key: cord-0062888-auwgsj4c authors: Duprey, Thibaut title: Canadian Financial Stress and Macroeconomic Condition date: 2020-07-24 journal: nan DOI: 10.3138/cpp.2020-047 sha: 37a956dbf560dddc7126e1a466867318099485eb doc_id: 62888 cord_uid: auwgsj4c I construct a new composite measure of systemic financial market stress for Canada. Compared with existing measures, it better captures the 1990 housing market correction and more accurately reflects the absence of diversification opportunities during systemic events. The index can be used for monitoring. For instance, during the coronavirus disease 2019 pandemic, it reached a peak second only to the 2008 global financial crisis. The index can also be used to introduce non-linear macro-financial dynamics in empirical macroeconomic models of the Canadian economy. Macroeconomic conditions are shown to deteriorate significantly when the Canadian financial stress index is above its 90th percentile. Introduction market, and the housing market. The systemwide nature Extreme financial market stress around the coronavirus of financial stress is reinforced by combining correlation disease 2019 pandemic and the associated real and importance weights. Correlation weights ensure that economic damages highlight the importance of gauging the index only picks up episodes when several markets are the extent of macro-financial spirals. I develop a new severely impaired at the same time. Importance weights measure of financial market stress for Canada consistent ensure that the markets most important for the funding of with the narrative of stressful events and illustrate the role the Canadian economy contribute more to the stress index. of financial stress as a non-linear propagation of shocks In other words, the index emphasizes the periods in which in the Canadian economy. it is harder for investors and borrowers to substitute away Periods of systemic financial stress are characterized assets that face market stress. by a sharp correction happening simultaneously on those The innovation is twofold compared with the two exkey markets that provide the most important sources of isting measures of financial stress for Canada (Cardarelli, funding to the Canadian economy. The Canadian financial Elekdag, and Lall 2011; Illing and Liu 2006) . First, they do stress index (CFSI) builds on the methodologies of Illing not cover stress on the housing market, although it is a and Liu (2006 ) , Hollo, Kremer, and Lo Duca (2012 ) , and crucial source of shocks for the Canadian economy. Indeed, Duprey, Klaus, and Peltonen (2017 ) . Using data from 1981 Canada experienced a major housing market correction in onward, I consider financial stress that spans seven market the 1990s. Because of its elevated imbalances, the housing segments, namely the equity market, the Government of market is an important source of concern for policy-Canada bonds market, the foreign exchange market, the makers in Canada (International Monetary Fund 2017). money market, the bank loans market, the corporate bonds Second, stress that is systemic is most likely to contribute to macroeconomic downturns. Therefore, it is important to capture this systemic notion to accurately quantify the role of financial stress. Existing indexes are computed as the sum of stress on individual markets. However, this method ignores the correlation across market segments that occurs during systemic events. Using a portfolio analogy, the pres ence of correlated risks means that the risk of the portfolio is greater than the sum of the risk of the individual assets. I capture this idea using a portfolio aggregation method: during systemic stress events, the CFSI is greater than the sum of the stress on individual components. The CFSI can be useful for at least two purposes. First, it is a useful metric for benchmarking the intensity of fi nancial stress against historical episodes. For instance, the stress associated with the COVID-19 pandemic reached a level comparable only to that of the 2008 global financial crisis. 1 Second, financial market stress is often associated with non-linear macro-financial dynamics that can ampli fy negative shocks. Above its 90th percentile, the CFSI is typically associated with more fragile macroeconomic conditions in Canada. I illustrate how financial stress and worsening macroeconomic conditions amplify each other in the context of a Bayesian threshold vector autoregres sive model (TVAR). The model explicitly relates episodes of high financial market stress, as signalled by the CFSI, to a deeper correction of gross domestic product (GDP). In practice, the CFSI is part of the tool kit for the risk management framework of the Bank of Canada (Poloz 2020) , allowing for an analysis of the state dependence of policy measures (Poloz 2016) . The CFSI is an input to non linear macro-financial models used to gauge risks, such as the risk amplification macroeconomic model (RAMM; Traclet and MacDonald 2018) and the growth at risk model (Duprey and Ueberfeldt 2020) . Indeed, non-linear macro economic models are becoming increasingly popular in an attempt to capture tail events by postulating the existence of different macroeconomic dynamics in periods of severe financial stress. In the context of a Bayesian TVAR, monetary policy has a more severe impact on output when financial conditions are tighter (see, for the United States, Balke 2000 ; for Canada, Li and St-Amant 2010) . For the United Kingdom, Chatterjee et