Figure 1: Types and Prevalence of Financial
Covenants.
Notes: This chart displays the frequency of various
tight financial covenants per firm-quarter observation from 1990 to
2020. A covenant is defined as tight if the firm is within two standard
deviations of its binding threshold. Data are sourced from the Compustat
and DealScan databases and are based on a sample of publicly traded U.S.
firms.
This is a bar chart showing the frequency of various tight financial covenants per firm-quarter observation from 1990 to 2020. The x-axis lists different types of covenants, while the y-axis shows the count ranging from 0 to 3,000. The debt-to-EBITDA covenant is the most prevalent with approximately 3,000 occurrences, followed by fixed charge coverage at around 2,500. Other common covenants include tangible net worth, interest coverage, and net worth, each with over 1,000 occurrences. Less common covenants include senior leverage, debt-to-equity, and cash interest coverage, which show fewer than 500 occurrences each.
Figure 2: Distribution of the Number of Tight Financial
Constraints.
Notes: This chart displays the fraction of firms
with a given number of tight financial covenants per firm-quarter
observation from 1990 to 2020. A covenant is defined as tight if the
firm is within two standard deviations of its binding threshold. Data
are sourced from the Compustat and DealScan databases and are based on a
sample of publicly traded U.S. firms.
This is a histogram showing the fraction of firms with a given number of tight financial constraints per firm-quarter observation from 1990 to 2020. The x-axis displays the number of constraints ranging from 0 to 8, while the y-axis shows the fraction of firms from 0 to 0.3. The distribution reveals that approximately 20% of firms have no tight constraints, while about 25% have a single constraint. The fraction of firms with 2 constraints is around 22%, with 3 constraints about 15%, and with 4 constraints roughly 10%. The proportion continues to decline with each additional constraint, with very few firms (less than 5%) having 6 or more tight constraints.
Figure 3: Lease Share and Leverage
Notes: These charts display binscatter plots of firm
leverage against the share of leases in 2016. The left panel shows the
relationship for the pre-2018 period, while the right panel shows the
relationship for the post-2018 period.
This is a dual panel binscatter plot showing the relationship between firm leverage and lease share in 2016. The figure contains two scatter plots: "Pre-Shock" (left panel) and "Post-Shock" (right panel). In both panels, the x-axis represents lease share (2016) ranging from 0 to 0.8, and the y-axis shows leverage ranging from 0.2 to 0.6. The Pre-Shock panel shows a negative relationship between lease share and leverage, with leverage declining from approximately 0.5 to 0.3 as lease share increases. The Post-Shock panel shows this negative relationship has largely disappeared, with leverage remaining relatively constant around 0.35-0.4 regardless of lease share.
Figure 4: Diff-in-Diff around Lease Treatment Accounting
Change.
Notes: This chart presents the estimated impact of
lease share on the number of financial constraints using a
difference-in-differences approach around the year of the accounting
change (2019), based on the following equation:
\[\begin{equation*}
\begin{aligned}
\text{Nr.Constraints}_{i,t} = \beta_0 + \sum_{t \neq 2018} \beta_t
(\text{Year}_t \times \text{Lease Share}_{i,2016}) + \alpha_i + \gamma_t
+ \varepsilon_{i,t}
\end{aligned}
\end{equation*}\]
The vertical axis represents the estimated change in financial
constraints, and the horizontal axis shows the year. The shaded areas
represent 95% confidence intervals. \(\text{Nr.Constraints}_{i,t}\) is the number
of financial constraints faced by firm \(i\) at time \(t\). \(\text{Year}_t\) are year dummy variables
(with 2018 as the omitted base year), and \(\text{Lease Share}_{i,2016}\) is the lease
share of firm \(i\) in 2016. \(\alpha_i\) are firm fixed effects, \(\gamma_t\) are time fixed effects, and
\(\varepsilon_{i,t}\) is the error
term. The figure plots the estimated coefficients \(\beta_t\), which capture the year-specific
effect of lease share on financial constraints relative to 2018.
Standard errors are double-clustered at the firm and date-quarter
levels.
This is a line chart showing the estimated impact of lease share on the number of financial constraints using a difference-in-differences approach around the 2019 accounting change. The x-axis spans years from 2011 to 2023, with 2018 as the omitted base year. The y-axis represents the change in number of constraints, ranging from -0.5 to 1. The chart shows coefficient estimates with 95% confidence intervals (shaded area). Before 2018, coefficients hover around zero with small confidence intervals, indicating no significant relationship between lease share and constraints. After 2019, there is a sharp increase in the coefficient to approximately 0.5, with widening confidence intervals, suggesting that firms with higher lease shares experienced a significant increase in the number of financial constraints following the accounting rule change.
