The impact of risk cycles on business cycles: a historical view

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1358 September 2022 The impact of risk cycles on business cycles: a historical view Jon Danielsson, Marcela Valenzuela, and Ilknur Zer Please cite this paper as: Danielsson, Jon, Marcela Valenzuela, and Ilknur Zer (2022). “The impact of risk cycles on business cycles: a historical view,” International Finance Discussion Papers 1358. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2022.1358. NOTE: International Finance Discussion Papers (IFDPs) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

The impact of risk cycles on business cycles: a ∗ historical view J´on Dan´ıelsson Marcela Valenzuela Ilknur Zer August 2022 Abstract We investigate the effects of financial risk cycles on business cycles, using a panel spanning 73 countries since 1900. Agents use a Bayesian learning modeltoformtheirbeliefsonrisk. Weconstructaproxyofthesebeliefsand show that perceived low risk encourages risk-taking, augmenting growth at the cost of accumulating financial vulnerabilities, and therefore, a reversal ingrowthfollows. Thereversalisparticularly pronouncedwhenthelow-risk environment persists and credit growth is excessive. Global-risk cycles have a stronger effect on growth than local-risk cycles via their impact on capital flows, investment, and debt-issuer quality. Keywords: Stock market volatility, uncertainty, monetary policy independence, financial instability, risk-taking, global financial cycles JEL classification: F30, F44, G15, G18, N10, N20 ∗ Corresponding author: Ilknur Zer. Federal Reserve Board, Washington DC, 20007, USA. ilknur.zerboudet@frb.gov. Jon Danielsson is at the London School of Economics (LSE) and the director of the Systemic Risk Centre at LSE. Marcela Valenzuela is at the School of Management,PontificiaUniversidadCat´olicadeChile. WethankAlejandroBernales,NelsonCamanho, Alessandro Rebucci, Consuelo Silva, Andreas Uthemann, Cristi´an Va´squez, and Jean-Pierre Zigrand, as well as seminar participants in the Nova School of Business and Economics, Banco de Portugal, Banque de France, Federal Reserve Board, IMF Macro-Financial Research Division, UniversityofCyprus,PontificiaUniversidadCat´olicadeChile,andAdolfoIba´n˜ezUniversity,the EuropeanEconomicAssociationmeeting, andthe EuropeanFinancialManagementAssociation meetings (GARP Risk ManagementAward, 2022)for valuable comments. Alessandro De Trane provided excellent researchassistance. Philipp Ad¨ammer wrote the LPIRFS R package we used in the analysis (Ad¨ammer, 2019). Danielssonthanks the Economic andSocial ResearchCouncil (United Kingdom)[grantnumber: ES/K002309/1]for its support. Valenzuela acknowledgesthe support of Fondecyt Project No. 1190477 and Instituto Milenio ICM IS130002. The views in this paperaresolelythoseofthe authorsandshouldnotbe interpretedasreflectingthe viewsof the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System.

1 Introduction The global financial crisis in 2008 reminded us of the importance of the financial sector for the macroeconomy, a lesson many had forgotten in the decades after the previous global crisis, the Great Depression. Financial risk matters. It is necessary for investment and growth but also drives uncertainty, inefficiency, recessions, and crises. While the interplay between financial risk and macroeconomy is complex, our interest in this work is on one particular dimension: how economic agents’ perception of financial risk affects business cycles. We refer to the map of rises and falls in agents’ perception of risk as the risk cycle and investigate how financial risk cycles, obtained from market prices and spanning 73 countries since 1900, affect business cycles. Whiletheobviouswaytoproceedempiricallywouldbetosimply modeltheimpact of risk measurements on economic growth, there is an important nuance that can only be captured by separating periods of high risk from low risk. As high risk is characterized by high uncertainty, it is detrimental to economic growth, in part, because it increases the real option value of delaying investments (Dixit and Pindyck, 1994; Bloom, 2009; Bloom et al., 2018; Pflueger et al., 2020). If high risk is detrimental to growth, one might therefore expect low risk to be similarly beneficial. We hypothesize that it is, but only in the short run. As time passes, a reversal of the impact on growth becomes increasingly likely — what we term the boom-to-bust effect of low risk on business cycles. While several factors might account for how low risk affects growth, we surmise that the inability to measure risk accurately and the evolution of financial leverage play a particularly large role. Risk is a latent variable, so one can only use a model to estimate it, implying all risk measurements are inaccurate. Consequently, the degree of economic agents’ beliefs in whether risk is high or low is of crucial importance to them. In our setting, the agents’ risk beliefs are reinforced by them learning from repeated observations of risk being low, in the spirit of Veronesi’s (1999) Bayesian learning model. In turn, the strength of the agents’ beliefs reinforces optimism and willingness to take on more risk, consistent with the literature on procyclical leverage.1 Moreover, during such tranquil periods, asset prices increase (Brunnermeier and Pedersen, 2009; Scheinkman and Xiong, 2003). Thus, beliefs, financial frictions, and risk-taking incentives interact: the willingness to take on more risk, increased asset prices, and easier credit conditions drive investment and hence, economic growth — the boom in the boom-to-bust cycle. 1In Geanakoplos(2001);Fostel and Geanakoplos(2008),agents are subject to collateralconstraints, which are loosened during low-risk periods. Similarly, value-at-risk constraints are loosenedwhenvolatilityislowasinBrunnermeierandPedersen(2009);Dan´ıelssonetal.(2012). Caballero and Simsek (2020) model low and high volatility states separately and show that investors do not require high compensation to invest in low-risk states. 2

However, eventually, the agents start running out of high-quality investments and asset prices revert, making risk and leverage constraints binding (Greenwood and Hanson, 2013; Adrian and Liang, 2018). Depressed asset prices reduce the value of borrowers’ assets, suppressing investment as in Bernanke and Gertler (1989); Bernanke et al. (1999) and laying the seeds for a reversal, along the lines of Minsky’s (1977) instability hypothesis — the bust in the boom-to-bust cycle. We further expect that the strength of the boom-to-bust cycle and the aggregate impact of low-risk perceptions on economic growth depends on the underlying credit market conditions and the length of the low-risk periods. When credit growth is “excessive”, the financial system is more likely to be in a vulnerable state (see e.g., Schularick and Taylor, 2012; Aikman et al., 2017). Increased risktaking — fueled by a longer-lasting low-risk environment — boosts the amplitude of the bust cycle because, in that case, even a small revision of beliefs can create a self-reinforcing feedback loop that impairs credit provision, lowers asset prices, and depresses economic activity. There is a strong global dimension in the impact of risk perceptions on growth and financial stability, stressed in the recent literature on global financial cycles (see e.g. Di Giovanni et al., 2021; Miranda-Agrippino and Rey, 2020; Rey, 2018; Jorda` et al., 2018; Durdu et al., 2020). Both global and domestic investors are guided by perceptions of global risk when raising funds in global capital markets and how they allocate those funds to investments. We consequently propose three channels for how global risk perceptions affect growth: domestic investment, international capital flows, and debt-issuer quality. When investors perceive risk as low globally, they seek riskier investment alternatives and are more inclined to reach for yield by allocating funds to riskier asset classes and countries, boosting capital flows (see e.g., Bruno and Shin, 2015). Easing global financial conditions transmit to domestic credit conditions and increase local lending and investment (Di Giovanni etal.,2021). Moreover, insuchperiodsofheightenedrisk-taking, evenpoor-quality borrowers are more likely to be financed (Greenwood and Hanson, 2013), further boostingshort-termgrowth, atthecostofincreasedfinancialvulnerabilities. Thus, weexpectasimilarboom-to-bustcycleininvestment, capitalflows, anddebt-issuer quality. This paper has three methodological contributions. First, we construct a model in which risk readings affect the agents’ posterior belief of risk being low or high. The second contribution is an empirical model of risk perceptions based on a proxy for the posterior belief, what we term the duration of low risk, or DLR. We estimate DLR with stock market returns for various countries in long time-series data, giving us a broad historical and international perspective on the nexus between financial risk and business cycles. Moreover, that approach enables us to examine whether risk perceptions in stock markets are an important driver of economic fluctuations. Our final methodological contribution is to create a measure of global 3

risk perception, global DLR (G-DLR), by aggregating the DLR estimates across each country in our sample. As both DLR and G-DLR affect agents’ willingness to assume risk, the rises and falls in DLR and G-DLR form the domestic and global risk cycles, respectively. We use G-DLR to study the relative importance of global and local risk cycles on country-specific business cycles. We start our analysis with a model of risk beliefs. Suppose stock market returns follow a stochastic volatility model containing a persistent Markov switching mean component that determines whether the volatility state is high or low. While the actual state is latent, the agents receive a noisy signal of it, which they combine with their prior belief of the risk state to construct a posterior belief of whether risk is low or high. Their posterior beliefs drive their appetite for risk, and hence, their investment decisions. While we cannot directly estimate the agent’s posterior beliefs, we know its characteristics and can therefore propose a proxy, DLR, which is highly correlated with the posterior. By construction, DLR increases at a decreasing rate along with the length of a low-risk environment. To estimate DLR, we first measure risk by realized stock market volatility2, and then, we quantify what “low risk” is. The lower the volatility, the higher the chance risk is low, and thus, we identify periods of low risk when the estimated volatility is below a threshold. One can think of that threshold as “usual” risk, so agents alter their investment decisions when risk deviates from such levels, as in Keynes’ (1936) animal spirits. The threshold cannot be constant across time and countries because the extant empirical evidence suggests that volatility has long volatility clusters, implying a particular volatility reading might be seen as high risk in one state of the world and low in another. It is therefore necessary to model the threshold as a dynamic variable similar to how dynamic volatility is modeled. To that end, we use the historical volatility trend as the threshold in the baseline specifications. To estimate the trend, similar to our earlier work (Danielsson, Valenzuela, and Zer, 2018), we use a one-sided Hodrick-Prescott (1997) filter using only past information to estimate the trend for a given time, necessary in our case because we run predictive regressions.3 As a prelude to our empirical analysis, we confirm that DLR is closely related to other measures of investor risk perception and risk appetite, including measures based on option prices and survey-based expectations of corporate credit conditions. In addition, in a panel regression setting, we show that DLR is significantly 2Alternatively, we could have used corporate bond spread data since spreads are especially informativeaboutcreditconditionsandtherealmacroeconomicoutcomes(Gilchristetal.,2009). However, country-level historical cross-sectional data on bond spreads are scarce. Moreover, traditional rational asset pricing models, including Bansal and Yaron (2004) suggest that stock pricesareforward-lookingandthus theagents’riskappetite shouldbe reflectedintheaggregate stock market prices (Pflueger et al., 2020). 3In Section 4, we show that our main findings do not change when employing the linear projection method proposed by Hamilton (2018). 4

correlated with contemporaneous stock market returns: lower perceived risk is associated with an increase in the prices of risky assets. Finally, DLR rises (risk perceptions fall) withthe arrivalof goodmacroeconomic news, lowmacroeconomic uncertainty, excess financial market liquidity, and looser than expected monetary policy decisions. Our empirical framework is impulse response functions obtained from Jorda`’s (2005) local projection method, which captures the impact of a one-year increase in the persistence of low or high risk on growth, contemporaneously and up to five years into the future. We find six sets of results: First, a positive shock to DHR — risk remaining high for an additional year — has an unambiguous negative impact on economic growth, contemporaneously and in the next year. A one standard deviation increase in local DHR decreases economic growth by 0.8% cumulatively, whereas the economic impact of global DHR is about double of its local counterpart, with a cumulative contraction of 1.5%. These results are in line with the extant literature, which associates high volatility with high uncertainty, harming growth, and emphasizes the importance of global financial factors (e.g., Bloom, 2009; Rey, 2018). Second, the impact of perceptions of risk being low is not merely the mirror opposite of its high-risk counterpart. Instead, a positive shock to DLR has a boomto-bust impact on economic growth: Growth increases contemporaneously and especially one year hence, with a significant reversal in year two. The impact of global DLR is about double of the local counterpart. Even with a correction in year two, a one standard deviation increase in global DLR increases economic growth by 0.7% across the boom-to-bust cycle. Thus, a low-risk environment has a cumulative positive impact on GDP growth. In the third set of results, however, we show that the cumulative impact of low risk on growth might be negative overall when the low risk has persisted for a particularly long time and when a country experiences a credit boom. The marginal impact of G-DLR on growth is concave: initially increasingly positive, but then turning negative. That is, a very-long low-risk environment this year leads to a decrease in cumulative growth over its boom-to-bust cycle. Moreover, if a country is in the highest decile of credit growth in a particular year, the amplitude of the bust cycle is triple what it would otherwise be and longer-lasting. In that case, a shock to global DLR translates into a 0.65% contraction in growth over the boom-to-bust cycle cumulatively. Thus, we conclude that if a country experiences “excessive” credit growth or if a low-for-long risk period persists, strengthening perceived low risk globally further exacerbates financial vulnerabilities, making the economy more fragile and reducing aggregate growth. The 2008 crisis illustrates these findings well. DLR was particularly low in the years before the crisis, while credit growth was excessive, suggesting that the overall boom-to-bust effect had a negative impact on growth. Taken together, these results provide support 5

