Case Study: Does the Lopez-Salido, Stein & Zakrajsek (2017) Sentiment Signal Speak to the 2020-2022 Cycle?

Case Study: Does the Lopez-Salido, Stein & Zakrajsek (2017) Sentiment Signal Speak to the 2020-2022 Cycle?#

Introduction#

What is this notebook doing? It takes the Lopez-Salido, Stein & Zakrajšek (2017, “LSZ”) credit-market sentiment first stage, estimated on 1929-2015, and applies it, unchanged, to the COVID cycle. The 2020-2021 period looked like the configuration LSZ call elevated sentiment. Right after the Fed’s March-2020 backstop, the Baa-Treasury spread compressed sharply and high-yield issuance surged. Their mechanism says that froth predicts a subsequent widening of spreads (and a slowdown), as credit conditions mean-revert. The question this notebook asks is simple: pointed at 2020-2022, which way does the signal lean, and does it match what happened?

#

Section

What it shows

1

The LSZ first stage on 1929-2015

The replication of the sentiment engine seen in previous notebooks

2

Coverage of the froth variable

How far the spliced high-yield share now extends

3

Out-of-sample probe, 2020-2022

Full-sentiment vs. spread-only prediction of \(\Delta s_t\), scored against realized spread changes

4

What we can and cannot conclude

Splice, sample-size, and generated-regressor caveats

The verdict is computed below, not asserted here. With a three-year window this is an illustrative probe, not a formal test, and the caveats in Section 4 bound how much weight it can carry.

import sys
from pathlib import Path

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

sys.path.insert(0, str(Path.cwd().parent / "src"))
import plot_style as ps
import replicate_table_2 as t2
from settings import config

OUTPUT_DIR = Path(config("OUTPUT_DIR"))

# Annual panel (Baa spread), 1929 through the extension endpoint. Same builder
# the Table II replication uses, so the case study inherits the exact series
# and lag conventions.
df = t2.build_panel(spread_col="BAA_Treasury_spread")

hy = df["ln_hys"].dropna()
print(f"Panel years : {int(df.index.min())}-{int(df.index.max())}")
print(
    f"ln_hys span : {int(hy.index.min())}-{int(hy.index.max())}  ({hy.notna().sum()} years observed)"
)

Panel years : 1929-2025
ln_hys span : 1929-2025  (96 years observed)

1. The LSZ First Stage, Replicated on 1929-2015#

Table II’s first stage forecasts the change in the credit spread from the twice-lagged sentiment:

\[\Delta s_t = a_0 + a_1 \ln(\mathrm{HYS})_{t-2} + a_2\, s_{t-2} + u_t.\]

The LSZ signs are \(a_1 > 0\) (a high past issuance share predicts the spread widening) and \(a_2 < 0\) (a wide spread mean-reverts). We fit it on the replication sample and read the coefficients off, before applying them out of sample.

res = t2.run_table_2(df)  # fit on the 1929-2015 replication window
aux = res["aux_spread"]
c = aux.params

print("First-stage  Δs_t = a0 + a1·lnHYS_{t-2} + a2·s_{t-2}   (fit 1929-2015)")
for k in ["const", "ln_hys_lag2", "spread_lag2"]:
    print(f"  {k:>12}: {c[k]:+.4f}   (p = {aux.pvalues[k]:.3f})")

s1 = (
    "high issuance share predicts widening (LSZ sign)"
    if c["ln_hys_lag2"] > 0
    else "UNEXPECTED sign"
)
s2 = (
    "wide spread mean-reverts (LSZ sign)" if c["spread_lag2"] < 0 else "UNEXPECTED sign"
)
print(f"\n  a1 (froth)  {c['ln_hys_lag2']:+.3f}  ->  {s1}")
print(f"  a2 (level)  {c['spread_lag2']:+.3f}  ->  {s2}")

First-stage  Δs_t = a0 + a1·lnHYS_{t-2} + a2·s_{t-2}   (fit 1929-2015)
         const: +0.8125   (p = 0.000)
   ln_hys_lag2: +0.1474   (p = 0.000)
   spread_lag2: -0.2448   (p = 0.000)

  a1 (froth)  +0.147  ->  high issuance share predicts widening (LSZ sign)
  a2 (level)  -0.245  ->  wide spread mean-reverts (LSZ sign)

Both signs reproduce the paper’s mechanism: the sentiment engine works on the historical sample. The rest of the notebook holds this 1929-2015 fit fixed and asks what it says about years it never saw.

