*“[A] central bank seeking to maximize its probability of achieving its goals is driven, I believe, to a risk-management approach to policy. By this I mean that policymakers need to consider not only the most likely future path for the economy but also the distribution of possible outcomes about that path.” *

Federal Reserve Board Chairman Alan Greenspan, 29 August 2003.

Alan Greenspan’s remarks were obvious, even when he made them. For several decades, central bankers have been the key risk managers for the economy and the financial system. Unfortunately, just a few years after Greenspan spoke, it was clear that they had failed spectacularly. The financial regulatory reforms since 2009—capital and liquidity requirements, resolution regimes, restructuring of derivatives markets, and an evolving approach to systemic risk assessment and (macroprudential) regulation—have all been directed at improving the resilience of the system to help sustain strong and stable economic growth. As a result, the likelihood of another crisis-induced plunge in GDP is much lower today than it was a decade ago.

But we still have plenty of work to do. We are at an early stage in the process of building a financial stability policy framework that corresponds to the inflation-targeting framework which forms the basis for monetary policy. Such a framework requires measurable financial stability objectives that are akin to a price index, tools comparable to an interest rate, and dynamic models that help us to understand the link between the two.

In this post, we describe a step forward in developing such a framework: the concept and measurement of *GDP at risk*.

To understand GDP at risk, start with *Value-at-Risk* (VaR), an idea that emerged 40 years ago following the stock market crash of 1987. At its most fundamental level, risk management requires controlling the probability of catastrophe. For a financial intermediary, that catastrophe is a large monetary loss. Financial risk managers use VaR to quantify the risk of such a catastrophe. VaR measures—at a given probability—the worst possible loss over a specific time horizon. Thus, a commercial bank risk manager might limit the daily worst-case loss of a trader who controls $100 million in assets to $10 million at a 0.1 percent probability. That means that, given the historical data used in the bank’s models, the trader cannot take a position that has more than one chance in a thousand of losing 10 percent in a single day. (The classic reference is the book by Philippe Jorion.)

VaR is computed by examining the worst episodes that could occur. These are the low-probability, high-cost events that are commonly known as *tail risks*. Simple measures of dispersion, like the standard deviation, often fail to account for the size of the bad (left) tail of the distribution. There are circumstances when the lower tail gets fatter―the probability of very bad events rises―without materially raising the standard deviation. This is one interpretation of what happened in the fall of 1998, when Russia defaulted on its domestic debt and Long Term Capital Management collapsed. At the time, point forecasts for the aggregate price level and the GDP gap, as well as the standard deviation of these projections, stayed roughly the same. But the probability in the left tail of the distribution—the chance of a very bad outcome—rose. When such tail risks rise, acting as risk managers, policymakers reasonably respond to their perception that *GDP at risk* has gone up (see, for example here).

Based on recent work by Adrian, Boyarchenko and Giannone, the October 2017 Global Financial Stability Report of the IMF estimates a time series for GDP at risk using a technique called *quantile regression* (see chapter 3). It is worth taking a small detour to understand this tool.

Standard statistical methods, the ones we commonly teach in college, allow us to address questions like the following: If some external factor, like oil prices or government spending, changes, how will that alter the *expected *path of growth, employment or inflation over the next year or two? Knowing the answer helps policymakers use their tools to stabilize the economy. That is, if a central bank is to successfully maintain inflation at its target, members of the monetary policy committee need to understand how the economy *usually* evolves for a given path of interest rates (their conventional tool) when conditions change.

The risk manager’s focus is not on the expected path, but on the worst possible outcomes. Their concern is about a question like this: If the path of bank credit or government debt rises by 10 percent of GDP, how will that alter the projected worst 5 percent of GDP outcomes over two, three or five years? Quantile regression provides an answer. (For a technical introduction, see here. For an early application, see here.)

Using this technique, the IMF researchers computed the probability distribution of the one-year-ahead forecast for global growth. The solid red line in the chart is the median of this forecast distribution: we can think of this as the central forecast for global growth. The upper and lower dashed lines are the 5th and 95th percentiles of the distribution, respectively. So, for example, in the fourth quarter of 2016, the median forecast for growth in 2017 was 3.67 percent—that’s the final point on the red line. The dashed lines tell us that the there is a 5 percent chance that growth will be above 5.58 percent and a 5 percent chance that it will be below 2.86 percent. The lower dashed line—the one that spikes down in late 2008—is a measure of *GDP at risk*.