for our notion of financial vulnerability-driven economic contraction. Whilewefindanunambiguousboom-to-busteffectofperceived lowriskongrowth, the results might be biased by endogeneity. An omitted variable can affect both the risk perceptions and growth or the causality may go from growth to volatility but not in the opposite direction. We attempt to address these concerns with two approaches. First, we employ a two-stage regression analysis similar to Lo´pez- Salido et al. (2017). In the first stage, we regress G-DLR on a range of plausibly exogenous variables (including natural disasters and liquidity shocks) that can affect agents’ perceptions of risk. In the second stage, we investigate the effects of the fitted values of G-DLR on growth. Second, we use the news shocks of Berger et al. (2020), derived from option prices and orthogonal to current realized volatility innovations. Our results continue to hold when we use either approach. The two exercises increase our confidence in the validity of our results that an increase in G-DLR leads to a boom-to-bust cycle. Moreover, our main findings are robust to a range of alternative specifications and parameterizations, including alternative definitions of volatility, volatility trend, and model specifications. Fourth, we examine three channels for how perceived low risk affects growth: domestic investment, capital flows, and debt-issuer quality (measured by the share of high-yield bond issuance). We find that a positive G-DLR shock has a significant and strong impact on domestic investment, portfolio capital flows, and the share of high yield bond issuance: initially positive, but turning negative in years two to four. Moreover, we find that the effects of local DLR on investment, capital flows, and debt-issuer quality are negligible. Fifth, because of the way G-DLR is constructed, we can add further nuance to the emerging literature on the importance of the United States for global financial cycles. We repeat our impulse response analysis, but this time replace G-DLR with the local U.S. DLR. We find supporting evidence that the United States plays a pivotal role in shaping global risk. Since US-DLR explains about 30% of the variation in G-DLR, with a large impact on country-level growth, yet weaker than that of G-DLR. Finally, by splitting the sample into countries classified by the IMF as developed or emerging, we find that the effects of global risk cycles on emerging countries’ growth are higher than that of the local risk cycles and developed countries. Taken together, we show that perception of high risk has an unambiguous negative impact ongrowth, whileperceived lowriskhasaninitialpositiveandthennegative impact. Astrengthening perceptionofriskbeinglowhasanoverall positiveimpact on growth, except in times of very high credit growth, when the supply of highqualityassetsislikelytobediminished. Theglobalriskenvironment isparticularly importantinshapinglocalbusiness cycles throughitseffectsoninvestment, capital flows, and debt-issuer quality. 6

Ourresultscontributetoseveralimportantpolicydebates, includingmacroprudential regulations, monetary policy independence, and the importance of the global risk environment. Policymakers should consider the joint impact of global risk perceptions, above and beyond local risk, and macroeconomic outcomes. Even if a domestic monetary authority intends to either stimulate or cool down its national economy by affecting the price and quantity of money, global risk perceptions and risk-taking incentives in global financial markets (or a central economy like the United States) can override national monetary policy decisions. Our paper relates to several branches of the literature. First, Kozlowski et al. (2020) model how agents form their beliefs, enabling tail events to trigger larger belief revisions. Meanwhile, Lochstoer and Muir (2020) find that due to agents’ slow-moving beliefs about stock market volatility, their expectations initially underreact to news, followed by an overreaction. In another related literature on agents’ perception of risk and its effects on the macroeconomy, Lo´pez-Salido et al. (2017) find that elevated credit sentiment in the United States harms growth, whereas, stock market sentiment hasno significant effect ongrowth. Pflueger et al. (2020)identifyapositiverelationshipbetweenriskperceptionandinvestment. Our proposed measure DLR is closely related to other risk perception/appetite proxies, including Pflueger et. al (2020)’s PVS. We then provide evidence that risk perceptions in stock markets are an important driver of economic fluctuations and risk cycles are not only isolated to the issuance and pricing of credit, as concluded by Lo´pez-Salido et al. (2017). Second, in earlier literature, Levine and Zervos (1998), Beck et al. (2000), Beck and Levine (2002), and Levine (2006), among others, stress the pivotal role of the structure of the financial system for economic growth. More recent literature, including Durdu et al. (2020), Avdjiev et al. (2016), Rey (2018), and Jorda` et al. (2018) focus on the importance of the U.S. financial system driving global financial system, which in turn affects economic growth. We add a broad historical and international perspective on the effects of global financial risk cycles on business cycles. Third, we draw on the methodological contributions of our earlier work, Danielsson, Valenzuela, and Zer (2018), where we identify the importance of separating low risk from high risk in predicting the likelihood of crises. In this paper, we study the effects of risk perceptions — based on a Bayesian learning model of a low-risk environment — on growth rather than banking crises. Moreover, while Danielsson, Valenzuela, and Zer (2018) solely focus on the domestic risk environment, in this paper, we underline the importance of the global risk environment. Finally, we show that different mechanisms are more appropriate for predicting growth than banking crises. We finally contribute to the vast literature on the effects of financial risk ongrowth (Bloom, 2009; Bloom et al., 2018) by showing an asymmetric impact of low and 7

high risk on growth. 2 Data and empirical approach 2.1 Volatility, risk perception and the duration of low risk The extant literature shows that agents’ perceptions of low or high risk alter their investment decisions (Caballero and Simsek, 2020; Pflueger et al., 2020). We capture the distinction between high and low risk by a binary variable that impacts volatility. Suppose the variance of financial returns (σ2) follows a discrete stochast tic volatility model with a first-order autoregressive process and a time-varying mean, similar to Hamilton (1989) and Danielsson (1994): y = σ ǫ , t = 1,··· ,T, ǫ ∼ N(0,1) (1) t t t logσ2 = γ +γ I +βlogσ2 +η , η ∼ N(0,ζ2), (2) t 0 1 t t−1 t t where I indicates whether the volatility state is high or low: t 0 if x = Low t I = (3) t (1 if x t = High. x is an unobservable Markov switching binary state variable with symmetric trant sition probabilities q, where q > 0.5 so that the risk state is persistent, consistent with empirical observations of volatility clustering: q if x = x t+1 t Pr(x | x ) = (4) t+1 t (1−q if x t+1 6= x t . Economic agents’ investment decisions are based on the risk state and we capture thedistinction between highandlowrisk by I . Furthermore, we assume γ > 0, so t 1 that (2) implies that volatility decreases when the risk state is low. Although the risk state is latent, the agents observe volatility and use it to form their posterior probability of it. Specifically, the agents’ signal is a transformation of volatility, which can be written as a noisy signal of the true risk state: 1 η s = logσ2 −γ −βlogσ2 = I + t . (5) t γ t 0 t−1 t γ 1 1 (cid:0) (cid:1) The agents start each year with a prior belief (α ) about the current risk state. t Conditional on having observed a history of signals, Bayesian updating implies 8

that the posterior belief of the risk state being low (α ) is updated by: t|t Pr(s | x = Low)α t t t α = (6) t|t Pr(s | x = Low)α +Pr(s | x = High)(1−α ) t t t t t t φ γ1st α ζ t = , (7) φ γ1st α + (cid:16) φ γ1 (cid:17) (st−1) (1−α ) ζ t ζ t (cid:16) (cid:17) (cid:16) (cid:17) where φ(·) is the standard normal density. Since η is normally distributed with t mean0andvarianceζ2,s |x = Low ∼ N(0,ζ2/γ2)ands |x = High ∼ N(1,ζ2/γ2). t t 1 t t 1 The agents then use α to update their prior beliefs in the next year. Given the t|t Markov transition probabilities, the prior belief in year t+1 is given by: α = qα +(1−q)(1−α ). (8) t+1 t|t t|t The posterior probability α has two important properties. First, the persistent t|t nature of the risk state along with (8) implies that the posterior probability is also persistent and increases at a decreasing rate with repeated low volatility signals. Second, the lower the volatility shock η is, and thus the volatility, the higher the t posterior probability. We cannot directly construct the posterior probability, as the model parameters are not observable to us. Consequently, we use (7) and (8) to construct a variable that proxies for the posterior belief, what we term the duration of low risk, DLR. DLR encapsulates the two key notions of the posterior that repeated observations of a low-risk state increase DLR at a decreasing rate and the lower the volatility is, the higher DLR becomes on average. Specifically: N 1−θ DLR = θj+1(1− t θ(1−θN+1) j=0 X 1 ), (9) t−j where the first term normalizes DLR so that it is bounded at one, N is the number of years the volatility state has been consecutively estimated as low, 0.5 < θ < 1, and 1 equals 1 if volatility is high and 0 otherwise. It is then straightforward to t show that: DLR = [θDLR +(1−θ)(1− t t−1 1 )](1− t 1 ). (10) t The persistence parameter θ captures the weight agents attach to historical observations when constructing their posterior beliefs. In order to see how θ is related to the model parameters, we use (7) and (8) to approximate θ as follows: (2q −1)φ (1−q)φ (2q −1)(φ −φ ) L L L H θ ≈ − , (11) (1−q)φ +qφ ((1−q)φ +qφ )2 L H L H 9

where φ = φ γ1st and φ = φ γ1(st−1) . See Appendix C for the derivation L ζ H ζ details. (cid:16) (cid:17) (cid:16) (cid:17) In order to evaluate how accurately DLR proxies the posterior and to identify the appropriate values for θ, we calibrate the volatility model parameters to five moments4 of the annual S&P 500 index returns. We then use the calibrated parameters to simulate representative volatilities, thus ensuring their time-series properties match those of the S&P 500. With the simulated volatilities in hand, we calculate the correlation between the posterior and DLR. We find that for θ ∈ (0.70,1), theDLR-posteriorcorrelationrangesfrom0.70to0.95. Furthermore, we calculate the average θ implied from (11) and finding that to be 0.92, opt to use that value for our main analysis. The corresponding correlation between the posteriorandDLRis0.81whenθ = 0.92, whichisalsoconsistent withtheaccurate weighing of historical annual volatility in volatility forecast models.5 The final step is the empirical estimation of DLR, which in turn depends on identifying the high and low volatility periods. It follows from (2) that if the volatility is very low it is more likely that the volatility state is low and that volatility is below some threshold. In other words, when volatility (σ ) is below a threshold (τ ) we t t can classify the volatility state as low, and high otherwise. This identification is noisy, consistent with (5). The threshold cannot be constant across time andcountries, because volatility cycles are both long and asynchronous across countries. Consequently, a particular measurement of volatility might be seen as worryingly high in one country/time and as comfortably low in another. Ultimately, we need to estimate both the volatility and the threshold dynamically. 2.2 Estimating risk cycles We estimate DLR (and DHR) for each country separately, by first calculating the annual realized volatility as the standard deviation of monthly real market returns over a year.6 To account for different inflation dynamics throughout time and 4The five moments we use are the mean, variance, skewness, and the first and second order autocorrelationof squared annual returns. 5The exponentially weighted moving average volatility model and (10) have a familiar functional form,not surprising as both models capture volatility clusters. The estimated persistence parameter in such volatility models is generally found to exceed 0.90, and hence consistent with our chosen value for θ. As a further robustness check, we show in Section 4 that our main findings are robustto a wide rangeof θ or when we do not consider any decayingfactor and instead simply count the number of years that a country stays in a low volatility stage. 6Instead,wecouldhaveestimatedaconditionalvolatilitymodelfromtheGARCHfamily(see Engle, 1982; Bollerslev, 1986, 1987). We do not think such models are suitable for the annual volatility we require. Not only is the half-life of shocks to GARCH volatility typically less than one year, but such models also require hundreds of observations for estimation, a luxury we do nothave. Similarly,wecouldhaveusedPakeletal.(2020)compositemaximumlikelihood,which 10

