well-known bubble episodes identified based on an extensive literature search also identified by our estimations. Concerns about a false classification of certain episodes can thus only refer to potentially identifying too many bubble episodes. Most asset price bubbles become famous because of causing turmoil when bursting. As we find asset price bubbles to be associated with increased systemic risk, falsely labeling episodes free of significant financial repercussions as bubbles would thus lead to an underestimation of the true effect. 8

10 controlled for. The estimation strategy follows Adrian and Brunnermeier (2016). Unlike Adrian and Brunnermeier (2016), we estimate CoVaR in a multi-country setup such that we cannot exclusively rely on control variables for the US market. Instead, we define four different financial systems, North America, Europe, Japan, and Australia and use a distinct set of state variables for each system. Details on these variables as well as the estimation strategy are provided in Section B of the appendix. To construct the sample, we collect market equity data from Datastream for all listed financial institutions located in the 17 countries in our sample. As we need balance sheet data in the main analyses, we include only those listed institutions for which such data is reported in the form of consolidated statements in Bankscope. Additionally, banks with less than 260 weeks of nonmissing equity market observations are discarded to ensure efficiency of the CoVaR estimations. This approach leaves us with monthly estimates of CoVaR for 1,438 financial institutions. The mean of CoVaR equals 1.96 such that the distress in some institution is associated with an average increase in the financial system s conditional VaR by 1.96 percentage points. Table 2 provides further summary statistics. Figure C.2 in the appendix provides an overview of the evolution of the aggregate CoVaR in each financial system over time. 3.3 Further Variables and Final Dataset We obtain data on leverage, total assets, maturity mismatch and loan growth from Bankscope. The leverage [Total Assets/Equity], size [log(total Assets)] and maturity mismatch [(Short-Term Liabilities - Short-Term Assets)/Total Assets] are known to drive an institutions systemic risk contribution (cf. Adrian and Brunnermeier, 2016). We additionally shed light on the role of loan growth [ log(loans)] as credit fueled bubbles are perceived to be particularly harmful (Jordà, Schularick, and Taylor, 2015b; Brunnermeier and Schnabel, 2016). We apply cubic spline interpolations to obtain monthly observations and winsorize the data at the 1 percent and the 99 percent level to deal with extreme values of leverage of institutions on the brink of default and extremely high loan growth of institutions starting from a very low level of loans. To be consistent, we also winsorize size and maturity mismatch. The results are robust towards the use of the non-winsorized version of these two variables. 9

11 We obtain data on credit to the private non-financial sector from the BIS, data on investment, 10-year government bond rates, the CPI and GDP from the OECD, and data on policy rates from Datastream and national Central Banks. Variables at quarterly frequency are adjusted to monthly frequency by cubic spline interpolations. We include credit-to-gdp growth [ log(credit/gdp)] to control for potentially harmful credit booms on an aggregate level. We use credit to the private non-financial sector which is more likely to actually fuel the bubble. Investment-to-GDP growth [ log(investment/gdp)] controls for the use of credit (investment vs. consumption; cf. Schularick and Taylor (2012)). Real GDP growth [ log(realgdp)] naturally affects the stability of the financial system and may influence asset price bubbles via investors expectations. The inflation rate [ log(cpi)] has been identified as a factor contributing to the occurrence of financial crises (Demirgüç-Kunt and Detragiache, 1998) and appears to play a role especially for the emergence of bubbles (Brunnermeier and Schnabel, 2016). The 10-year government bond rates [in logs] account for a potentially relevant sovereign-bank nexus. In robustness checks, we use monetary policy rates as extended periods of low rates can cause the build-up of risks in the financial sector by driving banks into overly risky investments and inadequate risk buffers (Diamond and Rajan, 2012, also see the discussion in the context of the recent financial crisis in Deutsche Bundesbank (2014)). Our results are robust towards the choice of interest rate. Table 2: Summary Statistics Size and Interest Rate enter the regressions in logs. Interest Rate refers to 10-year government bond rates. For descriptive statistics on the bubble episodes see Table 1. 10

