The Hairy Chart - Some Plots Have Tell-Tales

The federal funds rate & its often hairy predictions (often hairily bad predictions). An example of a bitemporal plot.

What Is a Hairy Chart?

A hairy chart shows a metric over time, with forecasts branching off at different points. You might also hear it called a porcupine plot, hairy caterpillar chart, Medusa or Fishhook (for dealing with revised instead of forecast data), or probably the most accurate, bitemporal charts.

The central line, or trunk or head, typically tracks an important metric that people want to forecast frequently and accurately. Each hair represents a forecast made at a particular point in time, showing how someone expected that metric to evolve. These forecasts might come from individual predictions, surveys of experts, securities/market prices, or sophisticated statistical models.

There’s something funny about looking at all those hairs. Each one represents a moment when some very smart people, perhaps backed by billions of dollars in market bets or enormous computing power & fancy models, stopped and said, “Okay, here’s what we think is going to happen.” And yet, as you’ll see, in many settings they manage to get it wrong with remarkable consistency.

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Hairy Plots in the Wild

Why Hairy Charts Are Interesting

For starters, so many of these plots you see in the wild really drive home how badly we forecast metrics that matter a lot to us.

Take the federal funds rate. There are plenty of ways to forecast it. You can survey experts, including Fed officials and professional forecasters, or infer market expectations from interest rate futures, options, and other financial instruments. And there’s plenty of incentive to get it right. This one rate influences borrowing costs across the economy, investment decisions, asset prices, the cost of financing the US government’s debt and so much more.

Given how much goes into forecasting it, you might expect the predictions to be pretty good. Historically, though, they’ve been pretty poor.

And not just a little wrong. Often wrong in the same direction for years. For example, from 2009 until the Fed finally raised rates in December 2015, forecasts repeatedly anticipated an earlier increase. Have a look at the plot: more often than not, they’re wrong.

There are several possible explanations. Forecasters tend to expect rates to return to familiar levels. Market-implied rates aren’t pure expectations: the Treasury forward curve includes a term premium, and options-implied SOFR is risk-neutral, which builds in a risk premium (both covered below). Markets also take cues from the Fed’s own guidance, so the Fed and market participants can end up making similar mistakes (several plots from the wild above show both). And, of course, some of the biggest changes in interest rates are responses to shocks that nobody saw coming.

But Sometimes They Get It Right

The forecasts aren’t always wrong. For example, the Fed’s median projection from June 2023 turned out to be close, as did market expectations implied by SOFR options in September 2023. But accuracy tends to deteriorate with the forecast horizon.

Two forecasts that held up: the FOMC’s median projection from June 2023 (left) and the options-implied path from September 2023 (right). Screenshots from the interactive; click or tap either to enlarge.

And, quite apart from what they tell us about forecasting, I think hairy charts just look pretty cool.

Interact with the Fed Funds Hairy Plot

Here’s an interactive version of the hairy plot for the fed funds rate. Zoom into any stretch of years, show or hide each series and recession shading, and hover over or tap any hair to see the forecast it made. I get into the four forecast series below.

Animate the Hairy Plot

And here’s an animation builder. It plays the fed funds rate forward in time, with each projection and forecast appearing as it was made. Pick the years, series and colors, press play, and screen-record it.

How to Make the Hairy Chart

Two Dates for Every Number

A bitemporal chart is a method to plot data which has two dates for each value. One date the value is from, and one date the value is about. For example with the fed-funds hairy chart, each projection has the date the forecast was made, and the date the forecast is about. (I like Toph Tucker’s bitemporal chart article on Observable, it’s a good tour of the idea.)¹

Selected example hair: the FOMC’s median fed funds projection, 16 Mar 2022.