al. (2017 ) find support for a feedback loop between real and financial stress. Another strategy relies on a Markov-switching vector autoregressive model (VAR) in which the change in regime is driven by an unob served Markov chain rather than an observable measure of financial stress, as in the Bayesian TVAR. For the United States, Hubrich and Tetlow (2015 ) show that regime changes into high financial stress coincide with known crisis epi sodes and are highly detrimental to real economic activity. In the next section, I present the new CFSI. Next, I high light the advantages of the CFSI over alternative measures and then the heightened macroeconomic costs associated with elevated financial market stress in Canada. The final section concludes. Financial stress is defined as simultaneous fi nancial market turmoil among the most important asset classes and is reflected by (a) the uncertainty in market prices, (b) sharp corrections in market prices, (c) a widening of spreads, and (d) the degree of commonality across asset classes. Asset classes are split along several dimensions: equities or bonds, long-term assets or short-term commercial papers, and financial or real assets (e.g., housing), denominated in Canadian dollars or foreign currencies. The construction of an index of financial market stress relies on three fundamental steps: collecting, aggregating, and back-testing measures of stress. The most common set of data relies on equity prices, government bond yields, and exchange rates. A limited dataset such as the one used by al lows for the inclusion of more than 50 years of data while ensuring large cross-country comparability. However, some indexes that focus on specific countries embed much more data. For instance, the National Financial Conditions Index of the Federal Reserve Bank of Chicago Butters 2011, 2012) includes more than 100 different time series of financial activity with varying frequencies, at the cost of a shorter time span. 2 One major shortcoming common to most existing indexes is that they fail to dir ectly capture developments in the housing markets. This is essential for Canada because one of the most stressful events occurred in the early 1990s, with a sharp correction to housing prices in Toronto and Vancouver. Likewise, this is a key concern in Canada moving forward because housing prices skyrocketed in Toronto and Vancouver in 2016-2017. One of the early contributions to this literature, Illing and Liu (2006 ) , develops an index for Canada, but it excludes housing. Various aggregation methods can be used to combine individual stress into a stress composite (for a survey, see Kliesen, Owyang, and Vermann 2012) . The main methods rely on (a) the loadings onto the first principal component (Brave and Butters 2011; Hakkio and Keeton 2009; Kliesen and Smith 2010) , (b) the relative weights of the different markets they represent (Illing and Liu 2006) , (c) variance-equal weights for standardized components (Cardarelli et al. 2011; European Central Bank 2009), or (d) cross-correlations of the different sub-indexes (Hollo et al. 2012; Oet et al. 2011) . Principal-components analysis is the easiest method. It identifies the trend, common to all underlying data, to avoid "informationally redundant" data. However, interpreting the meaning of the common components is not straightforward, even more so when allowing for time-varying factor loadings. Instead, simpler time-varying correlation weights allow for easy interpretation and decomposition of the contributing factors. In addition, systemic stress should not be limited to the summation of individual stress (Allen and Carletti 2013) : this is the supraadditivity property of systemic tail risk. During stressful periods, the overall level of financial market stress would be larger than the sum of financial stress on its constituent markets as a result of risk that cannot be diversifi ed away. Correlation weights are consistent with this approach and allow for an explicit decomposition between the systemic and non-systemic part of financial stress by isolating the contribution of correlated components. As a result, cor relation weights are the method favoured in this article, although, similar to Illing and Liu (2006 ) , I combine it with sectoral weights to account for the relative importance of different sectors over time. Once a financial stress composite has been successfully built, its ability to contemporaneously signal known stress events should be back-tested. Simple measures of financial stress such as Duprey et al.'s (2017 ) Country-Level Index of Financial Stress (CLIFS) capture almost all of the known crises in Europe but also react to additional stress events that were deemed not stressful enough to unfold into a full-fledged crisis. To ensure the financial stress compos ite is a fair representation of the sequence of financial crises, the aggregation technique could be optimized to capture a limited list of expert-identified events. To that extent, Chatterjee et al. (2017 ) suggest using information weights to avoid redundant data and discount those that do not match the narrative of financial stress events. Unfortunately, these tools are of limited use in Canada, a country that, according to Laeven and Valencia (2013 ) , never experienced a systemic banking crisis because its fi nancial system was much more resilient to the 2008 global financial crisis (Huang and Ratnovski 2009 The current index of financial stress for Canada developed by Illing and Liu (2006 ) was optimized to fit stress events as of 2003 and does not include several important dimen sions, such as housing or the supra-additivity property of systemic stress. Along seven market segments, the new monthly index combines 43 time series from 1981 onward (18 to measure market stress and 25 to measure market size), with some features from market stress is supra-additive) and Illing and Liu (2006; each market is weighted by quantities). The construction of the CFSI is represented in Figure 1 . 