12 4 Results To analyze the effect of asset price bubbles on systemic risk, we regress the systemic risk contributions ( CoV ar) of institution i at time t on bank fixed effects (α), the 4 variables indicating the episodes of emergence and bust of stock market and real estate bubbles (Bubble) in country c, the 4 lagged bank-level variables leverage, size, maturity mismatch and loan growth (H), interaction terms, and the lagged macroeconomic control variables (M): CoV ar i,t = α i + βbubble c,t + θh i,t 1 + λbubble c,t H i,t 1 + γm c,t 1 + u i,t. (3) A larger value of CoVaR corresponds to a higher systemic risk contribution. A positive sign of all coefficients included in β would thus be in line with a destabilizing effect of asset price bubbles on financial stability. Standard errors are clustered on the bank and country time level. The latter corresponds to the same level at which the main explanatory variables, the bubble indicators, have variation. Clustering on the bank and country level (as opposed to the bank and country time level) does not alter the estimated significance levels. We do not include time fixed effects as they would capture global factors only and thereby alter the interpretation of the estimated effects in an undesirable way. To clarify the argument, suppose we had only two countries in the sample and both countries would exhibit a bubble at the same time. In specifications with global time fixed effects, the coefficients on the bubble indicators would capture effects relative to the global average. That is, in the country with a weaker effect of the bubble, the coefficients would signal a negative effect (relative to the global average). However, we do not want to estimate such relative effects, but the absolute effect on systemic risk. We confirm the results with respect to the interaction terms of bubble indicators and bank-level variables in specifications with country time fixed effects. The subsequent exposition of results starts with the exploration of the effect of the bubble episodes. Afterwards, we shift focus towards the relevance of bank-level developments during the bubble episodes. The section concludes with a discussion of the analysis and additional robustness checks. 11

13 4.1 Asset Price Bubbles Effect on Systemic Risk To illustrate the correlations, CoVaR is first regressed on the bubble indicator and bank fixed effects only. The coefficient of each of the four bubble indicators is positive (cf. Table 3, Column 1). In line with the hypothesis, asset price bubbles are associated with increased systemic risk. We find such a significant increasing association between asset price bubbles and systemic risk for 12 out of the 17 countries in our sample. The relationship is insignificant in 4 countries and negative only in a single country. Despite this encouraging robustness of the effect across countries, we do not attempt to perform further analysis on a per country level, as the number of bubble episodes per country is very limited (cf. Table 1). When adding the macroeconomic control variables, the bubble indicators coefficients change rather slightly (cf. Table 3, Column 2). The general relation between asset price bubbles and systemic risk prevails. Including the demeaned bank-level variables has a considerably larger effect on the bubble indicators coefficients. The effect of the emergence of real estate bubbles now is insignificant (cf. Table 3, Column 3). The coefficients on the three other bubble indicators are affected only quantitatively, yet also significantly. 9 In line with the results in Adrian and Brunnermeier (2016), we thus find systemic risk to be significantly driven by bank characteristics. In Column 4 of Table 3, we report the results of the baseline regression formulated in equation (3). The inclusion of the interaction terms has almost no effect on the coefficients of the bubble indicators. As demonstrated in the next subsection, the developments on the bank level during the emergence of a bubble are nevertheless highly relevant. Likewise, it is demonstrated that real estate bubbles can pose a severe threat to financial stability already when emerging. To assess the economic significance of the results, consider the effect of a stock market bust. This bust ceteris paribus leads to an increase in the additional financial system s VaR associated with a single institution s distress by 0.36 percentage points. Intuitively, the coefficient reflects how much more a single institution s distress endangers the functioning of the financial system during the 9 The inclusion of bank-level variables reduces the sample size by about 50 %. We re-estimate the regressions without bank-level variable using only the observations for which bank-level variables are available. The results confirm that the differences in coefficients between the regressions in Columns 3 and 4 in Table 3 are only partly due to the changing sample. 12

14 Table 3: The Effect of Asset Price Bubbles on Systemic Risk Dependent variable: systemic risk estimated by CoVaR (cf. Appendix B).... Boom and... Bust indicate the respective bubble phases estimated based on the BSADF approach (cf. Appendix B). Macro variables are credit-to-gdp growth, investment-to-gdp growth, 10-year government bond rates, the inflation rate, and real GDP growth. Bank-level variables consist of leverage, size, maturity mismatch, and loan growth. Coefficients on bank-level variables as of regression (5) are displayed in Table 4. Standard errors are clustered at the bank and country time level. ***, **, * indicate significance at the 1%, 5% and 10% level. P-Values are in parentheses. episode of the burst of a stock market bubble. Since the effect applies to all institutions within a country at the same time, we can speak of an increasing effect on systemic risk, not just an effect on systemic risk contributions. The increase in systemic risk caused by the burst of a stock market bubble thus corresponds to 17 % (=0.36/2.08) compared to bubble-free times. The corresponding increase caused by the burst of real estate bubbles amounts to 12 percent. The burst of asset price bubbles thus significantly threatens to impair the functioning of the financial system. The effects of the macroeconomic control variables (cf. Table C.2 in the appendix) are all in line with economic theory. Credit booms on the aggregate level and inflation lead to increased systemic risk. GDP growth and investment-to-gdp growth are both negatively associated with systemic risk. The effect of the 10-year government bonds is insignificant. 13