One-Year-Ahead Density Forecast for Global Growth, 1991-2016

The chart also reveals some fundamental properties of the IMF’s estimates. The level of the top dashed line hardly changes. In fact, over the entire 25-year period studied, the 95th percentile of the GDP growth distribution moves between a high of 5.99 percent and a low of 4.57 percent. This is in sharp contrast with the measure of GDP at risk (the lower dashed line), which ranges from +3.59 percent to ‑14.53 percent. Importantly, these large downward movements are temporary: for most of the period since 1991, GDP at risk is not far below the median.

The IMF’s estimates exhibit an interesting pattern: as the forecast dispersion widens, the median forecast falls. This relationship is unlikely to be an accident: increases in uncertainty typically are associated with projections of weaker growth, but (like recessions) these are relatively short in duration. The second chart below highlights the correlation between the dispersion and the median: a one-percentage point decline in the median forecast (shown on the horizontal axis) is associated with a 5½ percentage point increase in the spread, nearly all of which reflects an increase in GDP at risk. (The fit of the line does *not* depend on the outliers at the top left.)

One-year-ahead Median Growth Forecasts versus Spread, 1991-2016

These patterns are consistent with Milton Friedman’s “plucking model” of business fluctuations, based on his observation that growth tends to be characterized by extended episodes of smooth, upward movement, punctuated by occasional cyclical contractions of shorter duration. That is, business cycles are inherently *asymmetric*: while the unemployment rate displays temporary jumps in recessions—say, from 5 percent to 10 percent; it does not plunge in booms from 5 percent to 0 percent. And, usually, it is not very far from 5 percent.

Why is the lower tail of the growth distribution so much bigger than the upper tail? One explanation starts with the fact that there are short-run capacity constraints such that producing above that level entails sharply higher costs. By contrast, on the downside, the only limit is that firms shut down. That’s a decline of 100 percent. Twenty years ago, Chang-jin Kim and Charles Nelson showed that U.S. GDP is well characterized by this asymmetry. More recently, Stéphane Dupraz, Emi Nakamura and Jón Steinsson develop a model that generates these features.

We see GDP at risk as a big step forward for policymakers. It is a complement to SRISK, which measures capital shortfalls in the financial system. SRISK is an indicator of financial vulnerability that also tells us which individual intermediaries are contributing to that vulnerability. GDP at risk helps us to understand the linkages between the financial sector and the real economy at an aggregate level. For example, GDP at risk can tell us whether an increase in leverage *outside* of the financial sector increases the likelihood of a severe economic collapse.

GDP at risk has four useful characteristics. First, it is directly based on our ultimate objectives: high real economic growth and low unemployment. These are the basis for improvements in social welfare.

Second, because GDP already is one of the most widely understood economic concepts, using GDP at risk simplifies policy communication. Imagine two conversations, both between a policymaker and elected officials charged with overseeing the central bank to which they have delegated the role of maintaining financial and economic stability. The first discussion focuses on a measure based on the details of stress tests and network effects―the nuts and bolts of macroprudential policy. The second is anchored by the idea that policymakers should limit the likelihood of an outsized fall in GDP over the next several years. For example, they might say that the odds of a 5 percent drop over the coming two years should be less than one in ten (a 10 percent probability). While technical experts need to have the first conversation among themselves, the second is likely to be much more effective in helping others anticipate policy choices, and in accounting for them after the fact.

Third, provided we accept the centrality of GDP at risk, we can translate much of the machinery of inflation targeting into a financial stability policy framework. “Financial Stability Reviews” would look like today’s central bank “Inflation Reports,” with forecasts of GDP at risk at various horizons replacing the path of inflation projections. Of course, such forecasts require an understanding of what makes GDP at risk rise or fall. How important is corporate leverage relative to household leverage? How important are equity versus property price booms? What is the impact of fiscal policy? What types of cross-border capital flows create the biggest vulnerabilities?

Finally, GDP at risk can help discipline discussions of policy tradeoffs. At short horizons, central bankers *aim* to encourage risk-taking when they lower interest rates: faced with an economic slowdown, they wish to stimulate lending. Over longer horizons, however, increased private leverage can create fragilities. So, policymakers want to know the extent to which lower interest rates reduce GDP at risk in the near term, and raise it in the longer term. There are surely many other examples as well.

For several decades prior to the crisis, many central banks with a price stability objective had achieved low and stable inflation. Today, with financial stability taking on such importance, we also expect central bank policies that will lower the probability and the severity of a crisis. But delivering on this means having appropriate risk measures, the tools for maintaining stability, and models that link the two.

GDP at risk is an important step forward in meeting this challenge.