3 The proposed CFSI is composed of measures of financial stress that capture seven different markets. The parsimoni ous nature of the dataset-I use 18 time series to compute 19 stress indicators covering more than seven marketsensures that I capture different aspects of similar stress periods without having too much redundant informa tion (see Table A .1 in Appendix A for more details). In addition to the equity (EQU), government bonds (GOV), and foreign exchange (FOR) markets, captured in a way very similar to that of , I consider the money market (MON), the bank loans market (BAN), the corporate sector (COR), and the housing sector (HOU). Stress s t , m on each market segment m = {EQU, GOV, FOR, MON, BAN, COR, HOU} is captured by the aver age of two (I = 2) or three (I = 3) raw stress measures r t,m,i that are transformations of the data-realized volatilities, interest rate spreads, or variations compared with a local maximum or minimum. Indeed, financial stress can be characterized by larger volatilities, widening spreads over the risk-free rate, or price corrections for large assets. 4 I mostly use simple transformations but include a more complex measure, such as the distance to default, which is a standard measure of systemic banking risk, averaged over all Canadian financial institutions (MacDonald, Van Oordt, and Scott 2016) . The different raw stress indicators r t,m,i do not have the same unit, so an additional normalization is required before aggregating them into the seven market stress components s t,m . Each raw stress indicator is normalized to lie in [0; 1] by using the empirical cumulative distribu tion (rank) over an expanding window (see, e.g., Hollo et al. 2012) . 5 New data are normalized against historical data in a recursive manner. 6 Stress on each market segment is computed as the average of the I raw stress indicators r t, for this market: Stress on each market segment is displayed in Figure 2 . Equity market stress is high during the stock market crash of October 1987, the burst of the dot-com bubble in the 2000s, and the 2008 global financial crisis. Stress on the government bonds market is the highest during the 1980s and early 1990s, when government debt was higher and Canada experienced two downgrades, in October 1992 by Standard & Poor's and in February 1995 by Moody's. Moody's further downgraded Canada in April 2000, but it was quickly followed by better ratings from all three main rating agencies in the 2000s. Stress on the corporate bonds market was also high during the 1990s and in 2015 with the Notes: Stress on each market segment corresponds to the average of two or three stress measures described in Table A .1 in Appendix A and normalized using the empirical cumulative distribution over a backward-expanding window, starting with a fixed window until 1991 (i.e., 10 years since the start of the index in 1981).A-BBB = difference in the yield of A-rated and BBB-rated corporate bonds. Source: Author. oil price shock that triggered a recession. Housing market stress was high in the early 1980s, in the early 1990s, and in 2008. However, the 1990s appear to be most stressful with a sustained decline in prices, whereas 2008 was partly driven by temporary loss of consumer confidence. Last, the foreign exchange market, the bank loans market, and the money market also peak at the expected time, around the European exchange rate crisis of 1993, the aftermath of the Russian default and collapse of Long-Term Capital Management (LTCM) in the late 1990s, or the 2008 global fi nancial crisis. Similar to Hollo et al. (2012 ) or , I aggregate the different market segments by relying on a portfolio theory approach that weights each sub-index by its cross-correlation U , , ' with the others, where m' z m. By aggregating correlated sub-indexes, I show that the resulting index reflects increased systematic risk as a result of a stronger co-movement across market segments. In contrast, less correlated market segments result in a lower composite index because the risk can be diversified away across market segments. ( 3 ) , , ' The EWMA method is computed pairwise and is a simpler alternative to a multivariate GARCH that would require the estimation of a larger number of parameters. Optimizing over a cross-country dataset of 27 European financial stress indexes, found that a smoothing parameter λ = 0.85 generates a monthly financial stress index that is closest to a multivariate GARCH. Therefore I also choose λ = 0.85, which strikes a balance between the stability of the estimate and the ability to include new observations. 