15 4.2 The Role of Bank Characteristics The results presented in the previous subsection establish the harmful effect of asset price bubbles on financial stability. Additionally, they point towards the importance of bank-level developments for the size of this effect. Both the harmful effect of the bubbles as well as the dependence on developments within the financial sector are in line with the theory discussed in Section 2. Asset price bubbles are a source of a shock which itself threatens financial stability. Additionally, they can lure banks into behavior threatening the stability of the financial system, thereby worsening the situation. The degree of financial turmoil should thus depend on both the existence of the bubble itself and the state of the financial system. The subsequent exposition further analyses the role of bank-level developments. Table 4.2 reports the coefficients on the bank-level variables estimated in our baseline regression (cf. Equation (3) and Table 3, Column 4). In line with Adrian and Brunnermeier (2016), the systemic risk contributions increase with the size of an institution. During most of the bubble phases, this relationship is more pronounced. Similarly, leverage generally increases the systemic risk contributions. The effect is more pronounced during the emergence of real estate bubbles, but turns insignificant during the other bubble phases. Loan growth generally appears to be beneficial for financial stability if it occurs in bubble-free times, but becomes problematic in combination with the burst of real estate bubbles. The effect of the maturity mismatch also depends on the presence of a bubble. The results on the interaction terms are robust towards the inclusion of country time fixed effects. While we do emphasize the general importance of bank characteristics for the degree of harmfulness of asset price bubbles, we take our results regarding the role of a specific variable with a sense of caution. Our dependent variable is an estimate of systemic risk. While the measure we rely on is widely accepted, it is not the only one available. For instance, SRISK (Acharya, Engle, and Richardson, 2012; Brownlees and Engle, 2015) appears to be an equally attractive alternative for the estimation of systemic risk contributions. In the aggregate, this measure shows a similar evolution over time as CoVaR. However, SRISK is known to be driven by the variables we analyze to different extents. While CoVaR e. g. generally reacts more to changes in the size of banks, 14

16 Table 4: Coefficients on Bank-Level Variables The table displays the coefficients of lagged bank-level variables and their interactions with the bubble indicators from the baseline regression (cf. equation (3)). The coefficients on further variables are provided in Table 3, column 4. Standard errors are clustered at the bank and country time level. ***, **, * indicate significance at the 1%, 5% and 10% level. P-Values are in parentheses. SRISK is more driven by leverage. The size of the effects of bank-level variables on systemic risk should thus not be over-interpreted. 10 So far, bank-level variables entered regressions demeaned. For the regressions reported in Table 5, we subtract the value of a certain percentile of the distribution of each of the bank-level variables from themselves. This de-percentilizing changes the interpretation of the bubble indicators. While they previously referred to the effects of asset price bubbles for a bank of average size, leverage, maturity mismatch and loan growth, the conditioning now refers to a certain percentile. Moving from left to right through the columns of Table 5, the coefficients are valid for increasingly large banks which, at the same time, have increasingly high leverage, maturity mismatch, and loan growth. The effect of asset price bubbles on systemic risk increases with the percentile on which we condition. The higher the size, loan growth, leverage, and maturity mismatch banks are, the more asset price bubbles threaten financial stability. These results can also be seen as an assessment of the economic significance of the effects of bank characteristics. If accompanied by unfavorable developments on the bank level, real estate bubbles can be harmful already during their emergence (cf. Table 5, Columns 4 and 5). The harmful effects of asset price bubbles are thus not limited to the turmoil induced by the burst of the bubble. Instead, they are 10 We intend to provide a more complete picture by assessing the robustness of our results with respect to the chosen systemic risk measure ( CoVaR vs. SRISK) at later stages of the project. 15

17 Table 5: Importance of Bank Characteristics Dependent variable: systemic risk estimated by CoVaR (cf. Appendix B).... Boom and... Bust indicate the respective bubble phases estimated based on the BSADF approach (cf. Appendix B). The coefficients report the effect of the bubble phases given that all bank-level variables are at their indicated percentile. Bank-level variables consist of leverage, size, maturity mismatch, and loan growth. Macro variables are credit-to-gdp growth, investment-to-gdp growth, 10-year government bond rates, the inflation rate, and real GDP growth. Standard errors are clustered at the bank and country time level. ***, **, * indicate significance at the 1%, 5% and 10% level. P-Values are in parentheses. present and can be measured already before. Generally, the effect of an asset price bubble is more pronounced during the period of its burst compared to the time of its emergence. The burst of an asset price bubble can increase systemic risk by up to 40 % (=0.83/2.08). Parts of the literature (e. g. Jordà, Schularick, and Taylor, 2015b) suggest that real estate bubbles are more harmful than their stock market counterparts. Our results do not support such a general ordering. Instead, we find real estate bubbles to be more harmful only if simultaneously accompanied by a large size of banks, high loan growth, high maturity mismatch and high leverage. If banks show more favorable developments during bubble episodes, stock market bubbles appear to be more harmful than real estate bubbles (cf. Table 5). These results are in line with a higher importance of developments within the financial sector compared to a bubble s asset class, which is advocated in Brunnermeier and Schnabel (2016) with respect to loan growth. 16