across countries, we adjust nominal returns with the consumer price index (CPI). In Section 4, we show that using nominal market returns or absolute value of returns to estimate annual volatility does not materially change our findings. Alternatively, given that corporate bond spreads are informative about credit conditions and real macroeconomic outcomes (Gilchrist et al., 2009), we could have used spread data to drive DLR. However, country-level historical crosssectionaldataonbondspreads(includingTreasury–corporateyieldandhighyield– investment grade yield spreads) are scarce. Moreover, the agents’ risk appetite should be reflected in the aggregate stock market prices, consistent with traditional rational asset pricing models (Bansal and Yaron, 2004; Pflueger et al., 2020).7 Hence, we estimate DLR using stock prices, given that it is more readily available in a consistent form in any country with a stock market. Second, after calculating the realized volatility estimates, σˆ , we obtain the low i,t and high volatilities (σˆlow, σˆhigh), analogous to receiving high and low signals in i,t i,t (5): σˆ −τˆ if σˆ > τˆ σˆhigh = t i,t t i,t i,t 0 otherwise, (cid:26) (12) σˆ −τˆ if σˆ ≤ τˆ σˆlow = t i,t t i,t i,t 0 otherwise, (cid:26) where τˆ is the estimated trend of volatility. In particular, a country is in its i,t low volatility state, if the estimated volatility is below the trend. We estimate the requiresabalancedpanelandanassumptionthattheGARCHdynamicparametersareconstant across countries, an assumption we are unwilling to make. 7Inaddition,Gebhardtetal.(2005);Hongetal.(2012)findthatstockreturnshavepredictive power for bond returns as bond prices adjust slower than stock prices to information about changing default risk. Along similar lines, Downing et al. (2009) show that the US corporate bond market is less informationally efficient than the stock market. 11

trend via a one-sided Hodrick and Prescott (1997) (HP) filter.8,9 Ti τˆ (λ) = min [σ −τ (λ)]2 i,t i,t i,t {τi,t(λ)} T t= i 1 t=1 X Ti−1 +λ {[τ (λ)−τ (λ)]−[τ (λ)−τ (λ)]}2, i,t+1 i,t i,t i,t−1 t=2 X i = 1,...,N, (13) where T is the number of observations for country i, or a subperiod if the financial i markets were interrupted, and the smoothing parameter λ quantifies the degree to which volatility deviates from its trend and thus the shape of the estimated cycle. The choice of the smoothing parameter λ depends on the underlying series. The literature suggests a value of 6.25 to 1600 for different frequencies of GDP (Ravn and Uhlig, 2002). However, a larger λ is needed for volatility, because of its clustering nature. Otherwise, a very small λ would make the estimated trend very volatile and it would follow very closely the volatility series itself. Following our earlier work (Dan´ıelsson et al., 2018), we set λ = 5000. In Section 4, we apply various smoothing parameters, concluding that the results are indifferent to the chosen parameter. We collect monthly stock market indexes from the Global Financial Data (GFD), with data available for 73 countries, from 1900 to 2016. On average, we have 55 years of observation per country. At the beginning of the sample, we have observations on only seven countries, the United States, Great Britain, Germany, France, Belgium, Australia, and Denmark as shown in Figure 1. The number of countries increases steadily over time, (Table A1 in Appendix A lists individual countries’ coverage). There are two sharp upticks in the number of countries with stock markets following World War I and the 1990s. The largest increase in the sample size comes from newly independent emerging countries establishing stock markets, identified as the blue line in Figure 1. 8As our analysis builds on predictive regressions, we use only past information when constructing the explanatory variables. Hence, we employ a one-sided HP filter. Moreover,in some countries, there are gaps in the data, either because economic historians haven’t collected the dataormarketshavebeenotherwiseinterrupted. Inthosecases,werestartthecalculation,with a new HP filter. 9The HP filter has come under criticism from Hamilton (2018). However, as argued by Drehmann and Yetman (2018), the choice of an indicator is driven by the application, and in their particular case—the credit gap as an early warning indicator for financial crises—the HP filter performs better. We reach a similar conclusion in our empirical analysis. Although similar,the volatilitytrendobtainedfromtheHPfilterissmootherovertime thanthe Hamilton trend and hence, more suitable for our purposes. Accordingly, we use the HP filter in baseline specifications and provide the robustness of our findings by using the linear projection method proposed by Hamilton (2018) in Section 4. 12

Figure 1: Data coverage The number of countries with available stock market return data from 1900 to 2016. The classification into developed and developing is from the International Monetary Fund. Data source: Global Financial Data. 60 50 40 30 20 10 fo rebmuN seirtnuoc All Developed Developing 1900 1920 1940 1960 1980 2000 We show the volatility and the estimated trend for the United States in Figure 2 while presenting the remainder of the countries’ volatilities and trends in the webappendix, available at modelsandrisk.org/appendix/risk-cycles/. Figure 2: United States volatility and trend Annual volatility and estimated trend for the United States. Volatility is calculated as the standarddeviationoftheprevious12monthlyrealstockmarketreturns. Thetrendiscalculated by a one-sided Hodrick-Prescott filter with a smoothing parameter of λ = 5000. Data source: Global Financial Data and author calculations. 20% Trend Volatility 15% 10% 5% 1900 1920 1940 1960 1980 2000 Finally, we use the estimated low and high volatilities to calculate DLR and DHR. and calculate DLR (and DHR). We present DLR and DHR estimates for each country in our sample in the webappendix, available at modelsandrisk.org/ appendix/risk-cycles/. 13

2.3 The global risk cycle Themapofrises andfallsinglobalDLRconstitutes theglobalriskcycle, capturing the aggregate risk appetite of economic agents across the globe. The global DLR (G-DLR ) is obtained as the GDP-weighted average of the local measure (DLR ) t i,t across all countries with data in year t. G-DHR is calculated similarly.10 The Gt DLR measure in Figure 3 highlights NBER recession dates and marks key events in world economic history. Visual inspection indicates that high G-DLR presages stress events—for example, in the late 1920s before the Great Depression, in the mid-1990s before the Asian crisis, and in the mid-2000s before the 2008 crisis. Within the entire sample, one episode stands out as anomalous, World War II. Not only do the number of countries in the data set fall, but many of the countries with open stock markets in the sample were also occupied, and markets were disrupted in various ways, with arbitrary closures and confiscation, currency reforms, or very high inflation. We, therefore, drop the World War II years (1939–45) from the regressions. Figure 3: Global duration of low risk The global duration of low risk (G-DLR ) is calculated as the gross domestic product-weighted t average of the local measure (DLR ). DLR is defined in (10), considering the consecutive i,t i,t numberofyearsinwhichstockmarketvolatilityremainslowforcountryiinyeartwithdecaying weights. NBER recession dates are highlighted and relevant economic events are marked in the figure. Data source: Global Financial Data, NBER, and author calculations. 0.4 Global Asian Pa 1 n 9 i 0 c 7 of WW2 starts crisis fin c a ri n s c is ial Recession of 1960-61 Euro Great crisis 0.3 Depression WW1 starts Bretton Woods ends 0.2 0.1 0.0 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 10Asthenumberofcountriesvariesovertime,theglobalriskisconstructedfromanunbalanced panel. Hence,wechecktherobustnessofourfindingswhenglobalriskisobtainedfromabalanced panel considering current G7 constituents (United States, United Kingdom, France, Germany, Italy, Canada, and Japan). The results are presented in Section 4 and the main findings are robust. 14

2.4 Assessing the validity of DLR as a risk perception measure We assess the validity of our proposed measure DLR in three different ways. First, we expect DLR to be correlated to other proxies of risk perception and risk appetite, such as forward-looking volatility and various credit market indicators. Second, because a lower perception of risk should induce agents to take on more risk, weexpect ahigherDLRtoincreasethedemandforstocks. Finally, weexplore why DLR could vary over time. Astheliterature focuses onU.S. proxies ofriskappetite, we pick theU.S. DLRand calculate the correlation between DLR and various proxies: The CBOE Volatility Index (VIX), Bekaert et. al (2019)’s risk aversion measure (BEX), Pflueger et. al (2020)’s PVS, demand and credit standards of corporate loans from the Federal Reserve Board’s Senior Loan Officer Opinion Survey (SLOOS), and finally corporatebondspreads, measured as the difference between BAA andAAA yields. Table 1 Panel A shows that the Pearson correlation coefficient between DLR and the measures we consider ranges from 0.35 to 0.74 (in absolute terms), all significant at a 5% level. Increases in DLR are associated with lower levels of the VIX and BEX risk aversion measures. Being one of the closest measures, at least conceptually, PVS is derived by using firm-level stock price volatility. We find that when PVSisrelatively high, so doesDLR.Measures of corporatecredit conditions, in particular, the fraction of banks that report strong demand for commercial and industrial loans and the tightening of credit standards for such loans (rows 4 and 5) are both significantly correlated with DLR. Finally, DLR significantly increases at the same “good” times when corporate spreads tighten (row 6). We further expect DLR to be significantly correlated with contemporaneous stock returns because agents’ risk perceptions should be reflected in aggregate stock prices. A lower perception of risk should induce agents to take on more risk, causing prices to rise. Weinvestigate that assertion ina panel setting by regressing real stock index returns on DLR, controlling for the standard determinants of stockreturns; including dividend yields, realizedstockmarket volatility, changesin short-term interest rates, term premium, and macroeconomic variables (inflation, the degree of institutionalization, and the level of GDP), along with year and country fixed effects. Data are from the Global Financial Data, Maddison (2003), Polity IV, and Baron and Xiong (2017). We report the results in Panel B of Table 1. We find that DLR is significantly related to contemporaneous stock market returns at a 5% level. A one standard deviation increase in DLR is associated with an increase of 1.3% in annual real returns. UltimatelywefindthatDLRishighlycorrelatedwithextent proxiesofriskperception and strongly correlated with stock returns when controlling for the standard 15

determinants of stock returns, lending further support to our assertion that DLR is a good proxy for risk perception. Then a question remains: why do risk perceptions vary and what could be the possible shocks driving DLR over time? Considerable evidence suggests that financial risk varies with 1) the arrival of news (Bomfim, 2003; Pflueger et al., 2020); 2) macroeconomic or policy uncertainty (Pastor and Veronesi, 2012); 3) market liquidity (Valenzuela et al., 2015); and 4) monetary policy shocks (Rey, 2018). To identify such connections, we regress U.S. DLR on the contemporaneous positive macroeconomic news surprises of Scotti (2016), Bekaert’s et al. (2019) uncertainty index, liquidity shocks as in Bali et al. (2014), and Romer and Romer’s (2004) monetary policy shocks.11 We show the univariate regression results in Table 2. Positive macroeconomic news is associated with falling risk perceptions (higher DLR) as the expectations of consumers and investors adjust following good news arrivals (Forni et al., 2017; Barsky and Sims, 2011). Moreover, DLR is positively associated with low macroeconomic uncertainty, excess financial market liquidity, and looser than expected monetary policy decisions. 3 Empirical methodology and results 3.1 Econometric set-up Our main empirical device is impulse responses obtained from Jorda´’s (2005) local projection method. Specifically, we use a panel setting to regress the dependent variable t + h years in the future, on a variable that is shocked as well as other independent variables observed at t or earlier. We indicate country by i and year by t: ∆y = βhS + L δh∆y + L φhX +αh +ηh +ε , (14) i,t+h i,t k=1 k i,t−k k=1 k i,t−k i t i,t+h h = 0,...,5, P P S = DLR ∨ G-DLR ∨DHR ∨ G-DHR , i,t i,t t i,t t 11TheScotti(2016)surpriseindexaggregatesmacroeconomicU.S.newsreleases(suchasGDP, industrialproduction,retailsales)andconsidersthedeviationofthereleasefromtheBloomberg consensus forecasts. A positive value suggests “good news”: economic releases on balance are higherthanconsensus. Bekaertetal.(2019)uncertaintyindexapproximatesmacroeconomicuncertaintyandisbasedontheconditionalvarianceofU.S.industrialproductiongrowth. Liquidity shocks are defined as the difference between the stock market turnover and its past 12-month average,per Bali et al. (2014). Finally, Romer and Romer (2004)identify changes in the federal funds rate targets surrounding Federal Open Market Committee meetings based on the Federal Reserve Greenbook forecasts. A positive monetary policy surprise value indicates looser-thanexpected monetary policy decisions. 16