7 The time-varying cross-correlation matrix C t combines all pairwise correla tion coefficients U t m m : The cross-correlations are presented in Figure 3 . Dur ing stressful periods, around 1990, 1998, 2008, and 2015 , cross-correlations tend to be positive. This means that there is little room for hedging across market segments. Most market segments tend to co-move, which is a key characteristic of systemic stress. In particular, the median pairwise correlation across market segments started to increase from extremely low levels in 2003 and peaked in 2008. Consistent with Illing and Liu (2006) , I also weight each market segment m by its size in the overall Canadian econ omy ω t,m . For instance, the growing volume of residential mortgage loans should be reflected by a higher import ance of housing market stress in the overall financial stress composite. Each market segment is weighted by the volume of lending it is associated with as a proportion of total lending (Table A. 2). The equity market is weighted using equity finance by Canadian businesses. The government bonds market is weighted using the amount of outstanding government bonds with medium-to long-term maturities issued in Canadian dollars by the different levels of government. The foreign exchange market is weighted by the amount of funding for governments and corporations denomin ated in foreign currencies (loan, securities, or bonds). The money market is weighted by the amount of short-term commercial papers issued in Canadian dollars by cor porations and treasury bills issued in Canadian dollars by the different levels of government. The banking sector is weighted by the amount of business or consumer loans issued in Canadian dollars by chartered banks, excluding residential mortgages. The corporate bonds market is weighted by the amount of medium-to long-term bonds and debentures issued by Canadian businesses in Can adian dollars. Finally, the housing market is weighted by the amount of residential mortgages held on balance sheets by financial institutions, including chartered banks, credit unions, mortgage credit companies, and financial trusts. Figure 4 displays the evolution of the weights of each market segment over time w t {w t,EDU, w t,GOV, w t,FOR , w t, BAN, = w t,HOU, w t, COR, w t, MON }. The financial stress composite is as follows: where w t is the 1 × 7 vector of market segment weights with Σ m w m,t = 1; s t is the 1 × 7 vector of standardized stress bounded in [0; 1] for each market segment m; ʘ denotes the element-wise multiplication such that w t ʘ s t is also a 1 × 7 vector; C t is the 7 × 7 time-varying matrix of crosscorrelation among all pairs of market segments. As a result, the CFSI is also bounded on [0, 1]. Next, I compare episodes of high financial stress with the narrative of episodes of financial stress in Canada. Figure 5 shows the contribution of each market segment to the CFSI. It emphasizes the role of cross-correlations in identifying episodes of heightened financial stress. Crosscorrelations are represented by the white area below the black CFSI line. The index can be extended backward to start as early as 1964, but with more limited data (see Appendix B). The peaks of the CFSI coincide very well with known events of financial stress. The main spikes of financial stress, namely 1982, 1990, and 2008 , coincide with periods of recessions and corrections in industrial production and housing prices. The decomposition of financial stress shows that 1982 was driven by the housing, banking, equity, and money markets; 1990 was driven by the hous ing, money, and government bonds markets; and 2008 was driven by the banking, housing, money, and equity markets. In March 2020, during the COVID-19 pandemic, the CFSI had the strongest one-month increase, reaching a peak second only to the 2008 global financial crisis. However, it is worth noting that financial market stress does not always bring macroeconomic underperformance, and macroeconomic underperformance does not always yield severe financial market stress. For instance, the Notes: Stress on each market segment corresponds to the average of two or three stress measures described in Table 2 and normalized us ing the empirical cumulative distribution.Vertical bars for the government bonds market display downgrades and upgrades by rating agencies. Source: Author's calculations. banking crisis of 1985-1986 with the bailout of the Can adian commercial banks and the liquidation of Northland Bank of Canada did not trigger a recession. This regional banking crisis did not spill over to the rest of the economy, in part thanks to the actions of the Bank of Canada and federal authorities. The default of Russia and associated collapse of LTCM in 1998 triggered an international fi nancial market shock, with limited consequences for the Canadian real economy. The oil price shock of 2015 trig gered a recession in Canada, with higher fi nancial market stress driven by the corporate sector, but the disruption to the financial system was limited. Next, I compare the CFSI with alternative financial stress measures for Canada ( Figure 6 ). Simple measures of financial stress usually capture stress in one specific segment of the market. The corporate bond spread in Figure 6a is sometimes used in the absence of financial stress composites. It signals well the 1982 and 2008 crises as well as the 2015 oil price shock. However, it does not signal well other events occurring more specifically in the banking sector (1985) (1986) or in the housing market (1990). Alternatively, the volatility index in Figure 6b is a broader measure of financial market stress related to overall stock market volatility. As such, it places more emphasis on the stock market corrections, such as Black Monday in 1987, the Asian crisis