Take one hair. On 16 March 2022, the FOMC raised its target range to 0.25% to 0.50%, its first increase since 2018, and published its participants’ projections for the federal funds rate at the end of 2022, 2023 and 2024.² The medians, all made that day, each about a different date:

Forecast Made On	Forecast About	Projected rate	Actual rate
16 Mar 2022	16 Mar 2022		0.375%
16 Mar 2022	31 Dec 2022	1.90%	4.375%
16 Mar 2022	31 Dec 2023	2.80%	5.375%
16 Mar 2022	31 Dec 2024	2.80%	4.375%

This hair starts on the head at its made date, at the rate set that day (0.375%, the middle of the new range), and runs through the three projections. Every meeting leads to another set of projections, adding another hair.

This hair missed badly: the rate ended 2022 at 4.375%, not 1.9%, and 2023 at 5.375%, not 2.8%.

There are other types of these bitemporal charts. For a policy rate, the outcome is known the day it happens, so the head never moves. Plenty of numbers aren’t like that. GDP, employment and population keep being revised long after the day for the estimate has passed, so their heads grow hairs of their own. Imagine the release of an economic number, say one quarter’s GDP estimate: it sets a point on the plot. Each time the number is revised, a line grows forward in time, connecting the new estimates for the same quarter, to the date of the revised estimate. The x-axis shows the date each value was released. I’ve seen this called a “fishhook” chart; I think I’d borrow from nautical nomenclature and call them telltale plots.

Forecasts of the Federal Funds Rate

For the federal funds rate, the head is the FOMC’s target, and the hairs need forecasts made on many days, each about many days ahead. Many of the best-looking hairy plots I’ve seen use fed funds futures and overnight index swap (OIS) curves, which price every upcoming FOMC meeting every trading day. Those come from providers like Bloomberg, and I couldn’t access (afford) them. Fortunately, four free sources have the same two-date shape, each on its own schedule:

• Treasury forward curves: a hair at every FOMC meeting since 1994, cut at three years.
• Options on SOFR futures: a hair every trading day since March 2023, about three years long.
• The FOMC’s median projection: a hair four times a year since September 2015, up to about three years ahead.
• The Survey of Professional Forecasters: a hair every quarter since 1982, about a year long.

I created reproducible notebooks that document how I got and parsed these datasets. The R notebook and the Python notebook walk through each one, from loading the data to the final plot.³ And here’s a repo with cleaned data in data/, and scripts in scripts/ that download and build those datasets.⁴

Here’s a bit about each series.

Federal Funds Target Rate

First, let’s set up the “head” every “hair” grows from.

NoteSource Detail: The FOMC Target (click to expand)

The rate the Federal Open Market Committee announces it is aiming for. It was a single number until December 2008, and a quarter-point range since. The New York Fed: “The Federal Open Market Committee establishes the target rate, or range, for trading in the federal funds market.”

FRED DFEDTAR is the single target, 27 September 1982 to 15 December 2008. DFEDTARL and DFEDTARU are the lower and upper limits of the range from 16 December 2008, when the Committee cut to 0 to 0.25 percent and has used a range ever since. Verified at the join: DFEDTAR ends 2008-12-15 at 1.00, DFEDTARL/DFEDTARU begin 2008-12-16 at 0.00/0.25.

Values before 1994 are a reconstruction: the FOMC began announcing its target decisions in February 1994, and FRED’s series notes say the 1982 to 1993 values come from Thornton (2005), a Federal Reserve Bank of St. Louis working paper.

Citations.

• https://fred.stlouisfed.org/series/DFEDTAR
• https://fred.stlouisfed.org/series/DFEDTARU
• https://fred.stlouisfed.org/series/DFEDTARL
• Thornton, Daniel L. (2005), “A New Federal Funds Rate Target Series: September 27, 1982 - December 31, 1993”, Federal Reserve Bank of St. Louis
• https://www.newyorkfed.org/markets/reference-rates/effr

Treasury Forward Curve

The rate the Treasury bond market implies for each future date, from the yield curve that Federal Reserve Board staff fit every day, taken at each FOMC meeting since 1994.

NoteSource Detail: GSW Nominal Yield Curve (click to expand)

What the Treasury bond market implies about future short rates, backed out daily by Federal Reserve Board staff from a smooth curve fitted across the whole maturity spectrum.