Figure 5: Local Projections: Effect of Tightening and Easing
Shocks on External Financing by Constraint Status.
Notes: This figure displays coefficient estimates
from the following specification:
\[\begin{equation}
\begin{split}
\Delta _{h} ExFin_{i,t+h} =\ & \beta_{c,m}^h (\text{Contr. MP
Shock}_{t} \times \text{Mult. Constraint}_{i,t}) + \beta_{a,m}^h
(\text{Acc. MP Shock}_{t} \times \text{Mult. Constraint}_{i,t}) \\
& +\ \beta_{c,s}^h (\text{Contr. MP Shock}_{t} \times \text{Single
Constraint}_{i,t}) + \beta_{a,s}^h (\text{Acc. MP Shock}_{t} \times
\text{Single Constraint}_{i,t}) \\
& +\ \beta_{c,u}^h (\text{Contr. MP Shock}_{t} \times
\text{Unconstrained}_{i,t}) + \beta_{a,u}^h (\text{Acc. MP Shock}_{t}
\times \text{Unconstrained}_{i,t}) \\
& +\ \textbf{X}_t' \gamma + \epsilon_{i,t} \nonumber
\end{split}
\end{equation}\] where \(\Delta_h
ExFin_{i,t+h}\) is the cumulative debt and equity financing flow
between the end of quarter \(t{-}1\)
and the end of quarter \(t{+}h\),
scaled by total assets. Contr. MP Shock\(_t\) and Acc. MP Shock\(_t\) denote contractionary and
accommodative monetary policy shocks, respectively. The variables
Mult. Constraint, Single Constraint, and
Unconstrained are dummy variables equal to 1 if the firm in
that quarter faces multiple tight constraints, a single tight
constraint, or no tight constraints, respectively. Panels (a)–(c) show
responses to tightening shocks; Panels (d)–(f) show responses to easing
shocks. The monetary surprise in quarter \(t\) is constructed by summing the monthly
monetary policy shocks from Miranda-Agrippino and Ricco, 2021. Shaded areas represent 90%
confidence intervals.
This is a 2×3 grid of line charts showing impulse response functions over 10 quarters. The top row displays responses to contractionary monetary policy shocks, while the bottom row shows responses to accommodative shocks. The columns represent different firm constraint categories: multiple constraints (left), single constraint (middle), and no constraints (right). The y-axis shows percentage changes in external financing ranging from -10% to 0%. For contractionary shocks: Multiple-constraint firms show the strongest negative response (about -8% by quarter 10), single-constraint firms show a moderate response (about -5%), and unconstrained firms show a similar response (about -4%). For accommodative shocks: Multiple-constraint firms show almost no response (line near zero), single-constraint firms show a moderate positive response (about 4%), and unconstrained firms show the strongest positive response (about 4%). This demonstrates clear asymmetry in how multiple-constraint firms respond to monetary policy changes.
Figure 6: Relationship between Number of Financial Constraints
and Responsiveness to Easing and Tightening
Shocks.
Notes: This chart plots the marginal effects of a
one standard deviation monetary policy shock on the two-year response of
external financing, as a function of the number of constraints the firm
faces, based on the following equation:
\[\begin{equation*}
\begin{split}
\Delta_8 \text{ExFin}_{i,t+7} & = \beta_1 \textit{Contr.
Shock}_{t} \times \textit{Nr. Constraints}_{i,t} + \beta_2 \textit{Acc.
Shock}_{t} \times \textit{Nr. Constraints}_{i,t} \\ &
+ \textbf{X}_t' \gamma + \epsilon_{i,t}
\end{split}
\end{equation*}\]
where \(\Delta_8
\text{ExFin}_{i,t+7}\) denotes the cumulative debt and equity
financing flows over seven quarters (two years) following the shock.
\(\textit{Contr. Shock}_{t}\) is
defined as the Miranda-Agrippino and Ricco, 2021 monetary policy shock when
positive, and \(\textit{Acc.
Shock}_{t}\) is defined as the same shock when negative.
