library(tidyverse)
library(patchwork)
library(scales)
library(knitr)

1. Background: What Is the Yield Curve?

A yield is the annual return an investor earns on a bond. The yield curve plots those yields against the bonds’ maturities (time until repayment — e.g., 3 months, 2 years, 10 years).

Under normal conditions investors demand higher yields for longer maturities — compensation for tying up money longer. The curve slopes upward.

An inverted yield curve occurs when short-term yields exceed long-term yields — the curve slopes downward. Economists watch the 10-year minus 2-year Treasury spread (10Y–2Y) most closely. When this spread goes negative, the curve is inverted.

2. Why Does Inversion Signal Recession?

The intuition has three channels:

Channel 1 — Market expectations.
Long-term yields reflect what markets expect short-term rates to average over many years. If investors expect the Fed to cut rates (usually in response to a weakening economy), future short-term rates will be low — pulling long yields below current short yields.

Channel 2 — Bank profitability.
Banks borrow short and lend long. Inversion squeezes that margin, reducing incentive to make loans. Less credit → slower growth.

Channel 3 — Confidence signal.
Inversion signals that many smart-money bond investors collectively expect economic trouble ahead.

3. Building Our Dataset

We’ll work with simulated-but-historically-calibrated data for the 10Y–2Y spread alongside NBER recession indicators. The values below mirror real Federal Reserve data closely enough to teach the concepts accurately.

# --- Historical 10Y-2Y spread (approximate annual averages, 1977–2024) --------
# Negative = inverted. Source: calibrated from FRED data.

spread_data <- tribble(
  ~year, ~spread_pct, ~recession_started,
  1977,  0.60,  FALSE,
  1978,  0.00,  FALSE,
  1979, -0.80,  TRUE,   # → 1980 recession
  1980, -1.50,  FALSE,
  1981, -2.40,  TRUE,   # → 1981-82 recession
  1982,  0.90,  FALSE,
  1983,  2.10,  FALSE,
  1984,  1.30,  FALSE,
  1985,  2.00,  FALSE,
  1986,  1.80,  FALSE,
  1987,  0.80,  FALSE,
  1988,  0.10,  FALSE,
  1989, -0.40,  TRUE,   # → 1990-91 recession
  1990,  0.30,  FALSE,
  1991,  1.60,  FALSE,
  1992,  2.90,  FALSE,
  1993,  2.70,  FALSE,
  1994,  0.80,  FALSE,
  1995,  0.70,  FALSE,
  1996,  0.60,  FALSE,
  1997,  0.60,  FALSE,
  1998,  0.60,  FALSE,
  1999,  0.20,  FALSE,
  2000, -0.50,  TRUE,   # → 2001 recession
  2001,  2.30,  FALSE,
  2002,  2.80,  FALSE,
  2003,  2.60,  FALSE,
  2004,  1.60,  FALSE,
  2005,  0.30,  FALSE,
  2006, -0.10,  TRUE,   # → 2007-09 recession
  2007,  0.50,  FALSE,
  2008,  1.50,  FALSE,
  2009,  2.50,  FALSE,
  2010,  2.50,  FALSE,
  2011,  1.60,  FALSE,
  2012,  1.40,  FALSE,
  2013,  2.30,  FALSE,
  2014,  2.10,  FALSE,
  2015,  1.50,  FALSE,
  2016,  1.20,  FALSE,
  2017,  1.00,  FALSE,
  2018,  0.20,  FALSE,
  2019, -0.20,  TRUE,   # → 2020 COVID recession
  2020,  0.80,  FALSE,
  2021,  1.20,  FALSE,
  2022, -0.50,  TRUE,   # → predicted recession that did NOT materialize
  2023, -1.00,  FALSE,  # deeply inverted — no recession as of writing
  2024, -0.30,  FALSE
)

glimpse(spread_data)
## Rows: 48
## Columns: 3
## $ year              <dbl> 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985…
## $ spread_pct        <dbl> 0.6, 0.0, -0.8, -1.5, -2.4, 0.9, 2.1, 1.3, 2.0, 1.8,…
## $ recession_started <lgl> FALSE, FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE…
# Add useful derived columns
spread_data <- spread_data %>%
  mutate(
    inverted     = spread_pct < 0,
    spread_label = if_else(inverted, "Inverted", "Normal"),
    decade       = paste0(floor(year / 10) * 10, "s")
  )

# Quick look at the inverted years
spread_data %>%
  filter(inverted) %>%
  select(year, spread_pct, recession_started) %>%
  kable(
    col.names = c("Year", "10Y–2Y Spread (%)", "Recession Followed?"),
    caption   = "Years with Inverted Yield Curve (10Y–2Y < 0)"
  )
Years with Inverted Yield Curve (10Y–2Y < 0)
Year 10Y–2Y Spread (%) Recession Followed?
1979 -0.8 TRUE
1980 -1.5 FALSE
1981 -2.4 TRUE
1989 -0.4 TRUE
2000 -0.5 TRUE
2006 -0.1 TRUE
2019 -0.2 TRUE
2022 -0.5 TRUE
2023 -1.0 FALSE
2024 -0.3 FALSE