of the late 1990s, and the burst of the dot-com bubble in the 2000s. The Senior Loan Offi cer Survey ( Figure 6c ) reports the change in domestic credit conditions for business loans from 1999 onward. It does not reflect the pos sibility of arbitrage between bank loans and market finance and does not include consumer loans or mortgage lending. Table A .2 in Appendix A. The historical levels are adjusted backward for the following three breaks: in November 1981, changes in the treatment of foreign bank affi liates in the Bank of Canada statistics; in January 1984, the volume of residential mortgages from trust and mortgage loan companies not collected before; and in November 2011, change in accounting standards, from generally accepted accounting principles to IFRS. Under IFRS, securitized mortgages still held by the originating institution are no longer treated as items that are off balance sheets. Missing entries in the early 1980s for some items presented in Table 3 are extrapolated backward by keeping their percentage contribution to a given market fi xed and equal to the last known value. IFRS = International Financial Reporting Standards. Source: Bank of Canada credit statistics and author's calculations. Figure 6d displays a simple index of fi nancial stress for Two indexes of fi nancial stress are already available for Canada computed with the principal-components method Canada. The Illing and Liu (2006 ) index was constructed on the same raw stress measures as the CFSI. This illus-before the 2008 global fi nancial crisis to coincide with trates the issue with the principal-components method. pre-2008 stressful events specifi cally for Canada ( Figure The Figure 6e instead com bines the first fi ve principal components, because adding is reported for the sake of comparison because the CFSI, the fi fth component seems to improve the metric's ability although more complete, shares many similarities. 8 None to signal stress events. of these alternative indexes for Canada include housing The CFSI can be extended backward to 1964 but with less data; see Appendix B.The lower chart displays crisis episodes. Laeven and Valencia (2013 ) and Reinhart and Rogoff (2011 ) identify crises of different types (banking, equity, currency). House price corrections correspond to periods characterized by more than 10 percent year-over-year drop in real housing prices from peak to trough. Industrial production drops correspond to drops in the seasonally adjusted index of industrial production of at least six months, possibly intertwined with one month of positive growth. Recessions are defined by at least two quarters of negative real output growth. CSFI = Canadian financial stress index; WCS = Western Canadian Select. Source: Author's calculations. stress. The last one encompasses only a very limited set of financial stress. I consider the same list of financial of inputs, and the first two do not satisfy the property stress episodes used by Illing and Liu (2006 ) An AUROC value greater than 0.5 indicates that the prediction is better than a random guess. An AU ROC of 1.0 means that the CFSI provides a perfect match for the stress event. 9 The AUROC is a generalization of the noise-to-signal ratio for any given preferences of the regulator between missing crises (Type 1 errors) and false signals (Type 2 errors). 10 I also report the partial AUROC that restricts the AUROC to focus on a partial, and more plausible, range of preferences between Type 1 and Type 2 errors. Last, the usefulness measure of Alessi and Det ken (2014 ) is computed conditional on a given preference parameter. It measures the ability of the stress index to better match the known episodes of stress as opposed to ignoring the stress index, that is, assuming Canada either never or always faced fi nancial stress. When restricted to the period from 1981 to 2003 used by Illing and Liu (2006; first set of rows in Table 1 ), the CFSI performs best in terms of contemporaneous identifi cation of stress events, according to both the AUROC and the partial AUROC. For balanced preferences (μ = 0.5) or preferences slightly biased toward an aversion to missing crises (μ = 0.6) or an aversion to false signals (μ = 0.4), the CFSI also performs best. When the most recent periods are added, including the 2008 global financial crisis and the 2015 oil price shock or the 1990 housing crisis (not identified in the 2003 survey), the CFSI performs bet ter than other indexes (second set of rows). Similarly, when I exclude the 1998 and 2000 stress events that were ranked as only somewhat stressful in the survey, the CFSI performs best across all metrics (last set of rows). This is mostly because the CFSI identifies those events as being mostly driven by stress on the equity market, not by overall fi nancial stress. Figure 7 displays the receiver operating characteristic (ROC) curves of the different financial stress indexes. This is a visual representation of the ability of the stress indexes to contemporaneously signal the sequence of stress events referred to in the last set of rows of Table 1 . The ROC of the CFSI shows that the CFSI always delivers a lower missed events rate than alternative stress indexes for any given false signal rate. The ROC curves of other indexes do not get as close to the top left corner of the chart, meaning that they tend to misclassify more expertidentified stress events, whatever the preference for Type 1 or Type 2 errors. Last, I briefly