Figure 1: Model solution
This figure shows the model’s solution along the \(\kappa_{t}\) (the term premium factor)
dimension (horizontal axis) for three different values of \(\rho\), the parameter capturing the
tightness of the incentive constraint. We set \(r_{t}=\overline{r}\). The upper-left panel
plots the term premium (\(TP_t\)). The
upper-right panel shows banks’ marginal value of wealth, or “Tobin’s Q”
(\(\psi_t\)). The middle-left panel
displays the expected return on wealth (\(\mu_{n,t}\)). The middle-right panel shows
banks’ leverage on loans (\(\alpha_t\)). The bottom-left panel shows
expected loan growth (\(\mu_{L,t}\)).
The bottom-right panel shows the diffusion component of loan growth
associated with \(\kappa_{t}\) shocks
(\(\sigma_{L\kappa,t}\)).
This figure shows the model's solution along the κ_t (the term premium factor) dimension (horizontal axis) for three different values of ρ, the parameter capturing the tightness of the incentive constraint. We set r_t at its unconditional mean. The figure contains six panels arranged in a 3x2 grid. The upper-left panel plots the term premium (TP_t), showing how it varies inversely with κ_t - more negative values of κ_t correspond to higher term premiums. The upper-right panel shows banks' marginal value of wealth, or "Tobin's Q" (ψ_t), which increases when the term premium is higher. The middle-left panel displays the expected return on wealth (μ_n,t), which also increases with the term premium. The middle-right panel shows banks' leverage on loans (α_t), which rises with the term premium. The bottom-left panel shows expected loan growth (μ_L,t), demonstrating that banks expect to expand lending when the term premium is higher. The bottom-right panel shows the diffusion component of loan growth associated with κ_t shocks (σ_Lκ,t). Three lines in each panel represent different values of ρ (baseline, higher constraint, lower constraint), illustrating that banks with lower ρ (higher leverage) exhibit stronger responses to term premium changes.
Figure 2: Impulse responses to a κt shock in the
model
This figure shows the model’s impulse-responses to a one
standard deviation shock to \(\kappa_{t}\) in quarter 11. The shock leads
to an increase in the term premium of approximately 50 bps (annualized),
corresponding to one unconditional standard deviation of \(\kappa_{t}\). The red-dotted and
yellow-dashed lines represent model responses under different values of
the incentive constraint parameter (\(\rho\)). The upper-left panel shows the
dynamics of the term premium (\(TP\))
following the shock. The upper-middle panel shows the evolution of
banks’ loans (\(L_{t}\)). The
upper-right panel shows the evolution of banks’ equity (\(n_{t})\). The lower-left panel shows banks’
leverage (\(\alpha\)). The lower-middle
panel shows the expected changes in banks’ marginal value of wealth, or
“Tobin’s Q,” (\(E_t[\text{d}\psi/\psi\)]). The lower-right
panel shows banks’ expected change in wealth (\(E_t[\text{d}n/n\)]).
This figure shows the model's impulse responses to a one standard deviation shock to κ_t in quarter 11. The shock leads to an increase in the term premium of approximately 50 basis points (annualized), corresponding to one unconditional standard deviation of κ_t. The figure contains six panels showing dynamics over 50 quarters. The upper-left panel shows the dynamics of the term premium (TP) following the shock, which jumps up and then gradually mean-reverts. The upper-middle panel shows the evolution of banks' loans (L_t), which initially decline due to mark-to-market losses but then recover and increase above steady-state levels. The upper-right panel shows the evolution of banks' equity (n_t), which exhibits a similar pattern to loans. The lower-left panel shows banks' leverage (α), which increases following the shock because Tobin's Q rises. The lower-middle panel shows the expected changes in banks' marginal value of wealth, or "Tobin's Q," (E_t[dψ/ψ]), which becomes negative as ψ is expected to mean-revert after jumping up. The lower-right panel shows banks' expected change in wealth (E_t[dn/n]), which increases due to higher term premium and leverage. The red-dotted and yellow-dashed lines represent model responses under different values of the incentive constraint parameter (ρ), showing that more leveraged banks (lower ρ) display stronger responses.