4. Visualizing the Spread Over Time

# Shade recession periods
recession_bands <- tribble(
  ~start, ~end,
  1980,   1980,
  1981,   1982,
  1990,   1991,
  2001,   2001,
  2007,   2009,
  2020,   2020
)

ggplot(spread_data, aes(x = year, y = spread_pct)) +
  # Shade recession years
  geom_rect(
    data        = recession_bands,
    aes(xmin = start - 0.5, xmax = end + 0.5, ymin = -Inf, ymax = Inf),
    inherit.aes = FALSE,
    fill        = "gray80", alpha = 0.5
  ) +
  # Zero line
  geom_hline(yintercept = 0, linetype = "dashed", color = "black", linewidth = 0.7) +
  # Spread bars, colored by sign
  geom_col(aes(fill = inverted), width = 0.7, alpha = 0.85) +
  scale_fill_manual(
    values = c("FALSE" = "#42A5F5", "TRUE" = "#EF5350"),
    labels = c("FALSE" = "Normal (positive)", "TRUE" = "Inverted (negative)")
  ) +
  scale_x_continuous(breaks = seq(1977, 2024, by = 4)) +
  scale_y_continuous(labels = label_number(suffix = "%")) +
  labs(
    title    = "10-Year minus 2-Year Treasury Spread, 1977–2024",
    subtitle = "Gray bands = NBER recessions  |  Red bars = yield curve inversion",
    x        = NULL,
    y        = "Spread (percentage points)",
    fill     = "Curve shape"
  ) +
  theme_minimal(base_size = 12) +
  theme(
    legend.position  = "bottom",
    panel.grid.minor = element_blank()
  )

Reading the chart: Every gray recession band was preceded by red (inverted) bars — but notice 2022–2023: deep red bars with no recession band following.

5. The Track Record: When It Predicted Correctly

outcomes <- tribble(
  ~episode,           ~inversion_years, ~recession,       ~lag_months, ~called_correctly,
  "1979–1981",        "1979, 1980, 1981", "1980 & 1981–82",  6,   TRUE,
  "1988–1989",        "1989",             "1990–91",         12,  TRUE,
  "1998–2000",        "2000",             "2001",             8,  TRUE,
  "2005–2006",        "2006",             "2007–09",         16,  TRUE,
  "2019",             "2019",             "2020 (COVID)",     8,  TRUE,
  "2022–2024 (ongoing)","2022, 2023, 2024","None yet",       NA,  FALSE
)

outcomes %>%
  kable(
    col.names = c("Episode", "Inversion Year(s)", "Recession",
                  "Lag (months)", "Recession Followed?"),
    caption   = "Inverted Yield Curve Episodes Since 1979"
  )
Inverted Yield Curve Episodes Since 1979
Episode Inversion Year(s) Recession Lag (months) Recession Followed?
1979–1981 1979, 1980, 1981 1980 & 1981–82 6 TRUE
1988–1989 1989 1990–91 12 TRUE
1998–2000 2000 2001 8 TRUE
2005–2006 2006 2007–09 16 TRUE
2019 2019 2020 (COVID) 8 TRUE
2022–2024 (ongoing) 2022, 2023, 2024 None yet NA FALSE

Five out of six inversion episodes (through 2021) correctly preceded a recession. The average lag between inversion and recession onset is roughly 6–16 months — which is why economists say the yield curve is a leading indicator, not an immediate alarm.

6. When It Hasn’t Worked: False Positives and Misses

near_misses <- tribble(
  ~year_range,  ~situation,                               ~outcome,
  "1966",       "Brief inversion; Fed pre-empted with hikes", "No recession",
  "1998",       "Brief inversion during LTCM crisis",        "Recession delayed to 2001",
  "2022–present","Deep inversion for 2+ years",              "No recession yet (as of 2024)"
)

kable(near_misses,
      col.names = c("Period", "Context", "Outcome"),
      caption   = "Cases Where Inversion Did Not Quickly Produce Recession")
Cases Where Inversion Did Not Quickly Produce Recession
Period Context Outcome
1966 Brief inversion; Fed pre-empted with hikes No recession
1998 Brief inversion during LTCM crisis Recession delayed to 2001
2022–present Deep inversion for 2+ years No recession yet (as of 2024)

Why Might It Fail?

  • Fed intervention: Quantitative Easing (QE) artificially depressed long-term yields post-2008, making the spread hard to interpret.
  • Global capital flows: Foreign demand for US Treasuries (a safe haven) keeps long yields compressed, independent of domestic conditions.
  • Structural changes: The 2022–2024 inversion coincided with the fastest rate hike cycle in 40 years. Labor markets stayed strong; the economy avoided recession — so far — suggesting the signal may have a longer or uncertain lag this cycle.
  • COVID distortions: Massive fiscal stimulus and pent-up demand created unusual economic dynamics that historically calibrated models didn’t anticipate.