compare the fit of the CFSI with the fi t of various principal components. The ability of the principal components to contemporaneously identify the financial stress events in Canada is worse for any principal com ponent taken individually compared with the CFSI (Table D .1 in Appendix D). From the sixth component onward, the AUROC is very close to 0.5, such that it is no better than a random guess. Combining principal components together can slightly improve the fit compared with the CFSI, but only when including the first and the fifth components, whereas the second, third, and fourth com ponents deteriorate the fit. It suggests that the fi rst and the fifth components may both reflect some aspect of the Canadian financial stress history, possibly one that em phasizes faster-moving variables that peak around 2008 and the COVID-19 crises and one that emphasizes the slower moving variables related to the housing market peak in the 1990s. However, the principal-components Illing and Liu (2006) 0 For other rows in the table, as robustness, additional events are either added or removed.AUROC is associated with an informative signal when it is above 0.5, whatever the preferences of the regulator. pAUROC is restricted to assess the informativeness of a signal under a subset of preferences of the regulator, in the range µ = [0.3; 0.7]. µ is the cost associated with T1 (i.e., the share of missed crises). Conversely, 1 − µ is the cost associated with T2 (i.e., the share of false signals).A higher µ is associated with an aversion to missing crises (thus a lower T1).When computing the different measures, the 12 months after a stressful event are removed unless another stressful event starts during this period. Otherwise, the assessment could be biased by the behaviour of the stress indexes during the recovery period.AUROC = area under the receiver operating characteristic curve; pAUROC = partial area under the receiver operating characteristic curve;T1 = Type 1 error;T2 = Type 2 error; U = usefulness indicator of Alessi and Detken (2011 ) analysis does not allow for an easy interpretation of the levels of financial stress above the 90th quantile of the components and uses constant factor loadings, such that CFSI are associated with negative real GDP growth. 11 In I prefer to use the approach that relies directly on time-this section, I provide a simple framework to illustrate varying correlation weights. the negative relationship between financial stress and economic growth. In the previous sections, I described a new index of fi- nancial stress for Canada that improves on the existing A Bayesian TVAR model allows for macroeconomic dy measures. However, the reason economists care about namics to differ across regimes, identified by the level of an financial stress is that it tends to be associated with a observed threshold variable. I use the CFSI as the threshold negative economic outcome. Figure 8 shows that high variable to make an explicit link between macroeconomic dynamics and known events of elevated fi nancial stress for the Canadian market. The model is estimated on monthly data from De cember 1981 to December 2019. It includes the seasonally adjusted annualized growth rate of real GDP (gGDP t ), 12 the seasonally adjusted annualized Consumer Price Index (CPI) inflation rate (gCPI t ), the three-month treasury bill rate (R t ), and the proposed measure of fi nancial stress (CFSI t ). Defining the vector of endogenous variables Y t = [gGDP t , gCPI t , R t , CFSI t ], the Bayesian TVAR with P lags and a constant μ is The Bayesian TVAR model distinguishes between periods with significantly different macroeconomic elasticities (β st ) that depend on the state of the economy S t ϵ{L;H }. The state of the economy is defined as being in a low (or high) financial stress regime if the CFSI is below (or above) an estimated percentile τ of the CFSI, possibly lagged by d periods. The Bayesian TVAR model can be thought of as a set of two VARs conditional on being above or below the cut-off level of financial stress τ. The Bayesian TVAR model is estimated with Bayes ian techniques, following Bruneau and Chapman (2017 ) . The CFSI is normalized using its minimal and maximal value so that it lies between 0 and 1, and the prior for the threshold variable can be modelled as a gamma distri bution. The estimation of the threshold requires at least 10 percent of the observations in the high-stress regime to have a meaningful estimation of the macroeconomic dynamics in the high-stress regime. The regime-specific decomposition Θ st of structural shocks t S t is th e Cholesky matrix with the same order as in Y t . 13 I choose a model specification with three lags P = 3 and one delay d = 1, as suggested by the information criterion. 