Figure 3: Treasury yields and the term premium during Taper Tantrum
This figure depicts the sharp and sustained rise in the 5-year
Treasury yield and in the 5-year term premium during the Taper Tantrum
episode following former Chair Ben Bernanke’s remarks on May 22, 2013,
in which he signaled the Federal Reserve’s intention to begin tapering
asset purchases under its QE program. The date of the remarks is marked
by the dashed vertical line. Sources: The Treasury yields series is
Federal Reserve Economic Data (FRED) series DGS5. The 5-year Kim-Wright
term premium series is FRED series THREEFYTP5.
This figure depicts the sharp and sustained rise in the 5-year Treasury yield and in the 5-year term premium during the Taper Tantrum episode following former Chair Ben Bernanke's remarks on May 22, 2013, in which he signaled the Federal Reserve's intention to begin tapering asset purchases under its QE program. The figure is a line chart showing two time series from January 2013 to December 2013. The blue line shows the 5-year Treasury yield, which increased from approximately 0.7% in early May 2013 to around 1.6% by July 2013. The red line shows the 5-year term premium from the Kim-Wright model, which increased from approximately -0.5% to 0.5% over the same period. A vertical dashed line marks May 22, 2013, the date of Chair Bernanke's congressional testimony. The figure clearly illustrates the sudden and persistent increase in both yields and term premium following the announcement.
Figure A-1: Bank’s marginal value of wealth and leverage across bank incentive
constraints
This figure shows the solution for bank’s marginal value of
wealth (or Tobin’s Q), \(\psi(\overline{r},\overline{\kappa})\), and
bank leverage, \(\alpha _{t}=x_{t}^{\left(
\tau \right) }P_{t}^{\left( \tau \right) }/n_{t}\), for different
values of the incentive constraint parameter, \(\rho\).
This appendix figure shows the solution for bank's marginal value of wealth (or Tobin's Q), ψ(r̄,κ̄), and bank leverage, α_t = x_t^(τ) P_t^(τ) / n_t, for different values of the incentive constraint parameter, ρ, evaluated at the unconditional means of the state variables. The figure has two panels. The left panel plots Tobin's Q (ψ) on the vertical axis against ρ on the horizontal axis, showing that ψ increases with ρ - banks that derive higher benefits from diverting assets have higher marginal valuations of wealth. The right panel plots bank leverage (α) on the vertical axis against ρ on the horizontal axis, showing that leverage decreases with ρ - banks facing tighter constraints (higher ρ) hold less leveraged positions. This figure illustrates the theoretical relationship between the tightness of the financing constraint and bank leverage that underpins the cross-sectional predictions of the model.
Figure A-2: Expected lending growth components, μn, t,
Et[dψ/ψ],
and covt[dψ/ψ, dn/n]
This figure shows the model’s solution for the components of
expected lending growth in Equation (11) across the
\(\kappa\) dimension. The top panels
show the solution for different values of \(\rho\). The bottom panels show the
solutions for different levels of the interest rate. \(\psi(\overline{r},\overline{\kappa})\) and
\(\alpha _{t}=x_{t}^{\left( \tau \right)
}P_{t}^{\left( \tau \right) }/n_{t}\) for different levels of
\(\rho\).
This figure decomposes expected lending growth into its key components from equation (ref:mu_L) in the model: μ_n,t (the expected return on wealth), E_t[dψ/ψ] (the expected growth rate of the marginal value of wealth), and cov_t[dψ/ψ, dn/n] (the covariance between the marginal value of wealth and wealth growth). The figure contains multiple panels arranged in two rows. The top panels show the components across the κ dimension for different values of ρ, while the bottom panels show the components across the κ dimension for different levels of the short rate r_t. The decomposition illustrates how each component contributes to overall expected lending growth and demonstrates that the positive effect of expected return on wealth (which increases with term premium) dominates the negative effect of expected change in ψ (which decreases with term premium due to mean reversion), resulting in overall positive expected lending growth when term premium rises.
Figure A-3: Model solution for different levels of rt
This figure shows the model’s solution across different values
of \(\kappa_{t}\) (the term premium
factor) dimension (horizontal axis) for three levels of \(r_{t}\) (the short rate). The solid line is
when \(r_{t}\) is at its unconditional
mean, the dashed (dotted) line is when \(r_{t}\) is two standard deviations above
(below) its mean. The upper-left panel shows the term premium (\(TP_t\)). The upper-right panel shows banks’
marginal value of wealth, or “Tobin’s Q” (\(\psi_t\)). The middle-left panel shows the
expected return on wealth (\(\mu_{n,t}\)). The middle-right panel shows
banks’ leverage on loans (\(\alpha_t\)). The bottom-left panel shows
the expected loan growth (\(\mu_{L,t}\)). The bottom-right panel shows
the diffusion component of loan growth associated with \(\kappa_{t}\) shocks (\(\sigma_{L\kappa,t}\)).