where ∆y = y − y with y is the log-GDP of each country in the i,t+h i,t+h i,t+h−1 i,t sample. We obtain annual GDP per capita from the from the Maddison (2003) database, availableathttp://www.ggdc.net/maddison/, used byseveral authors, including Acemoglu et al. (2008) and Reinhart and Rogoff (2009). The shock variable is S and the impulse response is hence βh. αh are country fixed effects, i,t i and ηh are decade fixed effects.12 We set the number of lags at five (L = 5). t X is the vector of control variables. Besides controlling for lagged growth, as i,t well as DLR and DHR and their global counterparts, we use other control variables identified in the literature affecting economic growth. Following Dan´ıelsson et al. (2018), we include the inflation rate and the institutional characteristics of a country as control variables. Inflation is calculated as the annual percentage change in the CPI, obtained from GFD. POLCOMP is the proxy for the institutional characteristics of a country and from the Polity IV Project database. We additionally include log per-capita income as a proxy for an aggregate financial development indicator (Levine and Zervos, 1998; Levine, 2006; Beck and Levine, 2002) and changes in three-month Treasury bill yields as short-term interest rates. Appendix B lists all variables used in the analysis, along with their definitions and data sources. 3.2 Risk cycles and growth We start by investigating the effects of global and local risk cycles on business cycles. Although our stock market data are available for 73 countries, the sample coverage of other series is more sparse. Considering the missing observations, the sample used to run (14) contains 55 countries, spanning 1900 to 2016. Figure 4 shows the impact of global and local risk cycles on growth. Panels (a) and (b) reveal that apositive shock tolocal DHR—that is, lengthening of ahighvolatility state—has an unambiguous negative impact on economic growth, contemporaneously and in the next year. The effect of global DHR (G-DHR) on growth is stronger than local. A one-standard-deviation increase in local DHR decreases economic growth by 0.8% over h = 0 and h = 1, whereas the economic impact of G-DHR is about double of its local counterpart, with a cumulative contraction of 1.5%. The short-term negative impact of DHR on growth is consistent with the extant literature. Increased DHR predicts a slowdown of economic activity in the short term, as it is expected to increase uncertainty, hence, delaying investment, or 12Weinclude10-yearfixedeffectstocontrolforfinancialandeconomicdevelopmentthroughout time. Year fixed effects are not considered, as we have global risk appetite as an explanatory variable,which does not change country by country. Including such a variable in a panel setting is akin to including a time-series trend. In section 4, we include 5-year and 20-year fixed effects as robustness. 17

Figure 4: The impact of risk cycles on growth ThisfigureshowstheestimatedimpulseresponsefunctionsusingJord`a’s(2005)localprojections along with its associated 95% confidence band of gross domestic product (GDP) growth rate to a shock to the duration of high risk (DHR) and duration of low risk (DLR). In Panel (a), we present the results for a shock in global DHR. Panel (b) shows the results for local DHR. In Panel (c), we present the results for a shock in global DLR (G-DLR). Finally, in Panel (d), we show the results for the local low-risk phase. Global and local measures are introduced in Section 2. In all cases, we run regressions (14) with log-GDP growthas the dependent variable. Allregressionsincludethe laggedvaluesofthe inflationrate,thedegreeofpoliticalcompetition, log-GDP,changeinshort-terminterestrates,thedependentvariable,durationoflowrisk(DLR), duration of high risk (DHR), their global counterparts (G-DLR and G-DHR), and country and decade fixed effects. We dually clustered standard errors at the country and year levels. Data sources: Global Financial Data, Maddison (2003) database, Polity IV Project database, and author calculations. 20% 10% 0% −10% −20% 0 1 2 3 4 5 Horizon in years htworg 20% 10% 0% −10% −20% 0 1 2 3 4 5 Horizon in years (a) A shock to G-DHR htworg (b) A shock to DHR 20% 10% 0% −10% −20% 0 1 2 3 4 5 Horizon in years htworg 20% 10% 0% −10% −20% 0 1 2 3 4 5 Horizon in years (c) A shock to G-DLR htworg (d) A shock to DLR to exacerbate information asymmetry problems, limiting credit available to firms (Dixit and Pindyck, 1994; Bloomet al., 2018; Gilchrist et al., 2014; Ferreira, 2016). We then examine the effects of DLR on growth in Panels (c) and (d). If its effect weresymmetric toDHR,wewouldobserve ashortboomeffect onthegrowthcycle, but that does not happen. The impact of the low-risk phase is quite different from 18

thatofthehigh-riskphase: bothlargerinmagnitudeandlonger-lasting—aboomto-bust growth cycle compared with a bust only. The impact of DLR on growth is positive contemporaneously and the following year, turning negative two years afterward. As the low-risk environment lasts longer, so does the risk appetite of economic agents, initially leading to higher growth, but ultimately resulting in a reversal amid accumulated financial vulnerabilities. A one standard deviation increase in G-DLR leads to a 1.5% increase in GDP growth of a typical country over the first two years, followed by a reduction of 0.8% in GDP growth. Overall, over the boom-to-bust cycle cumulatively, a onestandard-deviation increase in G-DLR increases GDP growth by about 0.7%. Furthermore, G-DLR has a stronger economic impact than its local counterpart in its contribution to local growth: The amplitude of its boom-to-bust growth cycle is significantly higher than that of DLR. Our findings on the importance of G-DLR on local economic cycles are in line with Cesa-Bianchi et al. (2020), who identify the global financial factor as the common shock driving country-specific realized volatilities. They show that the global factor explains a significantly higher variation of the country-specific output growth, compared to the proportion explained by the country-specific volatility shocks. Overall, our results raise questions about the specific mechanisms that lead to the boom-to-bust growth cycle, underscoring the importance of the global low-risk environment. For the rest of the empirical analysis, we address those questions, focusing on global low risk. 3.3 Global low risk and growth: endogeneity concerns When running the regression in (14), we assume that shocks to G-DLR are exogenous to growth, contemporaneously, and in the future. Such an assumption might be violated if some other large shock, such as a monetary policy shock, affects both realized volatility (and hence, G-DLR by definition) and the current state of the economy (through the changes in expected future volatility). In other words, the time-dependent nature of volatility might imply that current shocks are propagated into the future, causing identification issues. We use a two-pronged approach to alleviate the endogeneity concerns: 1) a two-stage regression specification similar to Lo´pez-Salido et al. (2017); 2) the news shock approach of Berger et al. (2020). In the first stage of the two-stage regression specification, we regress G-DLR on past values of a set of plausibly exogenous global variables, Z , that can affect t agents’ perceptions of risk. In particular, we include U.S. natural disasters, liquidity shocks, and realized volatility. We consider only U.S. series, rather than country-level data, to avoid the direct effects of natural disasters, liquidity, and 19

volatility shocks on the local GDP growth. Natural disasters are from Baker et al. (2020) since 1970. They include extreme weather events such as droughts, earthquakes, and floods obtained from the Center for Research on the Epidemiology of Disasters (CRED). Liquidity shocks are defined as the difference between the stock market turnover and its past 12-month average as in Bali et al. (2014). Finally, we control for the U.S. stock market realized volatility as it affects G-DLR by definition. We consequently run the following regression: 1 G-DLR = θ+ γ Z +ǫ , (15) i,t k t−k t k=0 X For completeness, we also estimate the fitted estimate of G-DHR using (15). We \ then regress the GDP growth rate on G-DLR controlled for the lagged values of \ \ G-DLR,G-DHR, along with the other variables used in our baseline specification (14). That is: 5 5 \ ∆y = βhG-DLR + δh∆y + φhX +αh +ηh +ε .(16) i,t+h t k i,t−k k i,t−k i t i,t+h k=1 k=1 X X We report the results in Table 3 panel A. As we use estimated regressors in the second stage, we bootstrap the standard errors with 1,000 sample draws clustering at the country and year level. The first-stage results show a significant relationship between the control set and G-DLR with an adjusted R2 of 70% with an \ F-statistics over 15. The second-stage results confirm our main finding: G-DLR has strong explanatory power for future growth. Indeed, under the two-stage approach, the impact of G-DLR on growth lasts longer and, in particular, continues to be significant in year three. Even though this approach mechanically resembles an instrumental variables (IV) approach, Z does not necessarily satisfy the exclut sion restrictions that are required in IV estimation. Thus, we still do not make strong identification claims. Second, wefollowthemethodologyproposedbyBerger etal.(2020). Sincerealized volatilityisautocorrelated(theso-calledGARCHeffect), current realizedvolatility affects future expected volatility (i.e., uncertainty about the future), which in turn is related to current economic conditions. Berger et al. (2020) suggest a methodology for addressing such identification problem, whereby we identify expected volatility shocks via a vector autoregression (VAR) model and then, orthogonalize them to current realized volatility innovations. Expected volatility shocks are driven by implied volatility, so they enable us to “directly” measure the perceived risk of investors, at least for the sample period we have data. As we need options markets data, for which long time horizons are only available in the United States, we focus on the U.S. from 1984 to estimate the 20

uncertainty shocks. Accordingly, we first estimate a VAR model with the following moving average representation: Y = (I −F(1))−1C +B(L)Aε , (17) t t where ∞ B(L) = B Lj = (I −F(L))−1. (18) j j=0 X Y includes stock market realized volatility, annualized one-month implied volatilt ity, changes in three-month Treasury Bill rates, CPI inflation, and GDP growth rate, i.e., [RV ,IV ,∆STIR ,INF ,∆logGDP ]. C denotes a vector of constants. t t t t t F(L) isa matrixofcoefficients inthestructural VAR setting, with thelagoperator L. The shocks to realized volatility are ordered first and uncertainty shocks are ordered second in the structural VAR setting. The identifying assumption is that uncertainty news shocks do not affect realized volatility contemporaneously, but realized volatility can affect uncertainty. We obtain changes in cumulative expected volatility up to time t+n by: n n n E RV −E RV = e B Aε , (19) t t+j t−1 t+j 1 j t ! j=1 j=1 j=1 X X X where e = [1,0,···] and n denote the horizon of the news shock. The RV shock 1 is e Aε and the uncertainty news shock is obtained by orthogonalizing (19) with 1 t respect to the innovation to RV by following Barsky et al. (2015) and Barsky and Sims (2011). We then use the estimated uncertainty shocks as an input, instead of using realized volatility, to calculate G-DLR in (10)—denoted as G-DLR . We report BDG the estimated coefficients from specification (14) in Table 3 panel B, when we shock G-DLR with and without controlling for realized volatility. As we use BDG estimated regressors, we bootstrap the standard errors with 1,000 sample draws clustering at the country and year level. We confirm our main finding that global risk perceptions affect growth. Overall, these analyses increase our confidence in the effects of G-DLR on economic growth, although we remain cautious about the identification. 3.4 Risk perceptions, credit growth, and non-linearities We have so far found that the aggregate effects of strengthening perceptions of low risk on growth are positive over the boom-to-bust cycle. In this section, we study two possible cases, where the impact of low risk on growth might be 21

