The tail that wags the economy: The origin of secular stagnation

Julian Kozlowski, Laura Veldkamp, Venky Venkateswaran

11 September 2016



The typical post-WWII recession has a distinct trough, followed by a sharp rebound toward a stable trend line. Following the Great Recession, however, this rebound is missing. The missing recovery is what Summers (2016) and Eggertsson & Mehotra (2014) call ‘secular stagnation’ (see also Teulings and Baldwin 2014).

Figure 1. Real GDP in the US and its trend

Notes: Dashed line is a linear trend that fits data from 1950-2007. By the start of 2015, real GDP was 12% below trend.

Why did the dysfunction in credit markets impact the real economy for so long? Many explanations for the real effects have been advanced, and these are still being compared to data (e.g. Gertler and Kiyotaki 2010, Brunnermeier and Sannikov 2014, and Gourio 2012, 2013). Existing theories about why the crisis took place assume that the shocks that triggered it were persistent. Yet such shocks in previous business cycle episodes were not so persistent. This differential in persistence is just as puzzling as the origin of the crisis. What most explanations of the Great Recession miss is a mechanism that takes some large, transitory shocks and then transforms them into long-lived economic responses.

Perhaps the fact that this recession has been more persistent than others is because, before it took place, it was perceived as an extremely unlikely event. Today, the question of whether the financial crisis might repeat itself arises frequently. Financial panic is a new reality that was never perceived as a possibility before.

Our explanation for persistently low output hinges on people’s assessment of tail risk. Why focus on tail risk?  All sorts of beliefs change over time in response to new events. We thought the volatility of shocks had diminished in the Great Moderation, estimated that productivity growth had slowed in the 1970s and 1980s, and have constantly updated collective wisdom on many other features of the modern economy, in light of new experiences. All of these changes in beliefs are quite persistent, far outliving the episodes that prompted them. Yet, tail risk is special for two reasons. First, it is prone to large, persistent belief revisions because data on tail events are scarce; second, tail risk incurs large real economic costs, particularly when firms finance investment with debt.

In our research, we combined a model with macroeconomic data to measure how much tail risk rose, to explain why it remained elevated, and to explore its economic consequences (Kozlowski et al. 2015). The model describes a production economy with agents who form beliefs in the same way an econometrician forms estimates. They use standard econometric tools to estimate the distribution of aggregate shocks in a flexible, non-parametric way. When they observe a new shock, they add that new piece of data to their dataset and use a kernel density estimator to re-estimate the distribution from which it was drawn. Transitory shocks have persistent effects on beliefs because, once observed, the shocks remain forever in the agents' dataset. Tail events have a particularly large effect on beliefs because data on tail events are scarce. It takes many observations over a long period of time to gradually change beliefs about the mean or variance of economic processes. However, one or two outlier events can drastically alter our perception of extreme event risk.

To gauge the magnitude of the real effects of this change in tail risk, we feed a time-series of actual macro data into our economic model. Specifically, we measure capital quality shocks using historical data on replacement and market value of the non-financial capital stock from the Flow of Funds reports. We then apply our kernel density estimator to construct beliefs, which are our agents’ best estimate of the distribution from which the capital quality data is drawn. Each period, when a new piece of data is observed, agents incorporate the new data point and re-estimate the distribution. Given the new distribution, agents invest, work, issue debt, and consume optimally. Our calibrated model predicts that capital, employment, and output drop 17%, 8%, and 12% after the financial crisis, with almost no rebound to trend. As Figure 2 illustrates, the 12% downward shift in trend output fits the data.

Figure 2. Output in the model falls and remains low, just as it does in the data

Source: National Income and Product Accounts (NIPA), 1950-2014.

One important reason why tail risk has such large aggregate effects is the fact that firms finance investment, at least in part, by issuing debt. Debt inflicts bankruptcy costs in the event of default. The cost of issuing debt, the credit spread, depends on the probability of default. Default risk depends on the likelihood of large aggregate shocks, or tail events. Thus, when the probability of a left tail event rises, financing investment with debt becomes less attractive. As a result, when tail risk rises, an economy with more highly-leveraged (indebted) firms experiences a larger drop in long-run investment and output. We show that the extent to which debt amplifies bad shocks is greater for large tail shocks than it is for events closer to the mean. Thus, debt financing interacts with tail risk to accentuate the difference between extreme recessions and their milder counterparts.