This figure shows the model's solution across different values of κ_t (the term premium factor) on the horizontal axis for three levels of r_t (the short rate). The solid line represents results when r_t is at its unconditional mean, the dashed line is when r_t is two standard deviations above its mean, and the dotted line is when r_t is two standard deviations below its mean. The figure has six panels in a 3x2 arrangement, identical in structure to Figure 1 in the main text: upper-left shows term premium (TP_t), upper-right shows Tobin's Q (ψ_t), middle-left shows expected return on wealth (μ_n,t), middle-right shows leverage (α_t), bottom-left shows expected loan growth (μ_L,t), and bottom-right shows the diffusion component (σ_Lκ,t). This figure demonstrates how the model's predictions vary across different interest rate environments, showing that the qualitative results are robust to different levels of the short rate.
Figure OA-1: Term Premium Shocks and Placebo Tests
(A) Term Premium vs. Term Premium Shocks
(B) Term Premium Level During Placebo Tests
Panel A shows (a) the 5-year term premium series from the term
structure model of and (b) high-frequency term premium
shocks estimated as changes in the Kim-Wright term premium on FOMC event
days. Panel B depicts the 5-year term premium during the period
over which we conduct placebo tests for the Taper Tantrum analysis
between 2012:Q2 and 2013:Q1, where we compare lending outcomes over
2012:Q4–2013:Q1 versus 2012:Q2–2012:Q3 (see Table OA-3). The term
premium series is the Term Premium on a 5-Year Zero Coupon Bond (FRED
series THREEFYTP5). See Section 2 for details on
the construction of term premium shocks.
This figure consists of two panels. Panel A (top) shows the relationship between the 5-year term premium level and high-frequency term premium shocks over the full sample period. The panel displays two time series from 1994 to 2019: (a) the 5-year term premium series from the Kim-Wright term structure model shown as a line chart, which fluctuates between approximately -1% and +3% over the period, and (b) high-frequency term premium shocks estimated as changes in the Kim-Wright term premium on FOMC event days, shown as vertical bars/spikes that represent quarterly aggregated shocks. Panel B (bottom) depicts the 5-year term premium during the period used for placebo tests (2012:Q2 to 2013:Q1), which compares lending outcomes over 2012:Q4-2013:Q1 versus 2012:Q2-2012:Q3. The panel shows the term premium was relatively stable during this placebo period, fluctuating around -0.5% without any major shocks, in contrast to the sharp increase during the actual Taper Tantrum period shown in main text Figure 3. This stability validates the use of this period for placebo tests.
Figure OA-2: Dynamic DiD Coefficient Plots around Taper Tantrum: Capital
surprises
(a) Loan Growth
(b) Loan Spread
(c) Loan Maturity
This figure shows the estimated DiD coefficients with the
associated 90% confidence levels of the dynamic variant of the
specification in columns 1–3 of baseline Table 4 (top panel) with
interaction effects between the main measure of bank leverage (capital
surprises) and quarterly dummies. Outcome variables are loan growth,
spread, and maturity (log). Confidence intervals are indicated by the
dashed vertical lines.
This figure shows estimated DiD coefficients with 90% confidence intervals from a dynamic variant of the baseline specification using capital surprises as the leverage measure. The figure contains three subfigures arranged vertically. Subfigure (a) shows coefficients for loan growth, subfigure (b) shows coefficients for loan spread, and subfigure (c) shows coefficients for loan maturity. Each subfigure plots quarterly coefficient estimates on the vertical axis against quarters relative to the Taper Tantrum (2013:Q2 = quarter 0) on the horizontal axis, spanning from quarter -4 to quarter +4. Dashed lines indicate 90% confidence intervals. For loan growth (subfigure a), pre-period coefficients are small and insignificant (close to zero), supporting parallel trends, while post-period coefficients become positive and significant, ranging from approximately 0.03 to 0.06. For loan spreads (subfigure b), pre-period coefficients are also near zero, while post-period coefficients are generally negative though with wider confidence intervals. For loan maturity (subfigure c), pre-period coefficients are small and flat, while post-period coefficients become positive and significant. These dynamic plots confirm parallel pre-trends and demonstrate that the differential lending response emerges after the Taper Tantrum and persists through the post-period.