2. The Froth Variable Now Reaches Past 2008#

The hand-transcribed Greenwood-Hanson high-yield share ends in 2008. We reconstructed the share from Mergent FISD (via WRDS) for later years and spliced it onto the historical series, so the series t2.build_panel reads is now continuous through the recent past. That extension is precisely what lets us form the full two-ingredient sentiment prediction for the COVID window rather than the spread-reversion leg alone.

last_hys = int(df["ln_hys"].dropna().index.max())
recent = df.loc[2016:2023, ["ln_hys_lag2", "spread_lag2", "d_spread", "dy"]].round(3)
print(recent)

# Predicting Δs_t needs lnHYS_{t-2}; so the full signal is available for year t
# whenever the froth variable exists at t-2.
covid_years = [y for y in (2020, 2021, 2022) if y in df.index]
full_ok = [yr for yr in covid_years if pd.notna(df.loc[yr, "ln_hys_lag2"])]
print(f"\nLast year with a high-yield-share observation: {last_hys}")
print(f"COVID years with a full-sentiment prediction available: {full_ok or 'none'}")

      ln_hys_lag2  spread_lag2  d_spread     dy
year                                           
2016       -0.884         2.53     -0.88  1.031
2017       -1.267         3.22     -0.52  1.737
2018       -1.306         2.34      0.48  2.333
2019       -1.224         1.82     -0.28  2.030
2020       -1.612         2.30      0.21 -2.504
2021       -1.363         2.02     -0.40  5.771
2022       -1.581         2.23      0.14  1.939
2023       -1.220         1.83     -0.35  2.077

Last year with a high-yield-share observation: 2025
COVID years with a full-sentiment prediction available: [2020, 2021, 2022]

3. Out-of-Sample Probe: 2020-2022#

We take the first-stage coefficients fit on 1929-2015 and, without re-fitting, form the predicted spread change for each COVID year:

\[\widehat{\Delta s_t} = a_0 + a_1 \ln(\mathrm{HYS})_{t-2} + a_2\, s_{t-2}.\]

We report two versions side by side: the full sentiment prediction (both ingredients) and the spread-reversion leg only (\(a_0 + a_2 s_{t-2}\)). The test is directional: does the sign of the predicted change match the sign of the realized change?

def predict_dspread(year, coeffs, use_froth):
    # Predicted change in the spread from the fixed 1929-2015 first stage.
    # use_froth=True adds the lnHYS_{t-2} term; if that value is missing, the
    # full-sentiment prediction is undefined (NaN) for the year.
    pred = coeffs["const"] + coeffs["spread_lag2"] * df.loc[year, "spread_lag2"]
    if use_froth:
        h = df.loc[year, "ln_hys_lag2"]
        if pd.isna(h):
            return np.nan
        pred = pred + coeffs["ln_hys_lag2"] * h
    return pred


rows = []
for yr in covid_years:
    rows.append(
        {
            "year": yr,
            "s_(t-2)": round(df.loc[yr, "spread_lag2"], 2),
            "lnHYS_(t-2)": (
                round(df.loc[yr, "ln_hys_lag2"], 3)
                if pd.notna(df.loc[yr, "ln_hys_lag2"])
                else np.nan
            ),
            "pred_full": round(predict_dspread(yr, c, True), 3)
            if pd.notna(predict_dspread(yr, c, True))
            else np.nan,
            "pred_spread_only": round(predict_dspread(yr, c, False), 3),
            "actual_dS": round(df.loc[yr, "d_spread"], 3),
        }
    )
scorecard = pd.DataFrame(rows).set_index("year")
print(scorecard)


def hit_rate(col):
    ok = n = 0
    for yr in covid_years:
        p, a = scorecard.loc[yr, col], scorecard.loc[yr, "actual_dS"]
        if pd.notna(p) and pd.notna(a):
            n += 1
            ok += int(np.sign(p) == np.sign(a))
    return ok, n


print()
for col, label in [
    ("pred_full", "full sentiment (froth + reversion)"),
    ("pred_spread_only", "spread-reversion leg only"),
]:
    ok, n = hit_rate(col)
    verdict = (
        f"correct direction in {ok}/{n} years"
        if n
        else "no usable years (froth variable missing in window)"
    )
    print(f"  {label:>34}: {verdict}")

      s_(t-2)  lnHYS_(t-2)  pred_full  pred_spread_only  actual_dS
year                                                              
2020     2.30       -1.612      0.012             0.249       0.21
2021     2.02       -1.363      0.117             0.318      -0.40
2022     2.23       -1.581      0.034             0.267       0.14

  full sentiment (froth + reversion): correct direction in 2/3 years
           spread-reversion leg only: correct direction in 2/3 years

How to read the scorecard?

Each row scores one COVID-window year by comparing a predicted change in the Baa-Treasury spread against what actually happened, and a row “hits” when the two share a sign: a predicted widening (\(\widehat{\Delta s_t}>0\)) paired with a realized widening, or a predicted narrowing paired with a realized narrowing. Signs are the whole test here, because the LSZ mechanism is a sign prediction - elevated sentiment two years earlier should show up as spreads moving wider (credit getting more expensive), which is the leading edge of the slowdown the paper documents. The size of the predicted number is not meant to match the size of the realized one; only its direction is.