18 4.3 Discussion of the Analysis and Further Robustness Checks At the beginning of Section 4, we argued that time fixed effects would capture developments on a global level only, thereby changing the interpretation of coefficients to a relative one. The robustness check of including country time fixed effects in our baseline regression support our estimates on interaction terms between bank-level variables and the bubble indicators. However, they do not allow us to conclude on the unbiasedness of the level effects. As Figure C.2 in the appendix shows, CoVaR spikes especially during early periods of the Global Financial Crisis. To exclude the results being driven by either this or other particular periods, we re-estimate our baseline regressions excluding certain sample periods. The results are highly robust to the exclusion of initial periods of our sample (cf. Table 6, Columns 1 and 2). Excluding the recent crises periods yields even stronger effects of asset price bubbles (Table 6, Columns 3 and 4). Table 6: Robustness Check - Sample Period The first column shows our baseline regression formulated in Equation (3) and already reported in Table 3, Column 4. Columns 2 to 4 contain estimates for this baseline regression with samples restricted as indicated in the 2nd row of the table. Dependent variable: systemic risk estimated by CoVaR (cf. Appendix B).... Boom and Bust indicate the respective bubble phases estimated based on the BSADF approach (cf. Appendix B). Macro variables are credit-to-gdp growth, investment-to-gdp growth, 10-year government bond rates, the inflation rate, and real GDP growth. Bank-level variables consist of leverage, size, maturity mismatch, and loan growth. Standard errors are clustered at the bank and country time level. ***, **, * indicate significance at the 1%, 5% and 10% level. P-Values are in parentheses. 17

19 A second potential concern relates to the applied measure of systemic risk, CoVaR. It is estimated based on return losses calculated from the market value of equity and thus relies on stock market prices. During times of a stock market bubble, the stocks are not priced according to their fundamental value and thus are subject to a mis-pricing. Can we have faith in the results if systemic risk is estimated based on data suffering from this mis-pricing? Our results show an effect for both stock market and real estate bubbles such that this concern applies only to parts of our results. Moreover, the mis-pricing in a stock market during the emergence of a bubble would result in a too rosy picture of the state of financial institutions and the system alike and thus in an underestimation of systemic risk. Consequently, our results would - if anything - underestimate the true effect of asset price bubbles on systemic risk. Since the estimation of CoVaR requires data on equity market returns, our sample includes only listed financial institutions. Especially small banks are much more frequently listed in the US than e. g. in Europe. As a consequence, our dataset includes significantly more observations on US banks than on banks located in other countries (cf. Table C.1 in the appendix). As already reported, the correlation (including bank fixed effects) of asset price bubbles with systemic risk is positive and significant in 12 out of the 17 countries in our sample. Only one country shows a negative significant correlation. As an additional robustness check, we exclude the US from all regressions. The results related to the burst of bubble episodes are robust towards this restriction of the sample. The effects concerning the emergence of bubbles become smaller and remain partly significant, depending on the percentile we condition the interaction terms on. 5 Conclusion Analyzing a broad sample of banks in 17 OECD countries over the period 1987 till 2015, this paper empirically assesses the effect of asset price bubbles on systemic risk. While this connection is explicitly studied neither by the theoretical nor the empirical literature, episodic evidence suggests two hypotheses: first, asset price bubbles lead to the build-up of systemic risk, and second, the emergence of bubbles accompanied by unfavorable developments on the bank level is particularly problematic. 18

20 Our results support both hypotheses. We find asset price bubbles to be associated with increased systemic risk. This relationship is not limited to the turmoil following the burst of a bubble, but exists already during its emergence. The results are neither driven by a single country nor by specific sample periods. In the light of these results, policies exclusively managing the turmoil after the burst of a bubble appear insufficient. From a financial stability perspective, the harmful effects of emerging asset price bubbles should be counteracted early on. Especially higher loan growth, bank size, and maturity mismatch lead to an increased effect of asset price bubbles on systemic risk. Consequently, policy interventions do not necessarily need to target a bubble itself. Instead, regulation strengthening the resilience of the financial system are suited to at least partly offset the effects of asset price bubbles. Moreover, our results do not support the conjecture of real estate bubbles being generally more harmful than stock market bubbles. While real estate bubbles are more harmful than stock market bubbles at high levels of loan growth, bank size, leverage and maturity mismatch, the ordering is reversed when these variables are at average levels. A sole focus on real estate bubbles thus is inappropriate. With our study, we aim to fill a gap in the literature by providing the first empirical assessment of the effects of asset price bubbles on systemic risk. We hope to contribute to a sounder basis for the design of policies aimed at preventing the occurrence of yet another financial crisis fueled by asset price bubbles. 19