Figure OA-3: Dynamic DiD Coefficient Plots around Taper Tantrum: Tier 1
Leverage
(a) Loan Growth
(b) Loan Spread
(c) Loan Maturity
This figure shows the estimated DiD coefficients with the
associated 90% confidence levels of the dynamic variant of the
specification in columns 4–6 of baseline Table 4 (top panel) with
interaction effects between bank Tier 1 leverage and quarterly dummies.
Outcome variables are loan growth, spread, and maturity (log).
Confidence intervals are indicated by the dashed vertical
lines.
This figure presents the same dynamic DiD analysis as Figure OA-2 but using Tier 1 leverage as the measure of bank leverage instead of capital surprises. The structure is identical: three subfigures arranged vertically showing (a) loan growth, (b) loan spread, and (c) loan maturity. Each plots quarterly coefficient estimates with 90% confidence intervals against quarters relative to the Taper Tantrum. The results are similar to those using capital surprises but generally show stronger magnitudes. For loan growth (subfigure a), pre-period coefficients are flat and close to zero, while post-period coefficients become strongly positive and significant, ranging from approximately 0.04 to 0.08. For loan spreads (subfigure b), pre-period coefficients are near zero, while post-period coefficients are negative and significant throughout, ranging from approximately -0.8 to -1.2. For loan maturity (subfigure c), the pattern is similar to that using capital surprises. The flat pre-trends across all outcomes support the parallel trends assumption, while the persistent post-period effects confirm the robustness of the main findings.
Figure OB-1: Instrumental variable vs. Term premium (Kim-Wright)
Panel A: Raw Data
This figure validates the instrumental variable approach using foreign official holdings of U.S. Treasuries for the analysis in Online Appendix Section B (Alternative IV Evidence). The figure contains two scatter plot panels side by side. The left panel shows the raw correlation between the instrument (quarterly changes in foreign official Treasury holdings, shown on horizontal axis) and the Kim-Wright term premium (shown on vertical axis), with a fitted regression line demonstrating a positive relationship. The right panel shows the conditional correlation after controlling for other macroeconomic variables including lagged values and forecasts, again with the instrument on the horizontal axis and residualized term premium on the vertical axis, with a fitted line. Both panels include confidence bands around the fitted lines. The strong positive relationships in both panels demonstrate that the instrument has sufficient relevance - increases in foreign official Treasury holdings are associated with increases in the term premium, consistent with preferred habitat theory. The R-squared values and first-stage F-statistics (reported in the related tables) confirm the instrument's strength.
Figure OB-2: Dynamic responses of bank lending and profits to a rise in the term
premium
This figure shows the evolution of bank loans (panel A) and
bank return on equity (ROE, panel B) over the eight quarters following a
50 bps increase in the Kim-Wright 5-year term premium. The results are
based on local projection estimations using foreign official holdings of
U.S. Treasuries (normalized by U.S. GDP) as the instrumental variable
for term premiums. The corresponding specifications for four-quarter
ahead outcomes are shown in column 2 of Table OB-3 and the same
regression with ROE as the outcome variable. The shaded areas represent
90% confidence intervals, with standard errors double clustered by bank
and quarter.
This figure shows local projection estimates of the dynamic response of bank loan growth and profitability to a 50 basis point increase in the term premium using Call Report data over 1994-2019. The figure contains multiple panels displaying impulse responses at different horizons (quarters after the shock) on the horizontal axis. Each panel shows separate lines for banks with different levels of Tier 1 leverage, typically showing responses for banks at the 25th percentile (low leverage, dashed line) and 75th percentile (high leverage, solid line) of the leverage distribution. The panels show that following a term premium increase: (1) loan growth increases for both groups but the effect is significantly larger and more persistent for higher-leverage banks, (2) profitability (ROE) increases more for higher-leverage banks, and (3) the effects persist for several quarters before gradually dissipating. Confidence intervals are shown around each line. These impulse responses provide additional external validity evidence that the relationship between term premium, bank leverage, and lending/profitability documented in the Taper Tantrum analysis holds more broadly over the full 1994-2019 period.