negative overall: when a country experiences a credit boom and when the low risk has persisted for a particularly long time. If a country is experiencing a credit boom, then its financial system is expected to be more fragile and less resilient to adverse shocks (see for example Schularick and Taylor, 2012; Aikman et al., 2017). Similarly, longer-lasting low-risk periods, compared with short-lived ones, could lead to a buildup of financial vulnerabilities, as financial vulnerabilities are procyclical and accumulate throughout economic expansions (Adrian and Liang, 2018). In either of the cases, even a small revision of beliefs can create a selfreinforcing feedback loop that impairs credit provision, lowers asset prices, and depress economic activity by amplifying the reversal in growth. To examine these conjectures, we first use excess private non-financial credit as a proxy of financial system vulnerability as in Adrian et al. (2015); Basel Committee on Bank Supervision (2010). We define an indicator variable Iq for whether a i,t particular country is above or below a quantile (q) of credit growth in a given year, compared with other countries. 1 if credit growth ≥ credit growthq I q := i,t t (20) i,t 0 otherwise, (cid:26) where credit growthq is the qth quantile in year t. We measure credit growth as the t t log first difference of credit to nonfinancial institutions, with data obtained from the Bank for International Settlements, available from 1953 for 40 countries. We then modify the baseline impulse panel regressions in (14) to allow for two states, when credit is above or below the quantile q: ∆y = Iq βh,highS +Γh,highX i,t+h i,t t i,t +(1−Iq ) βh,lowS +Γh,lowX +αh +ηh +ε , (21) i,t (cid:0) t i,t i (cid:1) t i,t+h h = 0,...,5, (cid:0) (cid:1) S = G-DLR . t t βh,low and βh,high are the impulse responses of growth to a shock of G-DLR condiq tioning on credit growth below and above the quantile threshold (credit growth ), t respectively. In what follows, we refer to results from βh,low and βh,high as low and high, respectively. Figure 5 shows the estimated impulse responses for high credit states for different horizons based on quantiles 0.50 and 0.90. The results highlight an almost monotonicrelationshipbetween theamountofexcessive creditandtheimpactofG-DLR on growth: the higher the excessive credit, the stronger the reversal in the second year. In particular, if a country is in the highest decile of credit growth in a certain year, the amplitude of the bust is triple what it would otherwise be, and is longerlasting, making the overall impact negative. A one-standard-deviation increase in G-DLR decreases economic growth by 0.65% across the three-year cycle. 22

Figure 5: The impact of global low risk on growth, conditional on the state of the credit cycle. ThisfigureshowstheestimatedimpulseresponsefunctionsusingJord`a’s(2005)localprojections along with its associated 95% confidence band of gross domestic product (GDP) growth rate to a shock to the global duration of low-risk (G-DLR) conditioning on excessive credit growth. G- DLRisintroducedinSection2. Highcreditgrowthisfrom(20)usingthelogdifferenceofcredit to nonfinancial institutions, with data obtained from the Bank for International Settlements, available from 1953 to 2016 for 40 countries. We run regression (21) and plot βh,high based on differentquantilestodefineexcessivecreditgrowth(0.5and0.9). Forcomparison,unconditional impulse responses for the period where we have available credit data are also plotted. All regressions include the lagged values of the inflation rate, the degree of political competition, log-GDP,changeinshort-terminterestrates,thedependentvariable,durationoflowrisk(DLR), duration of high risk (DHR), their global counterparts (G-DLR and G-DHR), and country and decade fixed effects. We dually clustered standard errors at the country and year levels. Data sources: GlobalFinancialData,Maddison(2003)database,PolityIVProjectdatabase,theBank for International Settlements, and author calculations. 0 1 2 3 4 5 Horizon htworG 20% G-DLR I0.5G-DLR I0.9G-DLR t i,t t i,t t 10% 0% −10% −20% −30% Second, we extend (14) so that GDP growth is modeled as a third-degree polynomial in G-DLR: ∆ y = βhG-DLR +βhG-DLR2 +βhG-DLR3 (22) h i,t+h 1 i,t 2 i,t 3 i,t L L + δh∆ y + φhX +αh +ηh +ε , k h i,t−k k i,t−k i t i,t+h k=1 k=1 X X where ∆ y = y −y is the h-year cumulative GDP growth rate. After h i,t+h i,t+h i,t−1 estimating(22),wecalculatethemarginalrateofreturnofcumulativeGDPgrowth to G-DLR as: ρ(G \ -DLR) = ∂∆ h y = βh +2βhG-DLR+3βhG-DLR2. (23) ∂G-DLR 1 2 3 In Figure 6 we plot ρ at differentcquantciles of G-DLRcover the boom-to-bust cycle—that is, two-year cumulative GDP growth. We find that for G-DLR smaller than its 85% quantile, the marginal impact of increasing G-DLR remains positive, b but at a decreasing rate. Beyond the 85% quantile, the marginal impact of G- DLR on growth turns negative: a very-long low-risk environment today leads to 23

a significant decrease in cumulative growth over the boom-to-bust cycle. In other words, the response of growth to increase in DLR is concave. Figure 6: The non-linear impact of G-DLR on growth ThisfigureshowstheestimatedmarginalrateofreturnofcumulativeGDPgrowthtoG-DLR(ρ), introduced in (23). We plot ρ at different quantiles of G-DLR. To estimate ρ, we run regression (22) so that cumulative GDP growth is modeled as a 3rd degree polynomial in G-DLR. Dabta sources: Global Financial Data, Maddison (2003) database, Polity IV Project database, and b b author calculations. tcapmi lanigraM 20% 0% −20% −40% −60% −80% 20% 40% 60% 80% 100% G−DLR percentiles Takentogether,theseresultsprovidesupportforournotionoffinancialvulnerabilitydriven economic contraction. The bust cycle (reversal on growth) is especially strong in times of high credit growth and when the low-for-long volatility environment persists. For instance, the 2008 global financial crisis was preceded by a long DLR period (in the United States, volatility stayed low for five consecutive years). Moreover, the episode was a clear example of increased vulnerabilities in the financial system: both corporate and particularly household lending was excessive. In this case, our analysis shows that the aggregate effect of G-DLR on growth was negative. 3.5 Why does low risk cause a boom-to-bust cycle: Possible mechanisms Why does perceived low risk affect economic growth? We surmise the reason lies in the particular interplay between risk-taking and growth through three primary channels: domestic investment, capital flows, and debt issuer quality. When investors perceive risk as low globally—G-DLR increases—they are more inclined to reach for yield. Free capital flows and the presence of a globalized banking system allow global investors to tilt their asset allocations towards riskier asset classes and countries (Bruno and Shin, 2015; IMF, 2019). The result is an immediate increase in capital flows, funded by global investors. Moreover, in such periods, increased 24

risk-taking implies that even poor quality borrowers are more likely to be financed as in Greenwood and Hanson (2013), again boosting the growth at the expense of lower issuer quality. Eventually, however, high-quality investment opportunities are increasingly exhausted, leading to a reversal in investment and capital flows. We use three data sources to examine three channels. First, we proxy private investment by gross capital formation (investment in fixed assets and inventories) as a percentage of GDP with data from the World Development Indicators (WDI) for 73 countries from 1960 to 2012. Second, we obtain total portfolio inflows data for each country (as a percentage of GDP) from the IMF, where the sample covers 55 countries from 1970 to 2012. Finally, we use the high-yield issuance share index constructed by Kirti (2020). Accordingly, when lenders are willing to allocate a larger share of credit to less-creditworthy borrowers, the high-yield share index increases. The data includes 38 countries with coverage going back to the early 1980s, primarily for advanced countries. We run the baseline specifications (14) by replacing the endogenous variable with the growth of investment, capital flows, and high-yield share index while keeping the same controls.13 Figure 7 shows that G-DLR strongly affects investment, capital flows, and debt issuerquality. G-DLRhasapositiveshort-runimpact, withareversal inthemedium to longer term. Specifically, as the world’s low-risk environment increases by one standard deviation, a typical country’s investment growth, changes in portfolioflows-over-GDP ratio, and high-yield share will have an immediate increase of 0.5%, 1.3%, and 2.7% but followed by a reversal of -1.8%, -1.3% and -1.1%, respectively. We then present the results for local DLR in Figure D1 in Appendix D, showing that it has negligible effects on investment growth, portfolio flows, and debt-issuer quality. Furthermore, weemploythetwo-stageregressionandnewsshockapproachesintroduced in 3.3 to alleviate possible endogeneity concerns. Table 4 shows that under both approaches there is a boom-to-bust cycle in investment, capital flows, and HY-share issuance following a shock in G-DLR. The timing of the cycles obtained via the former approach is in line with the main findings in Figure . Although we still find a boom-to-bust effect using the second approach, the results differ mainly due to the different sample periods. 13Because U.S. monetary policy decisions may also affect the relative return on investment in foreigneconomies,itmayaffectcapitalflowsacrosscountries. However,byincludingU.S.monetarypolicysurprisesinsteadofachangeininterestrates,oursamplesizeisreducedsignificantly. Hence, we leave the analysis with the surprise series estimated by Romer and Romer (2004) as a sensitivity analysis, reaching similar conclusions. 25

4 Robustness We execute 23 robustness tests, which can be classified under seven groups. First, we check whether the results are sensitive to the way we estimate the volatility trend, which is used to calculate low volatility. To this end, we estimate the volatility trend by applying the methodology proposed by Hamilton (2018). The estimated trend from the Hamilton filter is noisier than the estimates of the HP filter trend. To smooth them out, instead of keeping the last estimate for the trend at t, we calculate the average of the previous 20 years’ estimates. We then keep the HP filtering, but estimate the volatility trend under various smoothing parameters (λ = 1000, λ = 10000, in addition to λ = 5000). We further employ a one-standard-deviation band instead of the HP filter trend by marking a low volatility state if the current volatility is below its one-standard-deviation band. Second, we conduct robustness tests on the definitions of volatility. Instead of estimating annual volatility as the standard deviation of 12 real monthly returns, we calculate volatility as the sum of absolute monthly real returns. Moreover, instead of using real stock market returns, we use nominal returns to estimate volatility. In the third set of robustness tests, we examine whether our findings are sensitive to the definition of DLR. We examine different values for decaying factor θ ranging from 0.75 to 0.95 in equation (10), but for the sake of brevity we only report our results for θ = 0.85 and θ = 0.95. In addition, we check our findings when we do not apply any decaying factor and instead we count the number of consecutive years in which a country experiences a low volatility regime. Then, we consider the intensity of the deviations of volatility from its trend and calculate DLR as the sum of the volatility deviations when a country stays in a low volatility regime consequently. Fourth, we examine whether theunbalanced natureof data affectsour findings. G- DLR is calculated as the weighted cross-sectional average of local DLRs available in a given year in a highly unbalanced panel. We instead repeat the analysis using the current G7 countries (United States, United Kingdom, France, Germany, Italy, Canada, andJapan)andstartthesampleperiodintheyearwehaveavailablestock market information for all of those countries, which is 1921, and recalculate G- DLR. Finally, we define G-DLR by using U.S. DLR only, while omitting the rest of the countries in the sample. Thefifthset ofrobustness tests includes additionalcontrol variablesinourbaseline specifications: credit spreads, change in exchange rates, U.S. monetary policy shocks, economic policy uncertainty (EPU) of Baker et al. (2016), and geopolitical risk index (GPR) of Caldara and Iacoviello (2018). Krishnamurthy and Muir (2017) find that the changes in output can be explained by unusually high credit 26

growth coupled with unusually narrow bond credit spreads and thus credit spreads are useful predictors of economic activity. Therefore, we include U.S. bond spread datameasuredasthedifferencebetweenBAAandAAAyieldsasacontrolvariable. Avdjievetal.(2016)arguethattheU.S.dollarhasreplacedtheVIXasthevariable most associated with an appetite for leverage; that when the dollar is strong, risk appetite is weak. Therefore, we include the change in local exchange rates with respect to the U.S. dollar obtained from the GFD. We as well control for the U.S., monetary policy surprise series estimated by Romer and Romer (2004), covering 1970 to 2008. We include EPU and GPR indexes as we expect them to affect global risk-taking. Note that these variables are left as a robustness analysis because including them in the analysis reduces the sample size significantly. Sixth, we execute sensitivity analyses on the econometric specification we employ by including 5-year and 20-year fixed effects instead of decade fixed effects in the main specifications. Then, instead of calculating double-clustered standard errors, we calculate them using Driscoll-Kraay standard errors as they are widely used in a long panel with a smaller number of cross-sectional observations. Finally, we test the robustness of our findings during different subsamples. Our sample contains many distinct sub-periods, market structures, developments, and types of countries. The structure of financial markets was quite different in the early period, and stock markets became a much more central vehicle for financing economic activity, especially after World War II, with the general public investing in equities on a large scale. Moreover, emerging market economies started to develop stock markets. During the post-Bretton Woods era (after 1972), globalization increased, capital flows have become unrestricted, financial markets increasingly deregulated, trading computerized, and, most recently, global financial intermediation is taking place via the fixed-income markets rather than through banks. The number of developing countries is much larger in the past half a century than before, and the importance of capital flows is increasing. Moreover, we split our sample between developed and emerging countries classified by the IMF for the post-Bretton Woods era as it is when we have many emerging countries in the sample as seen in Figure 1. The results are reported in Table 5. To ease the interpretation of the results, instead of plotting impulse responses for all of the specifications, we present the estimated coefficients from (14) for both local and global DLR. Overall, we find that the main results are qualitatively unaltered under the various robustness checks. Row 25 presents the results when U.S. DLR is used as a proxy for global risk. Several authors have highlighted the pivotal importance of the United States for global financial cycles (Rey, 2018; Jorda` et al., 2018; Avdjiev et al., 2016). With its reserve currency, the world’s largest economy, and financial markets, financial risk in the United States could be particularly important for global risk, driving 27

international risk-taking and, thus, affecting growththroughouttheworld. Indeed, US-DLR is able to explain about 30% of the variation in G-DLR. In comparison to the overall results with G-DLR, we find that US-DLR can explain a significant part of the changes in local growth. Thus, we conclude that the United States plays a pivotal role in the global financial cycles. In Rows 41 through 48, we show that during the postwar and post-Bretton Woods eras, both local and global risk cycle matters in explaining economic growth, while the impact of global risk is significantly higher. The results are qualitatively similar over the whole sample period, supporting our findings. Finally, we find that the impact of G-DLR over three years is stronger for emerging countries than for developed countries, with higher amplitudes of the boom-to-bust cycle. This finding highlights the pivotal role of global capital markets intermediating funds to such countries. In the end, limits to domestic bank lending in emerging countries may make them more dependent on international capital markets than developed countries. The risk appetite both for international investors who provide capital and for domestic investors who undertake capital projects increases when global risk is perceived as low and falling. 5 Conclusion The financial sector plays a pivotal role in the macroeconomy, as has become increasingly apparent with the financial crisis in 2008, and since then, many researchers have contributed to the literature explaining the links between the two. We contribute to this literature by focusing on economic agents’ attitudes towards riskasanessential driver ofeconomicgrowth. Tothisend, weconstruct aBayesian learning model for how observations of risk affect the agents’ posterior belief of the state of the risk cycle. While the posterior is not directly observable, we proxy it by the duration of low risk (DLR). We then use a panel of 73 countries since 1900 to map the rises and falls in agents’ perceptions of risk onto contemporaneous and future economic growth. We show that perception of high-risk has an unambiguous negative short-term impact on growth, as expected. By contrast, a lengthening of the low-risk phase has a longer-term effect: initially positive but eventually followed by a reversal (a boom-to-bust cycle). Low-risk environments increase the optimism and agents’ willingness to take on more risk, boosting investment and growth in the short-tomedium term at the cost of increasing financial leverage, eventually followed by a reversal. Overall, onaggregate, low-risk perceptions arefollowedby higher growth, with two exceptions being excessive credit growth and very long-lasting low-risk environments. In these cases, the amplitude of the reversal in growth is stronger and longer-lasting than would otherwise be, with an overall negative impact on 28

growth. Global risk perceptions are particularly important in shaping local business cycles, affecting the investment decisions of both domestic and global investors, and they are manifested via three main channels: investments, capital flows, and the riskiness of bond issuance. Furthermore, risk perceptions in the United States play a pivotal role in economic outcomes throughout the world. Our results contribute to several important policy debates. Consider macroprudential regulations. After the crisis of 2008, policymakers, justifiably intent on preventing a repeat, have been actively aiming to reduce the amount of risk financial institutions can take — de-risking the financial system. In other words, they want to reduce their risk by requiring higher levels of capital and imposing stringent lending standards. While such de-risking promises to reduce the likelihood of a costly financial crisis, our findings show that it may reduce economic growth. The aggregate impact of a low-for-long volatility environment on growth depends on the prevailing level of financial vulnerabilities. When such vulnerabilities increase, such as in the form of excess non-financial sector credit, the economy is expected to be more fragile and less resilient to adverse shocks. Our results point to the importance of policymakers considering the joint impact of macroprudential and monetary policies on the likelihood of crises and growth. Our results also demonstrate thelimit to monetary policyindependence, especially when intended to use for macroeconomic objectives, almost always mandated in central bank legislation. Even if a domestic monetary authority intends to either stimulate or cool down its national economy by affecting the price and quantity of money, global risk perceptions and risk-taking incentives in financial markets can override national monetary policy decisions. After all, the global risk cycle affects capital flows, investment decisions, and credit conditions. This cycle is driven by the length of a low-risk environment and its effect on domestic economic growth is significantly higher than that of domestic risk perceptions. Our final policy conclusion focuses on the importance of global institutions like the IMF, the World Trade Organization, and the Financial Stability Board. Their tasks of enhancing the efficiency of the global financial and economic systems are important. Individual countries cannot ignore the global risk environment, however much they might want to because it contributes more strongly to the risk appetite of domestic agents than does their local risk environment. That consideration is especially important for emerging countries, those without deep domestic financial markets. 29

Appendix A: Sample details Table A1: Sample details This table lists the countries in our sample, whether they are developed or emerging markets based on the InternationalMonetary Fund classification,sample coverage,and the names of the market indexes. We report the name of the market index used at the end of the sample period. Giventhelonghistoricaldata,itisnotpossibletolistalloftheindexesusedforallcountries. For example,fortheU.S.,between1900to1923,theCowlesCommission’sback-calculatedcomposite of stocks is used. After 1923,S&P is used. See GFD for details. Source: GlobalFinancial Data. Country Classification Coverage Market Argentina Emerging Jan. 1956–June 1958/ Argentina Swan, Culbertson and Fritz/ Dec. 1966–Dec. 2016 Buenos Aires SE General (IVBNG) Australia Developed Jan. 1900–Dec. 2016 Australia ASX All-Ordinaries Austria Developed Jan. 1941–Dec. 2016 Wiener Boersekammer Share (WBKI) Bahrain Emerging June 1990–Dec. 2016 Bahrain BSE Composite Bangladesh Emerging Jan. 1990–Dec. 2012 Dhaka SE General Belgium Developed Jan. 1900–Dec. 2016 Brussels All-Share Price Brazil Emerging Jan. 1955–Feb. 2000/ Rio de Janeiro Bolsa de Valores (IBV) Bulgaria Emerging Oct. 2000–Dec. 2016 SE SOFIX Canada Developed Jan. 1915–Dec. 2016 Canada S&P/TSX 300 Composite Chile Emerging Jan. 1927–Dec. 2016 Santiago SE General (IGPA) China Emerging Jan. 1994–Dec. 2016 Shanghai SE Composite Colombia Emerging Jan. 1927–Dec. 2016 Colombia IGBC General Costa Rica Emerging Dec. 1994–Dec. 2016 Costa Rica Bolsa Nacional de Valores Cote d’Ivoire Emerging Jan. 1996–Dec. 2016 Cote d’Ivoire Stock Market Croatia Emerging Jan. 1997–Dec. 2016 Croatia Bourse (CROBEX) Denmark Developed Jan. 1921–Dec. 2016 OMX Copenhagen All-Share Price Ecuador Emerging Jan. 1994–Dec. 2016 Ecuador Bolsa de Valores de Guayaquil Egypt Emerging Jan. 1950–Sept. 1962/ Egyptian SE/ Dec. 1992–Dec. 2016 Cairo SE EFG General El Salvador Emerging Jan. 2004– Dec. 2014 El Salvador Stock Market Finland Developed Jan. 1920–Dec. 2016 OMX Helsinki All-Share Price France Developed Jan. 1900–Dec. 2016 France CAC All-Tradable Germany Developed Jan. 1900–Dec. 2016 Germany CDAX Composite Ghana Emerging Nov. 1990–Oct. 2016 Ghana SE Databank/ Ghana SE Composite Greece Developed Dec. 1946–Dec. 2016 Athens SE General Hungary Emerging Dec. 1924–Mar. 1948/ Hungary Stock Market/ May 2002–Dec. 2016 OETEB Hungary Traded 30

Table A1: Sample details (cont.) Country Classification Coverage Market Iceland Developed Dec. 1992–Dec. 2016 OMX Iceland All-Share Price India Emerging Jan. 1922–Dec. 2016 Bombay SE Sensitive Indonesia Emerging Jan. 1983–Dec. 2016 Jakarta SE Composite Iran Emerging Mar. 1990–Dec. 2016 Tehran SE Price (TEPIX) Ireland Developed Jan. 1934–Dec. 2016 Ireland ISEQ Overall Price Italy Developed Sept. 1905–Dec. 2016 Banca Commerciale Italiana Japan Developed July 1914–Dec. 2016 Tokyo SE Price (TOPIX) Kazakhstan Emerging July 2000–Dec. 2016 Kazakhstan SE KASE Kenya Emerging Jan. 1964–Dec. 2015 Nairobi SE Korea Developed Jan. 1962–Dec. 2016 Korea SE Stock Price (KOSPI) Kuwait Emerging Oct. 1996–Dec. 2016 Kuwait SE Index Luxembourg Developed Oct. 1954–Dec. 2016 LuxSE Malaysia Emerging Dec. 1973–Dec. 2016 Malaysia KLSE Composite Malta Emerging Dec. 1996–Dec. 2016 Malta SE Mauritius Emerging July 1989–Dec. 2016 SE of Mauritius (SEMDEX) Mexico Emerging Jan. 1931–Dec. 2016 Mexico SE Indice de Precios y Cotizaciones Mongolia Emerging Aug. 1995–Dec. 2016 Mongolia SE Top-20 Montenegro Emerging Mar. 2003–Dec. 2016 Montenegro NEX-20 Morocco Emerging Jan. 1988–Dec. 2016 Casablanca Financial Group 25 Share Netherlands Developed Jan. 1919–Dec. 2016 Netherlands All-Share Price New Zealand Developed Jan. 1931–Dec. 2016 New Zealand SE All-Share Capital Nigeria Emerging Jan. 1988–Dec. 2016 Nigeria SE Norway Developed Jan. 1914–Dec. 2016 Oslo SE OBX-25 Stock Pakistan Emerging July. 1960–Dec. 2016 Pakistan KarachiSE-100 Panama Emerging Dec. 1992–Dec. 2016 Panama SE (BVPSI) Paraguay Emerging Oct. 1993–Sept. 2008 PDV General Peru Emerging Jan. 1933–Dec. 2016 Lima SE General Philippines Emerging Dec. 1952–Dec. 2016 Manila SE Composite Poland Emerging Jan. 1921–Dec. 1939/ Warsaw SE 20-Share Composite/ Apr. 1994–Dec. 2016 Portugal Developed Jan. 1933–Dec. 2016 Oporto PSI-20 Qatar Emerging Dec. 1995–Dec. 2016 Qatar SE Russia Emerging Jan. 2002–Dec. 2016 Russia AK&M Composite (50 shares) Saudi Arabia Emerging Feb. 1985–Dec. 2016 Saudi Arabia Tadawul SE Singapore Developed July 1965–Dec. 2016 Singapore FTSE Straits-Times South Africa Emerging Jan. 1910–Dec. 2016 FTSE/JSE All-Share Spain Developed Dec. 1914–Dec. 2016 Madrid SE General 31

Table A1: Sample details (cont.) Country Classification Coverage Market Sri Lanka Emerging Dec. 1984–Dec. 2016 Colombo SE All-Share Sweden Developed Jan. 1906–Dec. 2016 Sweden OMX Aff¨arsva¨rldens General Switzerland Developed Jan. 1921–Dec. 2016 Switzerland Price Thailand Emerging Apr. 1975–Dec. 2015 Thailand SET General Tunisia Emerging Dec. 1997–Dec. 2016 Tunisia SE Turkey Emerging Jan. 1986–Dec. 2016 Istanbul SE IMKB-100 Price Ukraine Emerging Jan. 1998–Dec. 2016 Ukraine PFTS OTC United Arab Emirates Emerging Oct. 2004–Dec. 2016 Abu Dhabi All-share United Kingdom Developed Jan. 1900–Dec. 2016 UK FTSE All-Share United States Developed Jan. 1900–Dec. 2016 S&P 500 Composite Price Venezuela Emerging Jan. 1937–Dec. 2015 Caracas SE General Zambia Emerging Dec. 1996–Dec. 2016 Zambia Lusaka All-Share (LASI) Appendix B: Data definitions and sources • DLR : Duration of low risk, calculated as in (10). It considers the coni,t secutive number of years in which stock market volatility remains low for country i in year t with decaying weights. Volatility (VOLA) is annual realized volatility–the standard deviation of real monthly stock market returns over a year. Monthly stock market indexes are collected from Global Financial Data (GFD),with data available for 73 countries, spanning 1900to 2016. Data coverage is listed in Table A1. • G-DLR : Global DLR is calculated as the GDP-weighted cross-sectional avt erages of local DLRs (DLR ). i,t • DHR : Durationofhigh risk. Calculated analogousto DLR andconsiders i,t i,t theconsecutive number ofyearsinwhich stockmarket volatilityremainshigh for country i in year t. • G-DHR : Global DHR is calculated as the GDP-weighted cross-sectional t averages of local DHRs (DHR ). i,t • GDP growth: Log-real GDP growth rate. Annual GDP per capita and population numbers are from the Maddison (2003) database, available at http://www.ggdc.net/maddison/. Data from the Maddison project cover 32

72 countries from 1900 to 2016. • Log GDP: log per-capita income. Data from the Maddison project cover 72 countries from 1900 to 2016. • INF: The inflation rate is calculated as the annual percentage change of the consumer price index. Data are from the GFD. • POLCOMP: Political competition as a proxy for institutional quality. Data are from the Polity IV Project database. POLCOMP is the combination of the degree of institutionalization or regulation of political competition and the extent of government restriction on political competition. The higher the value of the POLCOMP, the better the institutional quality of a given country. • ∆STIR: Change in short-term interest rates. Three-month Treasury Bill yields, from the GFD from 1900. • ∆XR: Change in exchange rates, local currency with respect to U.S. dollar. Data from the GFD. • TERM: Term premium, defined as the difference between the long-term and short-term interest rates, from GFD. • DY: Dividend yields, from Baron and Xiong (2017). • VIX: The CBOE Volatility Index. • BEX: Bekaert et. al (2019)’s risk aversion measure • PVS: Pflueger et. al (2020)’s PVS. • Positive macro surprises: The average of the Scotti (2016) macroeconomic surprise index, provided that the index is positive. • BEX uncertainty: Bekaert et. al (2019)’s uncertainty index. • Liquidity shocks: The negative difference between stock market turnover and its past 12-month average. • MP shocks: U.S. monetary policy shocks introduced in Romer and Romer (2004). The authors use the FED Greenbook forecasts of output growth and inflation along with the fed funds rates to estimate shocks. The sample covers 1970 to 2008. 33

• ∆Flows/GDP: Change in total portfolio inflows as a percentage of the local country’s GDP, taken from the International Monetary Fund’s Balance of Payments statistics (BPM5). The sample covers 55 countries from 1970 to 2012. • Investment growth: Private investment growth is the first-log difference of gross capital formation (investment in fixed assets and inventory), as a percentage of GDP, obtained from the World Development Indicators for 1960 to 2012 and 73 countries. • HY share: Lending standards are proxied via the high-yield bond issuance data constructed by Kirti (2020). Data cover 38 countries from 1980 to 2016. 34

Figure 7: Impact of global low risk on investment, capital flows, and lending standards. This figure shows the estimated impulse response functions using Jord`a’s (2005) local projections along with its associated 95% confidence band of investment growth, changes in portfolio inflows,anddebt-issuerqualitytoashocktotheglobaldurationoflowrisk–G-DLR,introduced inSection2. Privateinvestmentisproxiedbygrosscapitalformation(investmentinfixedassets andinventories),asapercentageofgrossdomesticproduct(GDP),andweobtainthedatafrom WorldDevelopmentIndicatorsfor73countriesfrom1960to 2012. Totalcapitalinflowsdata(as a percentage of GDP) are obtained from the InternationalMonetary Fund for 55 countries from 1970 to 2012. Lending standards are proxied via the high-yield bond issuance data constructed by Kirti (2020), spanning 38 countries from 1980 to 2016. We run regressions (14) by replacing growthwith changesin portfolioinflows, growthofinvestment,and the log- high-yield(HY) shareindexasdependentvariables. Allregressionsincludethelaggedvaluesoftheinflationrate, the degree of political competition, log-GDP, change in short-terminterest rates, the dependent variable, duration of low risk (DLR), duration of high risk (DHR), their global counterparts (G-DLR and G-DHR), and country and decade fixed effects. We dually clustered standard errors at the country and year levels. All variables are standardized to ease the interpretation. Data sources: Global Financial Data, Maddison (2003) database, Polity IV Project database, the Bank for International Settlements, World Development Indicators, International Monetary Fund, and author calculations. 4% 2% 0% −2% −4% 0 1 2 3 4 5 Horizon in years htworg tnemtsevnI 4% 2% 0% −2% −4% 0 1 2 3 4 5 Horizon in years (a) Shock to G-DLR PDG/swolF (b) Shock to G-DLR 4% 2% 0% −2% −4% 0 1 2 3 4 5 Horizon in years erahs YH (c) Shock to G-DLR 35

Appendix C Re-write the posterior (7) using (8): φ (2q−1)α +(1−q) L t−1|t−1 α = , (24) t|t (φ −φ )(2q −1)α +(1−q)φ +qφ L H (cid:0) t−1|t−1 (cid:1)L H Aα +B t−1|t−1 = , (25) Cα +D t−1|t−1 where A = φ (2q −1) (26) L B = φ (1−q) (27) L C = (φ −φ )(2q −1) (28) L H D = (1−q)φ +qφ (29) L H γ s 1 t φ = φ (30) L ζ (cid:18) (cid:19) γ (s −1) 1 t φ = φ . (31) H ζ (cid:18) (cid:19) We apply a first-order Taylor approximation to (25): α ≈ α +α′ α (32) t|t t|t t|t t−1|t−1 (cid:12)α t−1|t−1=0 (cid:12)α t−1|t−1=0 (cid:12) (cid:12) B (cid:12) A CB (cid:12) ≈ +(cid:12) − α(cid:12) (33) D D D2 t−1|t−1 (cid:18) (cid:19) From (33) and (10), it follows that θ can be approximated as: A CB θ ≈ − (34) D D2 and by plugging (26) – (31) into (34), we reach the approximation for θ as: (2q −1)φ (1−q)φ (2q −1)(φ −φ ) L L L H θ ≈ − . (35) (1−q)φ +qφ ((1−q)φ +qφ )2 L H L H 36

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Figure D1: Impact of the perception of low risk on investment, capital flows, and lending standards. ThisfigureshowstheestimatedimpulseresponsefunctionsusingJord`a’s(2005)localprojections alongwithitsassociated95%confidencebandofinvestmentgrowth,changesinportfolioinflows, andlendingstandardstoashocktothelocaldurationoflowvolatility(DLR),whichisintroduced inSection2.2. Privateinvestmentisproxiedbygrosscapitalformation(investmentinfixedassets and inventories), as a percentage of GDP, and we obtain the data from the World Development Indicators for 73 countries from 1960 to 2012. Total portfolio inflows data (as a percentage of GDP) are obtained from the International Monetary Fund for 55 countries from 1970 to 2012. Lendingstandardsareproxiedviathehigh-yieldbondissuancedataconstructedbyKirti(2020). Data cover 38 countries from 1980 to 2016. We run regressions (14) by replacing growth, with capitalflows,growthofinvestment,andthe high-yield(HY) shareindex asdependent variables. Allregressionsincludethe laggedvaluesofthe inflationrate,thedegreeofpoliticalcompetition, log-GDP,changeinshort-terminterestrates,thedependentvariable,durationoflowrisk(DLR), duration of high risk (DHR), their global counterparts (G-DLR and G-DHR), and country and decade fixed effects. We dually clustered standard errors at the country and year levels. Data sources: GlobalFinancialData,Maddison(2003)database,PolityIVProjectdatabase,theBank forInternationalSettlements,WorldDevelopmentIndicators,InternationalMonetaryFund,and author calculations. 4% 2% 0% −2% −4% 0 1 2 3 4 5 Horizon in years htworg tnemtsevnI 4% 2% 0% −2% −4% 0 1 2 3 4 5 Horizon in years (a) Shock to local DLR PDG/swolF∆ (b) Shock to local DLR 4% 2% 0% −2% −4% 0 1 2 3 4 5 Horizon in years erahs YH (c) Shock to local DLR 44

Table 1: Correlations of DLR and G-DLR with other risk perception measures Panel A of this table presents the Pearson correlation coefficients between U.S. duration of low risk (US-DLR) and listed risk perception proxies specified in the last column. Specifically, we include the CBOE Volatility Index (VIX) index, the risk aversion measure (BEX) of Bekaert et al. (2019) and the price of volatile stocks (PVS) of Pflueger et al. (2020). We also consider the net percentage of U.S. banks reporting increased demand and tightening lending standards both obtained from the Federal Reserve Board’s Senior Loan Officer Opinion Survey (SLOOS). Finally, the last row use the default spread measured as the difference between BAA and AAA corporatebond spreadsfromthe FederalReserveBank ofStLouis. PanelB presents the results of a panel regression model of real returns on DLR, dividend yields (DY), realized volatility (VOLA), inflation (INF), degree of political competition (POLCOMP), changes in short-term interest rates (∆STIR), term premium (TERM), and GDP level. We obtained data from the Global Financial Data, Maddison (2003), Polity IV, and Baron and Xiong (2017). All variables used aredefined in Appendix B.Country and yearfixedeffects are included in the specification. ∗∗∗ ∗∗ ∗ Forthesakeofbrevity,onlytheestimatedcoefficientsofDLRarepresented. , ,and denotes significance at the 1%, 5%, and 10% levels. The standarderrorsare robust and dually clustered at the year and country level. Panel A: Pearson correlations Number Correlation Risk perception of Obs. with US-DLR measures ∗∗∗ 1 25 -0.744 VIX ∗∗∗ 2 28 -0.555 BEX ∗∗ 3 45 0.354 PVS ∗∗ 4 24 0.438 net % of banks reporting increased demand ∗∗∗ 5 25 -0.523 net % of banks reporting tightening standards ∗∗∗ 6 45 -0.400 Default spread (BAA-AAA) Panel B: DLR and real returns Dependent variable: R i,t Coefficient Standard estimate error DLR 1.291 ∗∗ 0.600 i,t DY -6.918 ∗∗∗ 2.431 i,t VOLA 6.317 ∗∗ 2.821 i,t INF -0.481 ∗∗∗ 0.065 i,t POLCOMP 0.532 1.401 i,t GDP -1.598 1.387 i,t ∆STIR -0.190 ∗∗∗ 0.058 i,t TERM -1.628 1.853 i,t Adj. R2 0.123 Nº Obs. 1,084 45

Table 2: Why does DLR vary? This table reports the results of simple regressions of U.S. DLR on (1) positive macroeconomic newssurprises,(2)uncertaintyshocks,(3)liquidityshocks,and(4)monetarypolicyshocks(MP shocks). To obtain positive macroeconomic surprises, in a given year, we calculate the average value of the Scotti (2016) macroeconomic surprise index, provided that the index is positive. BEX uncertainty is the Bekaert et al. (2019)uncertainty index. Following Bali et al. (2014), we define liquidity shocks as the difference between stock market turnover and its past 12-month average. Finally, MP shocks are the monetary policy shocks of Romer and Romer (2004). All variables are defined in Appendix B. The sample size is determined by the availability of the ∗∗∗ ∗∗ ∗ particular measure. All variables are standardized to ease the interpretation. , , and denote significance at the 1%, 5%, and 10% levels, respectively. Newey-West (1987) standard errors with 5 lags are reported. Dep. var. DLR β St. Error Adj.R2 N t Positive macro surprises 0.032 ∗∗ (0.012) 0.063 24 t BEX uncertainty -0.067 ∗∗∗ (0.017) 0.285 28 t Liquidity shocks 0.019 ∗ (0.010) 0.022 130 t MP shocks 0.050 ∗∗ (0.023) 0.184 37 t 46

Table 3: The impact of global low risk on growth: Endogeneity concerns In panel A, we report the results when using a two-stage regression approach in (15) and (16). In the first stage, we regress the global durationoflowrisk(G-DLR)onU.S.naturaldisasters,U.S.liquidityshocks,andU.S.stockmarketrealizedvolatility. Naturaldisastersare obtained from Baker et al. (2020). U.S. liquidity shocks are defined as the difference between stock market turnover and its past 12-month \ average as in Bali et al. (2014). We report the F statistics and corresponding p-value. In the second stage, we regress growth on G-DLR, \ \ while controlling for the lagged values of G-DLR and G-DHR along with the rest of the control variables in the baseline specifications, but forthe sakeofbrevity,estimatedcoefficientsofcontrolvariablesareomitted. Inthe firstrowofpanelB,we reportthe estimatedcoefficients for G-DLR , when we alter the definition and calculate G-DLR by using uncertainty shocks of Berger et al. (2020). In the second row, BDG we further control for realized volatility. Finally, in the third row, we present the results for (14) using the same sample period as in Panel B for comparison purposes. We follow the methodology proposed by Berger et al. (2020) to construct uncertainty shocks driven by implied volatility and orthogonal to current realized volatility innovations. For both panels, we bootstrap the standard errors with 1,000 sample draws clustering at the country and year level. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively. Panel A: Two-stage regression approach Second stage h=0 h=1 h=2 h=3 h=4 h=5 \ G-DLR 0.556*** 0.776*** -0.925*** -0.686*** -0.197 0.045 First stage F-stat p-value 1 (βUSnat.disasters+βUSLIQ+βUSVOLA)=0 15.09*** <0.01 j=0 j j j P Adj. R2 0.70 Panel B: News Shock approach Shocks controls h=0 h=1 h=2 h=3 h=4 h=5 G-DLR baseline 0.095 0.507*** 0.887*** -1.833*** -0.305 0.354 BDG G-DLR baseline + RV 0.113 0.522*** 0.893*** -1.834*** -0.263 0.374 BDG G-DLR baseline 7.027*** 11.562*** -9.369*** -3.196 -0.589 -1.279 47

Table 4: Why does low risk cause a boom-to-bust cycle? Endogeneity concerns In panel A, we report the results when using a two-stage regression approach. We use the first stage described in Table 3 and estimate \ \ G-DLR. In the second stage, we regress investment growth, changes in portfolio flow, and high-yield share of issuance on G-DLR, while \ \ controlling for the lagged values of G-DLR and G-DHR along with the rest of the control variables in the baseline specifications. For the sake of brevity, estimated coefficients of control variables are omitted. In Panel B, G-DLR is calculated as in Table 3. We replace the BDG endogenous variable economic growth with the growth of investment, changes in portfolio flow, and high-yield share index as dependent variables and keep the same control variables. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively. We bootstrap the standard errors with 1,000 sample draws clustering at the country and year level. Panel A: Two-stage regression approach Second stage Dep. Var h=0 h=1 h=2 h=3 h=4 h=5 Investment growth 0.688** 1.124*** -0.563 -1.476*** -0.836** 0.330 ∆Flows/GDP 1.359*** -1.602*** -0.304 0.759* -0.680 0.188 HY share 3.138*** 1.362 -1.144 -1.785 -4.578** 0.296 Panel B: News Shock approach Shocks: G-DLR BDG Dep. Var h=0 h=1 h=2 h=3 h=4 h=5 Investment growth 0.984*** -0.229 1.018** -1.059 -1.292*** -1.214** ∆Flows/GDP -0.195 1.239** -2.140*** 1.948** 0.500 -0.996 HY share 3.973*** 7.590*** -1.199 -2.797*** -1.660*** 0.538 48

Table 5: Robustness This table presents the robustness analysis. In the first column, we report whether the shock is to the global or local duration of low risk (G-DLR and DLR). In the second column, we report the type of robustness check. The rest of the columns report the estimated impulse responsesforh=0toh=5. Inthe firstsetofrobustnesstests,weemploythe methodproposedbyHamilton(2018)insteadofthe HPfilter to estimate the trend and when the smoothing parameter of the HP filter is set to 1000and 10000instead of 5000. In addition, we estimate the low volatility state if the current country’s volatility is below the one-standard-deviation band. Second, we estimate volatility as the sum of absolute monthly returns and also use nominal returns instead of real returns. Third, we examine our findings when the parameter θ is equal to 0.85 and 0.95 in equation (10) and when we do not apply any decaying factor and instead we count the number of consecutive yearsin which a country experiences a low volatility regime. We also consider the intensity of the deviations of volatility from its trend and calculateDLRasthesumofthevolatilitydeviationswhenacountrystaysinalowvolatilityregimeconsequently. Fourth,weobtainG-DLR from a balanced panel using G7 countries and using only DLR of the United Stated. Fifth, we include credit spreads (Credit spr), change in exchange rates (∆XR), the monetary policy surprise series from Romer and Romer (2004) (MPshock), the economic policy uncertainty (EPU) index of Baker et al. (2016) and the geopolitical risk index (GPR) of Caldara and Iacoviello (2018) in the control set. Sixth, we use 5 years and 20 years fixed effects instead of decade fixed effects and robustDriscoll Kraaystandarderrors. In the final set of robustness, we examine our results for the post–WorldWar II period (1946–2016),the post–Bretton Woods period (1972–2016)and for emerging countries and for developed countries in the post–Bretton Woods period. All regressions include the lagged values of the inflation rate, the degree of political competition, log-GDP, change in short term interest rates, the dependent variable, duration of low risk (DLR), duration of high risk (DHR), their global counterparts (G-DLR and G-DHR), and country and decade fixed effects. We dually clustered standard errors at the country and year levels except when using Driscoll Kraay standard errors. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively. Shock Robustness h=0 h=1 h=2 h=3 h=4 h=5 1 G-DLR Baseline 7.027*** 11.562*** -9.369*** -3.196 -0.589 -1.279 2 DLR Baseline 2.608*** 3.873*** -2.540* -0.221 1.432 -0.183 3 G-DLR Hamilton 5.726*** 9.952*** -7.264** -1.109 -1.781 -1.992 4 DLR Hamilton 2.159** 3.427*** -1.035 -0.223 1.131 -0.271 5 G-DLR λ=1000 6.795*** 13.473*** -8.862** -3.640 -1.610 -1.160 6 DLR λ=1000 2.316*** 3.245*** -1.970* -0.521 0.837 -0.385 7 G-DLR λ=10000 6.299*** 11.251*** -8.230** -3.479 -0.625 -1.476 8 DLR λ=10000 2.663*** 3.438*** -2.351* -0.473 1.356* 0.057 9 G-DLR one st. dev. band 48.415** 26.716 -91.805** -75.090* -21.646 -21.089 10 DLR one st. dev. band 3.260* 3.874 2.096 1.513 6.196*** 0.988 11 G-DLR Abs. ret. 9.280*** 12.812*** -9.881*** -5.242 -0.906 -1.378 12 DLR Abs. ret. 2.972*** 3.560*** -3.345*** -0.255 0.868 0.152 13 G-DLR Nominal ret. 7.899*** 11.715*** -9.568** -4.697 0.203 -1.304 14 DLR Nominal ret. 2.368*** 3.151*** -1.473 -0.129 1.938** -0.112 49

Table 5: Robustness (cont.) Shock Robustness h=0 h=1 h=2 h=3 h=4 h=5 15 G-DLR θ = 0.85 3.457*** 7.096*** -5.548*** -2.406 -0.393 -0.717 16 DLR θ = 0.85 1.310** 2.376*** -1.572* -0.285 0.960 -0.141 17 G-DLR θ = 0.95 8.143*** 16.609*** -13.601*** -5.843 -0.671 -1.841 18 DLR θ = 0.95 2.870* 5.391*** -3.703* -0.343 2.291* -0.214 19 G-DLR no decay. weights 0.447*** 0.738*** -0.627*** -0.208 -0.027 -0.086 20 DLR no decay. weights 0.156** 0.237*** -0.157* 0.002 0.092 -0.009 21 G-DLR Intensity 19.234*** 41.625*** -26.849** -14.073 -2.532 -10.462* 22 DLR Intensity 4.873** 9.089*** -5.494 0.021 1.161 -0.266 23 G-DLR Balanced G7 7.582*** 17.331** -19.910*** -5.381 8.074 7.377 24 DLR Balanced G7 0.495 2.965 -2.500* -1.372 0.492 0.556 25 G-DLR G-DLR US 4.516*** 6.643*** -4.591** -2.463 1.106 -0.393 26 DLR G-DLR US 2.764** 4.661*** -2.013 -0.297 1.475 0.209 27 G-DLR Credit spr 6.451*** 11.393*** -10.233*** -2.216 -0.504 -2.356 28 DLR Credit spr 2.502*** 3.675*** -2.696** -0.003 1.296 -0.279 29 G-DLR ∆XR 7.042*** 11.859*** -9.327*** -2.275 0.060 -0.947 30 DLR ∆XR 2.035* 4.543*** -2.698* -0.283 1.139 -0.246 31 G-DLR MPshock 5.693*** 11.054*** -10.604*** 0.901 0.855 -2.191 32 DLR MPshock 2.156** 3.099*** -2.214* 1.156 1.655* -0.102 33 G-DLR EPU&GPR 6.425*** 9.104*** -11.179*** 1.251 4.629** -0.876 34 DLR EPU&GPR 2.306*** 2.835*** -2.578** 0.717 2.490*** 0.215 35 G-DLR 5year FE 9.813*** 10.310*** -11.859*** 0.090 2.327 -3.912* 36 DLR 5year FE 2.911*** 3.128*** -2.726** 0.685 2.273** -0.412 37 G-DLR 20year FE 6.578*** 11.904*** -7.859** -2.151 0.743 -0.538 38 DLR 20year FE 2.564** 4.180*** -2.000 0.193 1.859* 0.042 39 G-DLR DriscollKraay 7.027*** 11.562*** -9.369*** -3.196 -0.589 -1.279 40 DLR DriscollKraay 2.608*** 3.873*** -2.540 -0.221 1.432 -0.183 41 G-DLR postWWII 6.960*** 11.696*** -9.759*** -3.896 -0.508 -1.723 42 DLR postWWII 2.466** 3.865*** -2.522* -0.327 1.303 -0.254 43 G-DLR postBW 7.125*** 11.298*** -10.509*** -2.701 0.294 -2.141 44 DLR postBW 2.727*** 3.846*** -2.568 0.320 1.637* -0.266 45 G-DLR Emerging 0.724*** 1.195*** -1.023*** -0.319 0.076 -0.423*** 46 DLR Emerging 0.483*** 0.706*** -0.695*** -0.110 0.133 -0.084 47 G-DLR Developed 0.542*** 0.767*** -0.750*** -0.005 0.122 -0.011 48 DLR Developed 0.226* 0.415** -0.292 0.112 0.153 -0.090 50