21 References Abreu, D., and M. K. Brunnermeier (2003): Bubbles and Crashes, Econometrica, 71(1), Acharya, V. V. (2009): A theory of systemic risk and design of prudential bank regulation, Journal of Financial Stability, 5(3), Acharya, V. V., R. Engle, and M. Richardson (2012): Capital Shortfall: A New Approach to Ranking and Regulating Systemic Risks, American Economic Review, 102(3), Acharya, V. V., L. H. Pedersen, T. Philippon, and M. Richardson (2010): Measuring Systemic Risk,. Adrian, T., and M. K. Brunnermeier (2016): CoVaR, American Economic Review, 106(7), Al-Anaswah, N., and B. Wilfling (2011): Identification of speculative bubbles using statespace models with Markov-switching, Journal of Banking & Finance, 35(5), Allen, F., and D. Gale (2000): Financial Contagion, Journal of Political Economy, 108(1), Asako, K., and Z. Liu (2013): A statistical model of speculative bubbles, with applications to the stock markets of the United States, Japan, and China, Journal of Banking & Finance, 37(7), Barth, A., and I. Schnabel (2013): Why banks are not too big to fail: evidence from the CDS market, Economic Policy, 28(74), Bernanke, B., and M. Gertler (1989): Agency Costs, Net Worth, and Business Fluctuations, American Economic Review, 79(1), Bernardi, M., G. Gayraud, and L. Petrella (2013): Bayesian Inference for CoVaR,. Bohl, M. T., P. Kaufmann, and P. M. Stephan (2013): From hero to zero: Evidence of performance reversal and speculative bubbles in German renewable energy stocks, Energy Economics, 37, Borio, C., and P. Lowe (2002): Asset prices, financial and monetary stability: exploring the nexus,. Breitung, J., and U. Homm (2012): Testing for Speculative Bubbles in Stock Markets: A Comparison of Alternative Methods, Journal of Financial Econometrics, 10(1),

22 Brownlees, C., and R. Engle (2015): SRISK: A Conditional Capital Shortfall Measure of Systemic Risk,. Brunnermeier, M. K. (2009): Deciphering the Liquidity and Credit Crunch , Journal of Economic Perspectives, 23(1), Brunnermeier, M. K., and M. Oehmke (2013): Bubbles, Financial Crises, and Systemic Risk, in Handbook of the Economics of Finance, ed. by G. M. Constantinides, M. Harris, and R. M. Stulz, vol. 2, pp North Holland, Amsterdam and London. Brunnermeier, M. K., and L. H. Pedersen (2009): Market Liquidity and Funding Liquidity, Review of Financial Studies, 22(6), Brunnermeier, M. K., and I. Schnabel (2016): Bubbles and Central Banks: Historical Perspectives, in Central Banks at a Crossroads - What Can We Learn from History?, ed. by M. D. Bordo, O. Eitrheim, M. Flandreau, and J. F. Qvigstad, pp Cambridge University Press, Cambridge. Busetti, F., and A. M. R. Taylor (2004): Tests of stationarity against a change in persistence, Journal of Econometrics, 123(1), Cao, Z. (2013): Multi-CoVaR and Shapley Value: A Systemic Risk Approach,. Capuano, C. (2008): The Option-iPoD: The Probability of Default Implied by Option Prices Based on Entropy,. Demirgüç-Kunt, A., and E. Detragiache (1998): The Determinants of Banking Crises in Developing and Developed Countries, IMF Staff Papers, 45(1). Deutsche Bundesbank (2014): Financial Stability Review,. Diamond, D. W., and R. G. Rajan (2011): Fear of Fire Sales, Illiquidity Seeking, and Credit Freezes, The Quarterly Journal of Economics, 126(2), (2012): Illiquid Banks, Financial Stability, and Interest Rate Policy, Journal of Political Economy, 120(3), Etienne, X. L., S. H. Irwin, and P. Garcia (2014): Bubbles in food commodity markets: Four decades of evidence, Journal of International Money and Finance, 42, Gârleanu, N., and L. H. Pedersen (2007): Liquidity and Risk Management, American Economic Review, 97(2), Girardi, G., and A. Tolga Ergün (2013): Systemic risk measurement: Multivariate GARCH estimation of CoVaR, Journal of Banking & Finance, 37(8),