Changes in measured tail risk not only explain the observed patterns in macro aggregates, they are also consistent with options data and with popular narratives. In Figure 3, the SKEW index – an option-implied measure of tail risk in equity markets – shows a clear rise since the financial crisis, with no subsequent decline. Popular narratives about the stagnation emphasise a change in ‘attitudes’ or ‘confidence,’ that we capture with belief changes that have ‘permanently reset’ peoples’ attitudes towards risk (Condon 2013).

Figure 3. The SKEW Index

Notes: A measure of the market price of tail risk on the S&P 500, constructed using option prices, 1990:2014. Source: Chicago Board Options Exchange (CBOE).

Hall (2016) argues that credit market data are inconsistent with a beliefs-based explanation for stagnation. He notes that credit spreads rose only temporarily during the Global Crisis and argues that the subsequent recovery to historically normal levels by 2010 implies a restoration of confidence. This argument does not account for the decline in investment and borrowing as beliefs become more pessimistic, which offsets the increase in spreads. Our model teaches us that a surge in tail risk is consistent with a modest change in the credit spread. When tail risk rises, borrowing is more expensive and firms borrow less. Since firms with less debt are less risky borrowers, their cost of borrowing goes back down. In our model, the net effect of these two opposing forces is only four basis points. In other words, observing tail events can suppress economic activity for a long time, even if credit spreads recover quickly.

Our results question one of the traditional logics of debt. Debt is typically thought of as information-insensitive because its payoffs are constant across most states of a firm (DeMarzo et al. 2005). Yet, the value of debt is sensitive to tail risks because tail events trigger default. However, the estimated probability of tail events is sensitive to new data because data on tail events are scarce. Thus, we find the value of debt is very sensitive to exactly the type of beliefs that are themselves sensitive to new information. This combination makes the value of debt quite sensitive to information that triggers a reassessment of tail risk.


Our beliefs govern every choice we make. When large aggregate events are observed by all, these events change the beliefs of many people in a systematic way and have important consequences for the macroeconomy. Economic outcomes are particularly sensitive to beliefs about the probability of extreme events, or tail risks. A barrier to exploring such tail risks is that these risks are exceptionally difficult to gauge because we have so little data on extreme outcomes. We argue that economic actors have just as hard a time estimating tail risks as economists do. Because data on tail risk are scarce, people who observe extreme events revise their beliefs substantially and persistently. A short-lived financial crisis can trigger long-lived shifts in expectations that in turn trigger secular stagnation.

A run on the financial sector had not been seen in the post-war US economy. Because of this, people were complacent. The onset of the Great Recession caused beliefs to change drastically and that change in beliefs will likely persist. For decades to come, the knowledge that such an event is not so improbable will influence decisions, prices, and output.


Brunnermeier, M and Y Sannikov (2014) “A macroeconomic model with a financial sector”, American Economic Review, 104(2).

Condon, B (2013) “AP IMPACT: Families hoard cash 5 yrs after crisis”, Huffington Post, 6 October.

DeMarzo, P, I Kremer and A Skrzypacz (2005) “Bidding with securities: Auctions and security design”, American Economic Review, 95(4): 936–58.

Eggertsson, G and N Mehrotra (2014) “A model of secular stagnation”, NBER, Working Paper No 20574.

Gertler, M, N Kiyotaki et al (2010) “Financial intermediation and credit policy in business cycle analysis”, Handbook of monetary economics, 3(3): 547–599.

Gourio, F (2012) “Disaster risk and business cycles”, American Economic Review, 102(6): 2734–66.

Gourio, F (2013) “Credit risk and disaster risk”, American Economic Journal: Macroeconomics, 5(3): 1–34.

Hall, R (2016) “Macroeconomics of persistent slumps”, in Handbook of Macroeconomics, J Taylor and H Uhlig (eds), Amsterdam: Elsevier, 2: 1-30.

Kozlowski, J., L. Veldkamp and V. Venkateswaran (2015), “The Tail that Wags the Economy: Belief-Driven Business Cycles and Persistent Stagnation”, NBER working Paper No. 21719.

Summers, L. H. "The Age of Secular Stagnation." Foreign Affairs. Mar/Apr 2016, 2-9.

Teulings, C., and R. Baldwin (2014). “Secular Stagnation: Facts, Causes and Cures”, A eBook.



Topics:  Global crisis Global economy Macroeconomic policy

Tags:  secular stagnation, beliefs, expectations, tail risk, debt, Great Recession, global crisis

PhD Candidate in Economics, New York University

Professor of Economics at the Stern School of Business, New York University

Assistant Professor of Economics, New York University's Stern School of Business