14 The log-likelihood of the Bayesian TVAR is highest for a cut-off level of financial stress τ in the 85 to 90 per cent range. This means that episodes of high financial stress correspond mainly to the 2008 global financial crisis and the correction in housing prices in Toronto and Vancouver around 1990. Policy-makers should then be concerned when the CFSI is above its 90th percentile because the economy moves to a regime with amplified elasticities. Negative Real Shocks Increase Financial Stress Figure 9 shows the impact of a real shock on GDP growth. It is more persistent in the high-stress regime and is as sociated with a larger increase in the CFSI. If a linear VAR is estimated instead, the two regimes of high and low financial stress are combined, and the impact of real shocks on the CFSI is diluted (black line). Figure 10 shows the impact of a financial stress shock. It has a more persistent negative impact on real GDP growth in the high-stress regime. In the case of a linear VAR, the negative impact of financial stress shocks on real GDP growth may be underestimated (black line). Figure 11 shows counterfactuals around two major epi sodes of financial stress: the housing market crash of the 1990s and the 2008 global financial crisis. I hold the policy rate at its historical value. I compute three counterfactuals and, together with the realized data, I obtain four cases: with or without financial stress shocks and with or with out a transition from the low-to the high-stress regime. In all counterfactuals, real GDP would have been signifi cantly higher. This suggests that financial stress has the greatest negative impact on GDP growth when there is a combination of financial stress shocks and a change to the high-stress regime. Financial stress shocks are an import ant source of concern for the macroeconomy mostly when they are amplified in the high-stress regime. 15 I construct a CFSI that captures the intensity of financial market turmoil in Canada that spans seven market seg ments. The index emphasizes the periods in which it is harder for investors and borrowers to substitute away assets that face market stress. The innovation is twofold compared with the existing measures of financial stress. First, I include stress on the housing market. This is a crucial source of shocks for Canada-for instance, around the housing market cor rection of 1990. Second, compared with the two existing measures of financial stress for Canada (Cardarelli et al. 2011; Illing and Liu 2006 ) , I capture the co-movement across market segments, which tends to be stronger dur ing systemic events. Those improvements lead to an index that better aligns with known episodes of fi nancial stress in Canada. The CFSI can be helpful for at least two purposes. First, it helps benchmark the intensity of financial stress against historical episodes. Second, financial market stress is often associated with non-linear macro-financial dynamics that can amplify negative shocks. Above its 90th percentile, the CFSI is typically associated with more fragile macro economic conditions in Canada. I illustrate how financial stress and worsening macroeconomic conditions amplify each other in the context of a Bayesian TVAR. The model ex plicitly relates episodes of elevated financial market stress, as reflected by the CFSI, with a deeper correction of GDP. The results suggest that using financial stress indexes to signal rapidly deteriorating financial conditions can be useful to better capture the deterioration of macro economic conditions when tail events materialize. Thus, the CFSI is included in either the RAMM (Traclet and MacDonald 2018) or the growth-at-risk model (Duprey and Ueberfeldt 2020) , two models used in the risk man agement framework of the Bank of Canada (Poloz 2020) to weight risks to the outlook. Assessing macro-financial risks and their real economic implications is especially relevant in the context of the COVID-19 pandemic, during which financial stress reached levels comparable only to the 2008 global fi nancial crisis. tional heteroskedasticity (GARCH) model to ensure more stability of the estimate at a higher frequency. These transformations aim to capture the evolution of risks in key Canadian markets, but they also partly refl ect the evolution of global risk premium to which Canada is large ly exposed as a small, open economy (Bauer et al. 2018) . Because high values are associated with more stress, most Notes of the raw indicators are right-skewed. The use of ordinal ranking therefore implies that the relative magnitude of 1 The April 2020 Monetary Policy Report (Bank of Canada the stress events during periods of high stress is lost. In the 2020, Chart 9) features the CFSI. meantime, there are fewer data points with very large stress, 2 For instance, in the Canadian case, one could consider daily and it may be harder to find an appropriate benchmark payments data (e.g., cards; Galbraith and Tkacz 2013), data without looking at other data points in the same neighbour on bankruptcies (Allen and Basiri 2018), or data from conhood of the quantile distribution rather than looking at the sumer credit rating agencies (Kartashova and Zhou 2020) . actual distribution. However, the alternative-for instance, 3 The index can also be computed at a higher frequency (e.g., normalizing using variance-equal weights-is less robust to weekly), with additional assumptions: some variables need outliers with large values. to be interpolated, and instead of using realized volatilities, 6 The index is robust to using a backward-expanding window, a rolling window, or the whole sample to normalize the data. 7 The covariance and volatilities are initialized at their longrun average. Figure C .1 in Appendix C displays an alter native CFSI when using a different λ parameter or when computing a multivariate GARCH. 8 I can back-cast the CFSI with fewer time series to start in 1964 instead of 1981, ultimately getting close to the few time series used in Klaus (2017 ) since 1964. 9 For more details on the AUROC, see, for example, Fawcett (2006 ) for a technical overview and Schularick and Taylor (2012 ) for an application to crisis identification. 