23 Gray, D. F., and A. A. Jobst (2010): Systemic CCA A Model Approach to Systemic Risk: Paper presented at a conference sponsored by the Deutsche Bundesbank and TU Dresden, October 2010,. Gutierrez, L. (2013): Speculative bubbles in agricultural commodity markets, European Review of Agricultural Economics, 40(2), Hautsch, N., J. Schaumburg, and M. Schienle (2015): Financial Network Systemic Risk Contributions, Review of Finance, 19(2), Huang, X., H. Zhou, and H. Zhu (2009): A framework for assessing the systemic risk of major financial institutions, Journal of Banking & Finance, 33(11), Jiang, L., P. C. B. Phillips, and J. Yu (2015): New methodology for constructing real estate price indices applied to the Singapore residential market, Journal of Banking & Finance, 61, S121 S131. Jordà, Ò., M. Schularick, and A. M. Taylor (2013): When Credit Bites Back, Journal of Money, Credit and Banking, 45(s2), (2015a): Betting the house, Journal of International Economics, 96, S2 S18. (2015b): Leveraged bubbles, Journal of Monetary Economics, 76, S1 S20. Kim, J.-Y. (2000): Detection of change in persistence of a linear time series, Journal of Econometrics, 95(1), Kim, J.-Y., and R. B. Amador (2002): Corrigendum to Detection of Change in Persistence of a Linear Time Series, Journal of Econometrics, 109(2), Kindleberger, C. P., and R. Z. Aliber (2005): Manias, Panics, and Crashes: A History of Financial Crises. Palgrave Macmillan UK, London, 5 edn. Kiyotaki, N., and J. Moore (2005): Liquidity and Asset Prices, International Economic Review, 46(2), Koenker, R. (2005): Quantile regression, vol. 38 of Econometric Society monographs. Cambridge University Press, Cambridge and New York. López-Espinosa, G., A. Moreno, A. Rubia, and L. Valderrama (2012): Short-term wholesale funding and systemic risk: A global CoVaR approach, Journal of Banking & Finance, 36(12), Mainik, G., and E. Schaanning (2012): On dependence consistency of CoVaR and some other systemic risk measures,. 22

24 Oh, D. H., and A. J. Patton (2015): Time-varying systemic risk: Evidence from a dynamic copula model of cds spreads,. Phillips, P. C. B., S. Shi, and J. Yu (2015a): Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500, International Economic Review, 56(4), (2015b): Testing for Multiple Bubbles: Limit Theory of Real-Time Detectors, International Economic Review, 56(4), Phillips, P. C. B., S.-P. Shi, and J. Yu (2011): Supplement to Two Papers on Multiple Bubbles,. Radev, D. (2013): Systemic Risk and Sovereign Debt in the Euro Area,. (2014): Assessing Systemic Fragility - A Probabilistic Perspective,. Rochet, J.-C., and J. Tirole (1996): Money, Credit and Banking, 28(4). Interbank Lending and Systemic Risk, Journal of Schularick, M., and A. M. Taylor (2012): Credit Booms Gone Bust: Monetary Policy, Leverage Cycles, and Financial Crises, , American Economic Review, 102(2), Segoviano, M. A., and C. Goodhart (2009): Banking Stability Measures,. Shi, S., and Y. Song (2014): Identifying Speculative Bubbles Using an Infinite Hidden Markov Model, Journal of Financial Econometrics, 0(0), Shin, H. S. (2008): Risk and liquidity in a system context, Journal of Financial Intermediation, 17(3),

25 A Estimation of Bubble Episodes The BSADF approach applies sequences of ADF tests to systematically changing fractions of a sample to identify episodes of explosive processes in price data. We follow the estimation strategy proposed by Phillips, Shi, and Yu (2015a). To fix notation, let r 1 denote some starting fraction of the sample and r 2 some ending fraction, implying r 1 < r 2. The fraction of the corresponding subsample is given by r w = r 2 r 1. Furthermore, let r 0 denote the fractional threshold which ensures that any analyzed subsample is large enough for the test to be efficient. The threshold is chosen according to r 0 = T, where T refers to the number of observations in the sample. The BSADF statistic (as opposed to the approach) for sample fraction r 2 is given by the supremum of all values of the test-statistics of ADF tests performed while holding the ending fraction of the sample fixed at r 2 and varying the starting fraction from 0 to r 2 r 0. Figure A.1 illustrates the idea. Formally, the BSADF statistic is thus given by BSADF r2 (r 0 ) = sup {BADF r 2 r 1 }. r 1 [0,r 2 r 0 ] (A.1) Figure A.1: Recursive Nature of the BSADF test Source: Phillips, Shi, and Yu (2015a, p. 1052) The identification of bubble episodes relies on a sequence of BSADF statistics resulting from varying ending fraction r 2. To fix the further notation, let the fraction of the sample at which the bubble starts be denoted by r e, the fraction of the sample at which it ends by r f and the estimators of both by ˆr e and ˆr f respectively. The starting fraction r e is estimated by the earliest point in time for which the BSADF test rejects the null hypothesis of no bubble existing. Similarly, the estimator 24