The Board describes the dataset as “smoothed yields on hypothetical Treasury securities that can be easily compared across maturities and over time, from 1961 to the present”. Its model “stipulates that the shape of the yield curve on any given date can be adequately captured by a set of six parameters”, estimated “by minimizing the discrepancy between the fitted Svensson yield curve and observed market yields”. Before 1980, “the Nelson-Siegel model—a model with fewer parameters—was used”.

On what goes into the fit: “only the coupon securities (Treasury notes and bonds) are used”; “on-the-run and first-off-the-run Treasury notes and bonds are not used”; and “Treasury bills and Treasury floating rate notes (FRNs) are not used”.

It is not an official statistic. The Board calls it “a staff research product and not an official statistical release”. A forward rate is the expected future short rate plus a term premium, so the hairs aren’t a pure expectations path: they can sit a little above or below it. And because bills are excluded and the curve is a six-parameter analytic function, the hairs are smooth by construction: they cannot show the discrete steps at FOMC meetings that market data pricing individual meetings shows.

Citations.

• https://www.federalreserve.gov/data/nominal-yield-curve.htm
• Gürkaynak, Sack and Wright (2006), FEDS 2006-28, https://www.federalreserve.gov/pubs/feds/2006/200628/200628pap.pdf
• Published in Journal of Monetary Economics 54(8), 2007, 2291-2304

Options-Implied (SOFR)

What options on SOFR futures imply the overnight rate will average over each coming three-month window, estimated daily by the Federal Reserve Bank of Atlanta since March 2023.

NoteSource Detail: Atlanta Fed Market Probability Tracker (click to expand)

What options traders are collectively betting, as a full probability distribution over where the overnight rate will average in a future three-month window.

From the data dictionary shipped inside the file: “The Market Probability Tracker uses Chicago Mercantile Exchange (CME) 3-month SOFR options to estimate the probability ditributions [sic] implied by their prices and specified reference window.” Their guide adds that it “transforms options on SOFR futures prices into probability distribution values”.

Two fields are used. reference_start is the “Start date of the 3-month window referenced by CME 3-month SOFR contracts”. Rate: mean is “The rate, in basis points, associated with the mean of the estimated distribution for a given reference window”.

The underlying rate is SOFR, published by the Federal Reserve Bank of New York: a broad measure of the cost of borrowing cash overnight collateralized by US Treasury securities. That makes it a secured rate, where the federal funds rate is unsecured lending between banks; the two are close but not identical. An option-implied distribution is risk-neutral, so it is what traders expect weighted by how much they care about being wrong each way, not literally what they expect. It starts in March 2023.

Each point comes from its own window’s option prices rather than from one fitted curve, but as a three-month average weighted across possible outcomes it does not resolve individual FOMC meetings.

Citations.

• https://www.atlantafed.org/research-and-data/data/market-probability-tracker
• https://www.atlantafed.org/research-and-data/data/market-probability-tracker/what-to-know
• https://www.newyorkfed.org/markets/reference-rates/sofr
• Estimation code published as mpt_source.zip on the tracker page

FOMC Median Projection

The median FOMC participant’s projection of the federal funds rate at the end of each of the next few years, from the Summary of Economic Projections, published since September 2015.

NoteSource Detail: The Summary of Economic Projections (click to expand)

Four times a year each of the Federal Reserve’s senior policymakers writes down where they think the federal funds rate should be at the end of each of the next few years. This is the middle answer.

The table is titled “Economic projections of Federal Reserve Board members and Federal Reserve Bank presidents, under their individual assumptions of projected appropriate monetary policy”: all 7 Governors plus all 12 Reserve Bank presidents. That is wider than the Committee’s voting membership: the Board says the Committee “consists of twelve members”, namely “the seven members of the Board of Governors of the Federal Reserve System; the president of the Federal Reserve Bank of New York; and four of the remaining eleven Reserve Bank presidents, who serve one-year terms on a rotating basis”. Staff produce a separate forecast, the Tealbook, released only after five years.