10 It is also standard to use the noise-to-signal ratio of Kamin sky, Lizondo, and Reinhart (1998 ) . However, the ratio im plicitly embeds a given trade-off between noise and signal. It can lead to counterintuitive results depending on the rela tive variation of the numerator or denominator. Therefore, I do not use this less robust method. 11 This simple approach is consistent with the quantile re gression framework of Adrian, Boyarchenko, and Gian none (2019 ) for the United States or Duprey and Ueberfeldt (2020 ) for Canada. 12 In the beginning of the sample, no monthly GDP measure is available for Canada. I use the quarterly GDP measure spliced with the monthly seasonally adjusted index of in dustrial production. Similar results are obtained when using the monthly seasonally adjusted annualized growth rate of the industrial production index instead. However, industri al production is a narrower definition of economic activity. 13 Similar results would be obtained with a signs restriction shock identification. 14 The assumption of the absence of thresholds can be rejected: the data favour the Bayesian TVAR over a standard VAR. 15 This holds true for different lags or different delay param eters. Appendix A The benchmark Canadian financial stress index (CFSI) starts in 1981. For any of these indexes of fi nancial stress, the trade-off is between data quality and data coverage. sector. Interbank spreads, bank funding spreads, corpor ate spreads, and households' mortgage spreads are not available in the first few years. Before 1981, the market segments reflecting stress for money markets, banks, corporations, and households encompass only one or two individual inputs instead of three to four. Before 1973, data that capture stress on those markets are more limited, and one could use the Country-Level Index of Financial Stress (CLIFS) index of , who extend the country coverage of to further back-cast the CFSI until 1964. The construction method of the CLIFS index for Canada shares similarities with that of the CFSI, but it uses only three to five main time series to reflect stress on three to fi ve market segments. The back-casted time series are presented in Figure B .1, and the episodes of high financial stress are con sistent with the narrative of stressful episodes, such as the monetary crisis of 1971 or the oil price shocks of the 1970s. The CFSI is the plain black curve and starts in 1981.The backward extended CFSI follows the same construction as the CFSI, but a few time series are missing from 1973 to 1981 for four of the seven sectors covered. Before 1973, a few sectors have no available data, and the CFSI cannot be computed. I extend the stress index back to 1964 using the CLIFS metric of , which follows a simplifi ed (but similar) construction procedure but focuses only on equity, government, foreign exchange, banking, and housing stress. CFSI = Canadian financial stress index; CLIFS = Country-Level Index of Financial Stress index. Source: Author's calculations. Illing and Liu's (2006) dates + 2008 global financial µ = 0.5 µ = 0.6 µ = 0.4 crisis + 2015 oil price shock + 1990 housing market correct -LTCM crisis - dot-com bubble burst AUROC pAUROC T1 T2 U T1 T2 U T1 T2 U CFSI Illing and Liu (2006 ) . It consists of the following events:August 1981 spike in interest rates, Latin American debt crises (early 1980s), Canadian commercial bank and Northland failures (1985), October 1987 stock market crash, early 1990s bank losses, Mexican crisis (1994) (1995) ,Asian crisis (1997) (1998) , Russian debt default and LTCM bailout (1998), the burst of the dot-com bubble (2000), and 11 September 2001 terrorist attacks.The 1998 and 2000 events were assessed as only somewhat stressful by most of the respondents and are thus removed.We added the following events that were not part of the survey: the 2008 crisis, the 2015 oil crisis, and the 1990 housing crisis.AUROC is associated with an informative signal when it is above 0.5, whatever the preferences of the regulator. pAUROC is restricted to assess the informativeness of a signal under a subset of preferences of the regulator, in the range µ = [0.3; 0.7]. µ is the cost associated with T1 (i.e., the share of missed crises). Conversely, 1 − µ is the cost associated with T2 (i.e., the share of false signals).A higher µ is associated with an aversion to missing crises (thus a lower T1).When computing the different measures, the 12 month after a stressful event are removed unless another stress event starts during this period. Otherwise, the assessment could be biased by the behaviour of the stress indexes during the recovery period. CFSI = Canadian financial stress index; LTCM = Long-Term Capital Management; AUROC = area under the receiver characteristic curve; pAUROC = partial area under the receiver characteristic curve;T1 = type 1 errors; T2 = type 2 errors; U = Alessi and Detken's (2011 ) usefulness indicator that measures the signal's ability to be informative under certain preferences µ. Source: Author's calculations. 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Using a cross-country dataset of 27 European fi nancial stress indexes, found that a parameter  = 0.85 generates a financial stress index that is closest to the multivariate GARCH. BEKK = Baba-Engle-Kraft-Kroner (Baba et al. 1985) ; CFSI = Canadian financial stress index; GARCH = generalized autoregressive conditional heteroskedasticity.Source: Author's calculations. Appendix D: