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Veldkamp, Laura

Article Beliefs, tail risk, and secular stagnation

NBER Reporter

Provided in Cooperation with: National Bureau of Economic Research (NBER), Cambridge, Mass.

Suggested Citation: Veldkamp, Laura (2019) : Beliefs, tail risk, and secular stagnation, NBER Reporter, National Bureau of Economic Research (NBER), Cambridge, MA, Iss. 3, pp. 7-10

This Version is available at: http://hdl.handle.net/10419/219440

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Beliefs, Tail Risk, and Secular Stagnation

Laura Veldkamp

Beliefs govern every choice we ters, can explain persistent low interest make. Much of the time, they lie in the rates, volatile equity prices, and secular background of our economic models. stagnation. We often assume that everyone knows everything that has happened in the Belief Formation past, as well as the true probabilities of all future events. The concept of ratio- There are two broad approaches to Laura Veldkamp is a research associate nal expectations means that the true explaining belief formation. The first is in the NBER’s Economic Fluctuations and distribution of future outcomes and the a behavioral approach, which departs Growth Program and is the Cooperman believed distribution of future outcomes from rational expectations by directly Professor of Economics and Finance at are the same. stating some belief formation rule that Columbia University. She is a co-editor of If the rational expectations assump- explains the phenomenon at hand. the Journal of Economic Theory, the first tion were true, there would be no need Such assumptions are often supported woman to hold that role. She also serves on for economists. If everyone knew all with survey or experimental data. These the Economic Advisory Panel of the Federal covariances, we would not need any assumptions may be right, but they Reserve Bank of New York and is the author empirical work. If everyone knew the rarely provide a reason for the agents’ of the Ph.D. textbook, Information Choice true model of the economy and could beliefs. If we don’t understand why the in Macroeconomics and Finance. reason through it, we would not need rule holds, we don’t know in what cir- Veldkamp’s research explores the role theorists. Luckily for us, the rational cumstances the rule will continue to of information in the aggregate economy. expectations assumption is not correct. hold. While such approaches provide Her topics range from business cycles and Yet most of the time it is a useful insights, there is more to be discovered. mutual fund performance to home bias and simplification. We have seen enough The second approach to belief for- female labor force participation. A unifying economic booms and recessions, firm mation is an imperfect-information theme of her work is that treating informa- and bank failures to have a reason- approach. Agents have finite data to esti- tion, or the ability to process information, as able estimate of their true probability. mate states and distributions. Despite a scarce and valuable resource helps to rem- However, when studying rare events, the limited information, they estimate edy many failures of full-information, ratio- often referred to as “tail events,” assum- efficiently, given the data they have, or nal expectations frameworks. Her recent ing rational expectations can lead econ- the information they have optimally work uses these information tools to under- omists astray. Because these events are chosen to acquire, attend to, or pro- stand the aggregate consequences of the dig- rare, data on them are scarce, and our cess. Agents in these models do what ital economy. estimates of their true probability are economists would do if we were in their Veldkamp received a B.A. in unlikely to be accurate. In these circum- place: They collect data and use stan- applied mathematics and economics stances, understanding belief formation dard econometrics to estimate features from Northwestern University and her becomes particularly important. of their environment. When a new out- Ph.D. in economic analysis and policy My research focuses on how indi- come is observed, they re-estimate their from Stanford University. She joined the viduals, investors, and firms get their model in real time. Columbia faculty in 2018 after teaching at information, how that information The imperfect-information New York University for 15 years. affects the decisions they make, and how approach overcomes one of the main A native of Lexington, Massachusetts, those decisions affect the macroecon- challenges of working on beliefs — the Veldkamp met her husband, Stijn Van omy and asset prices. It also examines fact that beliefs are hard to observe Nieuwerburgh, while at Stanford. She how people form beliefs about tail risk or measure. Survey data are informa- enjoys playing the viola, playing squash and how learning about tails, or disas- tive in many circumstances, but report- with her two boys, and sculling.

NBER Reporter • No. 3, September 2019 7 ing accurate probabilities of rare events Kozlowski and Venky Venkateswaran, we Tail Risks, Low Interest is particularly difficult, and surveys are explore this scarring effect as an explana- Rates, and Inflation rarely designed to elicit these beliefs. Also, tion for the slow rebound of investment, when beliefs change on short notice, cap- labor, and output, as well as tail risk-sensi- In follow-up work, we use a much turing this change with surveys is usually tive options prices.1 simpler economic environment to speak infeasible because of the costly and time- While logical, this effect could be to the persistently low interest rates on consuming nature of survey administra- tiny. To assess whether this is a plausi- safe assets.3 To create a link between tion. In contrast, when we model agents ble explanation for the persistence of the heightened tail risk and the interest rate, as econometricians, we can estimate their post-crisis output loss, we embed learn- or yield, on safe assets, we focus on two beliefs in real time with publicly observ- ing in a dynamic stochastic general equi- standard mechanisms. able data and standard econometrics. librium model. For our purposes, this First, faced with more risk, agents model needs two features. First, it needs want to save more. But not every agent Tail Risks, Secular Stagnation, to have shocks that had extreme (tail) can save more. The bond market has to and the Scarring Effect outcomes in the financial crisis. Second, clear. Therefore, the return on bonds the model needs enough non-linearity declines in order to clear that market. Tail risk beliefs have three proper- so that unlikely tail events can have some This force explains about a third of the ties that are helpful in explaining puzzling aggregate effect. For this purpose, we use decline in the interest rate. The sec- macroeconomic phenomena. They help an augmented version of a model devel- ond force at work is that safe assets explain persistent reactions to rare events, oped by François Gourio.2 In this model, offer liquidity that is particularly valu- biased expectations, and, in environments shocks have large initial effects, but there able in very bad conditions. When the where uncertainty matters, strong reac- is no guarantee of any persistent effects probability of these tail events rises, liq- tions to seemingly innocuous events. from transitory shocks. uid assets are more valuable and their One macroeconomic puzzle that tail The predictions of this model teach yield declines, clearing the market. That risk can help explain is the persistent us some new lessons. First, the change in liquidity effect explains the other two- aftermath of the 2008 financial crisis, beliefs is large enough to make the drop thirds of the persistent interest rate gap often referred to as secular stagnation, in in output a highly persistent level effect. from the pre-crisis period. which the real effects of that financial cri- This doesn’t mean that the positive shocks If re-estimating distributions with sis persisted long after the financial condi- in recent years cannot return the economy real-time data can make actions persis- tions that triggered it had been remedied. to trend. It does mean that, without the tently different following a crisis, does it Some of this persistence seems to come Great Recession, incomes today would matter how we estimate those distribu- from a scarring effect on beliefs. have been higher. Second, the equilib- tions? For some purposes, no. For oth- Consider this: In 2006, before the rium effects are surprising. Some econo- ers, yes. In the secular stagnation paper, financial crisis, were economists con- mists asserted that persistent economic the magnitude of stagnation depended cerned with financial stability, bank runs, responses to the Great Recession could on the size of the increase in tail risk. and systemic risk? Mostly not. Yet after- not be due to tail risk because high tail That measurement is robust to many ward, though banks are safer and risk is risk would imply wide credit spreads and estimation methods. They all produce more tightly regulated, the knowledge low equity prices. This logic would be cor- about the same effect, because they all that such possibilities are real has influ- rect if firms did not respond to higher risk fit the data by putting the same prob- enced research for more than a decade. by reducing their debt. But when risk and ability mass on extreme outcomes. Our Similarly, the knowledge that firms can the price of credit both rise, firms demand agents used classical, non-parametric suffer severe negative capital returns influ- less credit. They deleverage. Less indebted econometrics to estimate the shock dis- ences the actions and risks that firms are firms are less risky. As a result, their credit tribution. We adopted this approach for willing to take. Seeing the United States spread narrows and their equity price its simplicity. Simplicity was essential at the brink of financial collapse taught us rebounds. Because of these competing because of the non-linearity and com- that a financial crisis is more likely than forces, equity prices and interest rates putational complexity of our economic we thought. The fact that firms have not are not reliable indicators of tail risk. framework. What doesn’t work is a nor- seen another financial crisis in the last 10 However, the option prices offer a reliable mal or thin-tailed distribution. It rules years does not undermine that lesson. It measure of tail risk. Just as the Chicago out any tail risk by construction. is perfectly consistent with financial cri- Board Options Exchange’s volatility index The choice of whether to use a sis being a once-in-50-years event. Even if (VIX) measures option-implied volatil- Bayesian or classical estimator is not no more crises are observed for the next ity, the skewness index (SKEW) measures innocuous for all purposes. For example, 50 years, our estimate of this rare-event option-implied tail risk. After the Great in the presence of tail risk, finite-sample probability will still be informed by the Recession, the SKEW rose to record highs Bayesian estimators are biased.4 This bias 2008 event. In my research with Julian and never returned to its pre-crisis level. arises because agents are confident that

8 NBER Reporter • No. 3, September 2019 high inflation is more likely than extreme affects the probability distribution by I explore tail risk as a source of uncer- deflation. But they have few high-infla- adding probability mass locally around tainty shocks.6, 7 Uncertainty shocks tion data points with which to estimate the observed outcome and subtracting have been a popular way of generat- that probability. The probability of high a small probability everywhere else. But ing aggregate fluctuations in macroeco- inflation could be much higher than they with parametric systems, an observa- nomic models, but it is not clear where think. But it can’t be much lower and a tion in one part of the distribution can they come from. Somehow, we pretend probability can’t be below zero. change a parameter estimate that signif- that everyone wakes up one day know- Hassan Afrouzi, Michael Johannes, icantly alters the probability mass else- ing for certain that the variance of some and I use this mechanism to under- where. In other words, observing ordi- aggregate shock just rose. We do that stand why households, firms, and fore- nary, non-outlier events can affect our because it helps explain aggregate phe- casters consistently report inflation fore- assessment of tail risk. nomena, not because it makes sense. But casts with large positive bias.5 People Why are tail risk probabilities likely one reason we might all suddenly feel seem to think inflation will be much to be affected by observing nonlocal uncertain is if we all observe an aggregate higher than it turns out to be, month events? Because data on tail events are data point that makes disaster seem more after month, year after year. These biases scarce, tail probability estimates are likely than it was before. are shared by financial Using the post- market participants war series of quar- who pay too much for US GDP Per Capita, 1952–2014 terly GDP growth, inflation insurance rel- we apply Bayes’ law to Natural log of GDP per capita, normalized to 1 in 1952 ative to insurance on 2.4 estimate parameters of other risks. 1950–2007 trend a skewed distribution. If a perfectly 2.2 12% gap Asking GDP to gen- rational, Bayesian 2.0 erate large swings in forecaster observes the uncertainty is tough, 1.8 time series of US infla- Actual because GDP is not tion monthly from 1.6 a particularly vola- 1948 through 2018 tile series. Yet when and uses it to estimate 1.4 we allow agents to a three-state mixture 1.2 estimate a distribu- of normals, the esti- tion that admits skew- mated distribution 1.0 ness, on average they has positive skewness 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 estimate that GDP of 0.38, and the aver- growth has a skew- age 2010–18 fore- Source: J. Kozlowski, L. Veldkamp, V. Venkateswaran, NBER Working Paper No. 21719 ness coefficient of cast is 1.45 percent -0.3, which indicates higher than the aver- that production melt- Figure 1 age 2010–18 infla- downs are more likely tion realization. This is on par with the uncertain. Uncertain estimates are more than “melt-ups.” More importantly, the average size of the forecast bias from likely to experience large revisions. In a skewness estimate changes over time the University of Michigan Consumer parametric system, if there is a parameter and it “wags the tail” of the distribu- Sentiment Index. If firms and forecasters that largely governs tail risk, that param- tion. Since tail events are far from the observe additional data that are infor- eter will be tough to estimate with a mean and uncertainty measures proba- mative about inflation, the lower uncer- high degree of confidence. For example, bility-weighted distance from the mean tainty reduces their inflation biases. skewness is notoriously difficult to esti- squared, these outliers move levels of mate. Observations not too far from the uncertainty. We find that the standard Estimating Changes in Tail Risk mean can nudge the estimate of a skew- deviation of the resulting uncertainty ness parameter up or down. But a small series is one-third of its average level. A final reason that the procedure for change in skewness can double or triple Those are large uncertainty fluctuations estimating beliefs matters is that estimat- the probability estimate of an outcome from a mundane macro time series. ing parameters that govern tail risk can far out in the tail of a distribution. Macroeconomists have neglected make tail risk assessments and uncer- Such small adjustments in tail risk tail risk, in part, because it is so difficult tainty quite volatile. With a non-para- could be the origin of excess volatil- to measure. But the lack of data and dif- metric estimator, changes to a distri- ity or many apparent overreactions. ficulty of measurement are the things bution are local: Each new data point Nicholas Kozeniauskas, Anna Orlik and that make it interesting. Tail probability

NBER Reporter • No. 3, September 2019 9 estimates are likely to diverge from true Gourio F. NBER Working Paper 15399, H, Veldkamp L. Paper presented at the probabilities in ways that are persistent, October 2009, and American Economic Society for Economic Dynamics Annual volatile, and biased. All these econo- Review, 102(6), October 2012, pp. Meeting, St. Louis, MO, June 2019. metric problems, and human faults, 2734–2766. Return to Text offer possible explanations for some of Return to Text 6 “The Common Origin of the most puzzling findings in aggregate 3 “The Tail That Keeps the Riskless Uncertainty Shocks,” Kozeniauskas N, economics. Rate Low,” Kozlowski J, Veldkamp Orlik A, Veldkamp L. NBER Working L, Venkateswaran V. NBER Working Paper 22384, July 2016, and published 1 “The Tail that Wags the Paper 24362, February 2018, and as “What Are Uncertainty Shocks?” Economy: Beliefs and Persistent NBER Macroeconomics Annual 2018, Journal of Monetary Economics, 100, Stagnation,” Kozlowski J, Veldkamp 33, June 2019, pp. 253–283. December 2018, pp. 1–15. L, Venkateswaran V. NBER Working Return to Text Return to Text Paper 21719, November 2015, and 4 “Bias in Nonlinear Estimation,” 7 “Understanding Uncertainty Shocks Journal of Political Economy, forthcom- Box M. Journal of the Royal Statistical and the Role of Black Swans,” Orlik A, ing, 2019. Society, 33(2), 1971, pp. 171–201. Veldkamp L. NBER Working Paper Return to Text Return to Text 20445, August 2014. 2 “Disaster Risk and Business Cycles,” 5 “Biased Inflation Forecasts,” Afrouzi Return to Text

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