26 for ending fraction r f is given by the earliest point in time after the emergence of the bubble and some minimum bubble length δlog(t ) for which the BSADF test does not reject the null. Formally, ˆr e = and ˆr f = inf [r 2 : BSADF r2 (r 0 ) > scvr β 2 ] r 2 [r 0,1] inf [r 2 : BSADF r2 (r 0 ) < scvr β 2 ], r 2 [ˆr e+δlog(t ),1] (A.2) (A.3) where T is the number of observations of the analyzed time series and scv β r 2 is the critical value of the BSADF statistic based on T r 2 observations and confidence level β. T r 2 refers to the largest integer smaller than or equal to T r 2. Critical values are obtained by Monte Carlo simulations based on 2,000 repetitions. The parameter δ is to be chosen freely according to one s beliefs about what minimum duration should be required in order to call surging prices a bubble. The minimum length requirement excludes short blips from being identified as bubbles and prevents estimating an overly early termination of bubbles taking of slowly. We choose δ such that the minimum length of bubbles equals 6 months. The test identifies a few instances of bust-boom cycles which might be interpreted as negative bubbles. Unfortunately, their number is too low to be included as separate category in the main analyses. Attempts to do so result in these variables being dropped from the regressions due to their high collinearity with the constant. As the dynamics during such bust-boom cycles might be quiet different than those during customary bubble episodes, we ignore these bust-boom episodes when constructing the bubble indicators. B Estimation of CoVaR CoVaR is based on the concept of value at risk (VaR). The VaR captures the maximum return loss x i of institution i that will not be exceeded with probability q within a certain time. Following the notation in Adrian and Brunnermeier (2016), the VaR of institution i is implicitly defined by the following equation: P r(x i V ar i q) = q%. (B.1) 25

27 CoVaR is the VaR of the system conditional on event C(X i ) of institution i, which finds an implicit expression in P r(x system C(X i ) CoV ar system C(Xi ) q ) = q%. (B.2) CoV ar system i q captures the difference between the financial system s value at risk conditional on institution i realizing losses at the q-th percentile of its loss-distribution and the system s value at risk conditional on institution i realizing losses at the 50-th percentile: CoV ar system i q = CoV ar system Xi =V ar i q q CoV ar system Xi =V ar i 50 q. (B.3) A larger value of CoVaR thus corresponds to a higher systemic risk contribution of institution i. To estimate the measure, we obtain daily information on the number of outstanding shares, unpadded unadjusted prices of common equity in national currency, and the corresponding market capitalization in US Dollar from Datastream for all listed institutions in our sample. To exclude public offerings, repurchases of shares and similar activities biasing the results, observations for which the number of outstanding shares changed compared to the previous day are dropped. The daily observations are then collapsed to weekly frequency. From this data, we calculate the weekly return losses on equity (X) of institution i and those of the financial system: X i t+1 = P i t+1 N i t+1 P i t N i t P i t N i t X system t+1 = i MV i t i MV t i X i t+1, and (B.4) (B.5) where P i t is the price of common equity of institution i at time t in national currency, N refers to the number of outstanding shares and MV is the market value in US Dollar. We use national currencies to compute the return losses in equation (B.4) to prevent exchange rate fluctuations biasing our results. To clarify the relevance of the currency, suppose return losses of Eurozone banks were calculated in US Dollar. Further suppose, the Euro would depreciate vis-à-vis the US Dollar. Then, all other things equal, all banks in the Eurozone would simultaneously experience 26

28 return losses which would lead to increases in CoVaR. When calculating market shares of each institution (the ratio in equation (B.5)) we have to rely on a uniform currency, which is why we use the market values in USD there. While exchange rate fluctuations introduce noise into the calculation of system return losses, they do not bias the results. Note that we calculate the system returns including the returns of institution i. One might suspect this to introduce a bias into the subsequent estimations as it should increase the correlation between system returns and institution-specific returns. Given the large number of institutions in our sample, such a bias should be negligible. We assess the robustness of the estimations by defining a separate system for each financial institution by excluding the corresponding institution from the calculation of the returns of its system. As in Adrian and Brunnermeier (2016), the results are highly robust to this alternative specification. The sample is restricted to institutions with at least 260 weeks of non-missing return losses to ensure convergence of the following estimations. The return losses are merged with variables capturing general risk factors. Adrian and Brunnermeier (2016) use the following state variables: The change in the three-month yield calculated from the three-month T-Bill rate published with the Federal Reserve Board s H.15 release. The change in the slope of the yield curve as captured by the yield spread between the ten-year Treasury rate (FRB H.15) and the three-month T-Bill rate. The TED spread, measured as the difference between the three-month Libor rate (FRED database) and the three-month secondary market bill rate (FRB H.15). The change in the credit spread between the bonds obtaining a Baa rating from Moody s (FRB H.15) and the ten-year Treasury rate. The weekly market returns of the S&P 500. Equity volatility calculated as a 22-day rolling window standard deviation of the daily CRSP equity market return. 27