From the table notes: “The projections for the federal funds rate are the value of the midpoint of the projected appropriate target range for the federal funds rate or the projected appropriate target level for the federal funds rate at the end of the specified calendar year or over the longer run.” And: “For each period, the median is the middle projection when the projections are arranged from lowest to highest.”

It is not a forecast. The row is labeled “Memo: Projected appropriate policy path”, and projections rest on each participant’s “assessment of appropriate monetary policy”. Normative, conditional on each person’s own outlook, and never voted on.

Only 44 of 59 releases give a median. The median column was introduced with the September 2015 SEP; before that the table shows a central tendency and range only, and the dots exist solely as a figure.

Citations.

• https://www.federalreserve.gov/monetarypolicy/files/fomcprojtabl{YYYYMMDD}.pdf
• https://www.federalreserve.gov/monetarypolicy/fomc.htm
• https://fred.stlouisfed.org/series/FEDTARMD
• https://www.federalreserve.gov/monetarypolicy/fomc_projectionsfaqs.htm

Professional Forecasters

The Philadelphia Fed’s quarterly survey: the median forecast of the three-month Treasury bill rate for the current quarter and the next four, back to 1982.

NoteSource Detail: Survey of Professional Forecasters (click to expand)

Every quarter the Philadelphia Fed asks a few dozen professional forecasters where the three-month Treasury bill rate will be over the next five quarters, and publishes the median.

The Philadelphia Fed describes it as “the oldest quarterly survey of macroeconomic forecasts in the United States. The survey began in 1968 and was conducted by the American Statistical Association and the National Bureau of Economic Research. The Federal Reserve Bank of Philadelphia took over the survey in 1990.” Individual responses are “kept confidential by using identification numbers”.

The survey asks about the bill rate, not the federal funds rate, but the two track each other closely: a three-month bill pays roughly what investors expect overnight rates to average over its three months. The bill normally sits a little below fed funds, so a forecast of the bill rate works as a rough forecast of the policy rate that runs slightly low.

Citations.

• https://www.philadelphiafed.org/surveys-and-data/real-time-data-research/survey-of-professional-forecasters
• Documentation PDF: variable definitions p.10, horizon numbering p.20, survey timing p.7

Hairy Evaluations: How Well Does Each Forecast Perform?

The R and Python notebooks score every hair against what actually happened.⁵ Tables there show various ways the forecasts can be (somewhat) fairly compared: the average miss 6 to 36 months after each forecast, the error (mean absolute error) over three stretches of Fed history, and the error over windows where the sources overlap.

A few things stand out:

• Obviously, every source gets worse the further out it looks. A year out, the typical miss is between about half a point and a point; three years out, it’s about two points.
• Options-implied SOFR has the smallest misses overall, 0.44 points a year out, but it only covers forecasts made since March 2023. Over those same dates, the other three sources did better a year out.
• Compared over the same dates, the FOMC’s median projection does best: 0.24 points a year out since March 2023, the only window all four sources share. Not bad for a projection the Fed doesn’t call a forecast.⁶
• The professional forecasters look worst over their full history, back to 1982, but have done well recently, second only to the FOMC since 2023.

Footnotes

1. Toph Tucker, “Examples of bitemporal charts”, Observable.

2. The projections are in the FOMC’s Summary of Economic Projections for 16 March 2022, table 1 (PDF). The Fed’s FOMC meeting calendar links to the projections from each recent meeting.

3. The R notebook and the Python notebook.

4. The repo, EconomiCurtis/hairy-chart on GitHub; its cleaned data, data/; and its scripts, scripts/.

5. The Forecast Evaluation sections of the R notebook and the Python notebook.

6. The Fed’s FAQ on the projections calls the growth, unemployment and inflation numbers forecasts, but the rate path a projection of “the appropriate level of the target federal funds rate”: the path each policymaker judges most consistent with the Fed’s mandate.