7. Statistical Deep-Dive: Distributions and Patterns

7a. Spread Distribution by Curve Shape

ggplot(spread_data, aes(x = spread_pct, fill = spread_label)) +
  geom_histogram(binwidth = 0.25, color = "white", alpha = 0.85) +
  geom_vline(xintercept = 0, linetype = "dashed", linewidth = 0.8) +
  scale_fill_manual(values = c("Normal" = "#42A5F5", "Inverted" = "#EF5350")) +
  labs(
    title = "Distribution of 10Y–2Y Spread (1977–2024)",
    x     = "Spread (percentage points)",
    y     = "Count of years",
    fill  = NULL
  ) +
  theme_minimal(base_size = 12) +
  theme(legend.position = "bottom")

7b. Summary Statistics

spread_data %>%
  group_by(spread_label) %>%
  summarise(
    n       = n(),
    mean    = mean(spread_pct),
    median  = median(spread_pct),
    sd      = sd(spread_pct),
    min     = min(spread_pct),
    max     = max(spread_pct),
    .groups = "drop"
  ) %>%
  mutate(across(where(is.numeric), ~ round(.x, 2))) %>%
  kable(
    col.names = c("Curve Shape", "N Years", "Mean", "Median", "SD", "Min", "Max"),
    caption   = "Summary Statistics: Spread by Curve Shape"
  )
Summary Statistics: Spread by Curve Shape
Curve Shape N Years Mean Median SD Min Max
Inverted 10 -0.77 -0.50 0.71 -2.4 -0.1
Normal 38 1.33 1.25 0.86 0.0 2.9

7c. Recession Rate Conditional on Inversion

# Within 2 years of inversion, did a recession start?
# We'll score each inverted year by whether a recession began that year or next.
spread_data <- spread_data %>%
  mutate(
    recession_next2 = recession_started |
      lead(recession_started, 1, default = FALSE)
  )

spread_data %>%
  group_by(inverted) %>%
  summarise(
    n_years         = n(),
    recession_count = sum(recession_next2),
    recession_rate  = mean(recession_next2),
    .groups         = "drop"
  ) %>%
  mutate(
    recession_rate = percent(recession_rate, accuracy = 1),
    inverted       = if_else(inverted, "Yes (inverted)", "No (normal)")
  ) %>%
  kable(
    col.names = c("Yield Curve Inverted?", "N Years",
                  "Recession Within 2 Yrs", "Rate"),
    caption   = "Recession Probability Conditional on Yield Curve Shape"
  )
Recession Probability Conditional on Yield Curve Shape
Yield Curve Inverted? N Years Recession Within 2 Yrs Rate
No (normal) 38 6 16%
Yes (inverted) 10 8 80%

The conditional rates tell the core story: recession is much more common when the curve is inverted than when it is not — but inversion is neither necessary nor sufficient on its own.

8. Decade-by-Decade Pattern

spread_data %>%
  group_by(decade) %>%
  summarise(
    avg_spread    = mean(spread_pct),
    pct_inverted  = mean(inverted) * 100,
    .groups       = "drop"
  ) %>%
  pivot_longer(cols = c(avg_spread, pct_inverted),
               names_to  = "metric",
               values_to = "value") %>%
  mutate(metric = recode(metric,
    "avg_spread"   = "Average Spread (%pts)",
    "pct_inverted" = "% of Years Inverted")) %>%
  ggplot(aes(x = decade, y = value, fill = decade)) +
    geom_col(show.legend = FALSE) +
    facet_wrap(~ metric, scales = "free_y") +
    scale_fill_brewer(palette = "Blues") +
    labs(
      title = "Yield Curve Characteristics by Decade",
      x     = NULL, y = NULL
    ) +
    theme_minimal(base_size = 12) +
    theme(panel.grid.minor = element_blank())

9. Key Takeaways

Claim Evidence
Inversion reliably precedes recession 5 of 6 modern episodes produced a recession
It is a leading indicator, not immediate Lag ranges from ~6 to 18+ months
The signal is probabilistic, not deterministic ~40–60% of inverted years → recession within 2 yrs
2022–2024 is the most notable exception so far Deepest inversion in 40 years with no recession yet
External forces can distort the signal QE, global capital flows, fiscal stimulus all matter

10. Exercises

  1. Compute the lead time. For each successful inversion episode in the outcomes table, calculate the average number of months between the start of inversion and the start of recession. What is the mean and standard deviation?

  2. Filter and visualize. Using spread_data, filter to only years where inverted == TRUE and create a bar chart of spread_pct colored by whether recession_started is TRUE or FALSE. What pattern do you see?

  3. Running average. Use mutate() and lag() to compute a 3-year rolling average of spread_pct. Plot the original series and the smoothed series together using pivot_longer() and ggplot2. Does the smoothed version still dip below zero before recessions?

  4. Contingency table. Use table() or count() to build a 2×2 contingency table of inverted × recession_started. Calculate the odds ratio. What does it tell you about the association between inversion and recession?

  5. Research question. The 2022–2024 inversion is ongoing. Using what you know about the lag, when would you expect a recession to begin if the historical relationship holds? Write 2–3 sentences using your calculations to support your answer.

Data calibrated from FRED (Federal Reserve Bank of St. Louis). Recession dates per NBER Business Cycle Dating Committee. This document is for educational purposes.