29 The difference between the weekly real estate sector return (companies with a SIC code between 65 and 66) and the weekly financial system return (all financial companies in the sample). As usual for the estimation of CoVaR outside the US, we do not include the spread between the real estate sector return and the financial system return. 11 Since we estimate CoVaR in a multi-country setting, we assign each financial institution to one of the following four financial systems: North America, Europe, Japan or Australia. The association with a system is based on the location of an institutions headquarter. We use system-specific control variables. Table B.1 provides an overview of the data used to construct these control variables. Table B.1: Overview of System-Specific Data The 10-year government bond rates for Germany, Japan and Australia are only available at monthly frequency. In these instances, we use cubic spline interpolations to obtain the weekly observations required for the quantile regressions. 11 López-Espinosa, Moreno, Rubia, and Valderrama (See e. g. 2012); Barth and Schnabel (See e. g. 2013). 28

30 The return losses and control variables are used to estimate the VaR of institution i with the help of the following quantile regressions: 12 V ar i q,t = ˆX i t = ˆα i q + ˆγ i qm t 1. (B.6) M t 1 is a vector of control variables consisting of the general risk factors listed above. We apply a stress level of q = 98% in all regressions. Next, the relationship between institution-specific losses and system losses are estimated with the following quantile regressions: ˆX system i q,t = ˆα system i q + ˆγ q system i system i M t 1 + ˆβ q Xt i. (B.7) The conditional value at risk is calculated by combining estimates from the two previous regressions, namely: CoV ar i q,t = ˆα system i q + ˆγ q system i system i M t 1 + ˆβ q V arq,t i. (B.8) Following the definition provided in equation (B.3), the time series of CoVaR are calculated as CoV ar i q,t = ˆβ system i q (V ar i q,t V ar i 50,t). (B.9) We collapse these estimates to monthly frequency by taking simple averages in order to merge them with all other variables included in our main analyses. 12 Quantile regressions allow the estimated coefficient to depend on a quantile of the distribution of the dependent variable. This is achieved by minimizing the weighted absolute difference between some quantile q of the dependent variable and its fit. Unlike OLS, this least absolute deviation (LAD) estimator does thus not assign equal weight to all observations. For a detailed exposition of quantile regressions see Koenker (2005). The literature suggests a number of alternative estimation techniques: MGARCH (Girardi and Tolga Ergün, 2013), copulas (Mainik and Schaanning, 2012; Oh and Patton, 2015), maximum likelihood (Cao, 2013), and Bayesian inference (Bernardi, Gayraud, and Petrella, 2013). Neither of these alternative approaches is more widely applied than the quantile regressions. 29

31 C Additional Figures and Tables Table C.1: Geographical and Historical Coverage of the Sample Summation over years exclusively serves the ease of exposition. The development of the number of observations is smooth across years. See Section 4.3 and Table 6 for robustness checks regarding time periods and countries potentially driving the results. 30

32 Table C.2: Coefficients on Macroeconomic Control Variables The table reports the coefficients on the lagged macroeconomic control variables estimated in our baseline regression (cf. Equation (3) and Table 3, Column 4). Dependent variable: systemic risk estimated by CoVaR (cf. Appendix B).... Boom and... Bust indicate the respective bubble phases estimated based on the BSADF approach (cf. Appendix A). Bank-level variables are leverage, size maturity mismatch, and loan growth. Standard errors are clustered at the bank and country time level. ***, **, * indicate significance at the 1%, 5% and 10% level. P-Values are in parentheses. 31

33 (a) Stock Market Bubble Episodes Figure C.1: Bubble Episodes by Country and Asset Class (b) Real Estate Bubble Episodes (c) Robustness: Real Estate Bubble Episodes (Price-to-Rent Data) Periods colored in blue represent the time of emergence of an asset price bubble, periods in gray refer to the bust episode of a bubble. Panel C demonstrates the robustness of the bubble estimation results with respect to analyzing real price data vs. price-to-rent data. 32

34 Figure C.2: Evolution of CoVaR over time The figure displays the unweighted mean of CoVaR in weekly percentage points for the four financial systems in our sample: North America, Europe, Japan, and Australia. 33