Walking through the three rows:

  • 2020 - hit. The model predicts a small widening (pred_full = +0.012) and the spread does widen (actual_dS = +0.21). The predicted move is an order of magnitude smaller than what happened, which is expected: the pandemic shock, not a two-year-old sentiment reversal, is what actually moved spreads in March 2020.

  • 2021 - miss. The model predicts widening (+0.117) but the spread narrows sharply (-0.40) as continued Fed support and the reopening rally overpower whatever mean reversion the lagged sentiment reading implied.

  • 2022 - hit. Both predicted (+0.034) and realized (+0.14) changes are positive, coinciding with the start of the Fed’s 2022 tightening cycle.

The contrast between the two prediction columns is the actual point of the exercise, more than the hit count itself. pred_spread_only drops the froth term and only mean-reverts the lagged spread level (\(a_0 + a_2\, s_{t-2}\)). Because \(s_{t-2}\) sits below its long-run average in every COVID year (spreads had been compressed since 2010), this leg predicts widening almost mechanically, regardless of how hot issuance actually was. pred_full adds back \(a_1 \ln(\mathrm{HYS})_{t-2}\), and in this window it reduces the predicted move every single year. So the froth term is doing real work on the magnitude of the prediction, despite the identical 2/3 hit rate.

That the two columns tie on hit rate is itself informative: it says three years is too short a window for the froth ingredient to visibly earn its keep over the spread-reversion leg alone. That is the caveat that belongs here: three years cannot carry statistical weight. This is an illustrative direction check, not the formal out-of-sample test a longer sample would support.

ps.set_paper_style()
fig, ax = plt.subplots(figsize=(8.5, 4.5))
x = np.arange(len(covid_years))
w = 0.27
ax.bar(
    x - w,
    scorecard["pred_full"],
    w,
    label=r"Predicted $\Delta s$ (full sentiment)",
    color="#1f4e79",
)
ax.bar(
    x,
    scorecard["pred_spread_only"],
    w,
    label=r"Predicted $\Delta s$ (spread leg only)",
    color="#8faadc",
)
ax.bar(
    x + w,
    scorecard["actual_dS"],
    w,
    label=r"Actual $\Delta s$",
    color=ps.HIGHLIGHT_COLOR,
)
ax.axhline(0, color="grey", lw=0.8)
ax.set_xticks(x)
ax.set_xticklabels([str(y) for y in covid_years])
ax.set_ylabel("Change in Baa-Treasury spread (pp)")
ax.set_title(
    "LSZ Sentiment Out-of-Sample: Predicted vs. Realized " r"$\Delta s$, 2020-2022"
)
ps.style_axes(ax)
ax.legend()
fig.tight_layout()

OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
fig.savefig(OUTPUT_DIR / "case_study_covid_oos.pdf")
plt.show()
../../../_images/c554506723e1b0b4f078de57e09d69b14465165884c0fe0c923143deeeb2454f.png

4. What We Can and Cannot Conclude#

Four honest caveats bound the reading above:

  1. The splice is not seamless. The froth values in the COVID window come from the FISD reconstruction, whose construction (Moody’s-rated denominator, coverage starting in the early 1980s) differs from the pre-2009 transcribed series the first stage was largely estimated on. The ingredient we feed the model out of sample is measured a little differently from the one it learned on.

  2. Three years is illustrative, not inferential. A direction check on 2020-2022 cannot distinguish skill from luck; it can only show which way the signal leaned.

  3. Generated-regressor uncertainty. The prediction plugs in first-stage fitted coefficients; the standard two-step “plug-in” procedure used here does not propagate their sampling error, so any apparent precision is overstated.

  4. The first stage is held fixed at 1929-2015. This is a true out-of-sample application; re-fitting through the window would change the coefficients and is a different (in-sample) exercise.

Summary#

We re-fit the LSZ sentiment first stage on 1929-2015, confirm that the post-2008 FISD/WRDS reconstruction now extends the high-yield share into the COVID window, and use the fixed historical fit to form an out-of-sample prediction of the 2020-2022 spread changes. The scorecard in Section 3 reports the realized hit rate for the full-sentiment signal and for the spread-only leg — both correct in 2 of 3 years, with the froth term visibly shrinking the predicted move without changing which years hit or miss — and the chart shows the predictions against reality. Section 4 lays out why that record should be read cautiously: the froth-series splice, the three-year sample, and the generated-regressor uncertainty baked into the underlying coefficients. With only three years and a spliced froth series, the result is an honest directional probe rather than a formal test.