This is a scatter plot with connecting lines showing the predicted effect of monetary policy on external financing based on the number of constraints a firm faces. The x-axis shows the number of constraints from 0 to 8, and the y-axis displays the predicted effect ranging from -15 to 10. Two series are plotted: contractionary shocks (red) and accommodative shocks (blue), with error bars representing 90% confidence intervals. The contractionary shock line shows an increasingly negative effect as the number of constraints increases, falling from about -4 for unconstrained firms to below -10 for firms with 7-8 constraints. The accommodative shock line shows a decreasing positive effect, starting at about 5 for unconstrained firms and declining to near zero for firms with 7-8 constraints. This demonstrates that firms with more constraints respond more strongly to tightening but less to easing of monetary policy.
Figure 7: Responsiveness of Financial Constraints to Monetary
Policy Shock.
Notes: This chart plots the response of external
financing constraint tightness to a one standard deviation monetary
policy shock. The estimated equations are:
\[\begin{equation}
\begin{split}
\Delta_{h} \text{Constraint}^X_{i,t+h} = \beta_X^h \text{MP Shock}_{t} +
\textbf{X}_t' \gamma + \epsilon_{i,t} \nonumber
\end{split}
\end{equation}\]
where \(\text{Constraint}^X_{i,t+h}\) represents
one of the following: the current ratio, quick ratio, senior leverage
ratio, tangible net worth ratio, leverage ratio, debt-to-equity ratio,
debt-to-EBITDA ratio, senior debt-to-EBITDA ratio, cash interest
coverage ratio, interest coverage ratio, fixed charge coverage ratio, or
the negative of distance to default. \(\textit{MP Shock}_{t}\) is the Miranda-Agrippino and Ricco, 2021 monetary
policy shock. The estimated sensitivities are averaged over a two-year
horizon within the following categories: (i) leverage ratios (current
ratio, quick ratio, senior leverage ratio, tangible net worth ratio,
leverage ratio, and debt-to-equity ratio), (ii) debt-to-earnings ratios
(debt-to-EBITDA ratio and senior debt-to-EBITDA ratio), (iii) interest
coverage ratios (cash interest coverage ratio, interest coverage ratio,
and fixed charge coverage ratio), and (iv) distance to default (measured
as the negative of distance to default).
This is a bar chart showing how different types of financial constraints respond to a one standard deviation monetary policy shock. The y-axis shows interest rate sensitivity ranging from 0 to 0.04. Four categories of constraints are displayed: Leverage (including current ratio, leverage ratio, etc.), Debt to Earnings (debt-to-EBITDA ratios), Interest Coverage (various coverage ratios), and Distance to Default. Distance to Default shows the highest sensitivity at approximately 0.035, followed by Interest Coverage at about 0.025. Debt to Earnings shows moderate sensitivity around 0.015, while Leverage constraints display the lowest sensitivity at approximately 0.01. This indicates that market-based constraints and interest coverage ratios are most responsive to monetary policy changes.
Figure 8: Schematic Representation of Key Targets and of Key
Individual Dynamics.
This is a three-panel conceptual diagram illustrating theoretical relationships in the paper's model. Panel (a) shows "Target for net worth" with curves representing different relationships between variables. Panel (b) shows "Target for physical capital" with intersecting constraint lines. Panel (c) depicts "Dynamics" over an infinite age range. The diagrams use various curves, lines, and regions to represent the conceptual framework of how firms with different impatience levels (θ) make decisions under multiple financing constraints. The graphs illustrate where constraints bind and how optimal targets for firm net worth and capital are determined based on different constraint combinations.
Figure 9: Impulse Responses.
(a) Real
interest rate
(b) Real wage
(c) Aggregate
investment
(d) Borrowing: Unconstrained
(e)
Borrowing: One Constraint
(f) Borrowing: Two Constraints
(g) Investment: Unconstrained
(h) Investment: One
Constraint
(i) Investment: Two Constraints
Notes: Impulse responses to a monetary tightening
and a monetary easing of 25 basis points. The sign of the responses to
the monetary easing is flipped to facilitate comparison between the two
cases.
This is a 3×3 grid of line charts showing impulse responses to monetary policy shocks over 12 quarters. The top row shows macroeconomic variables: (a) real interest rate, (b) real wage, and (c) aggregate investment. The middle row shows borrowing responses for (d) unconstrained firms, (e) firms with one constraint, and (f) firms with two constraints. The bottom row shows investment responses for (g) unconstrained firms, (h) firms with one constraint, and (i) firms with two constraints. Each panel contains two lines: responses to a monetary tightening (solid line) and responses to a monetary easing (dashed line, with sign flipped for comparison). The aggregate investment panel (c) shows that tightening produces about twice the response magnitude (-2% vs -1%) as easing. Similarly, firms with two constraints (panels f and i) show much stronger responses to tightening than to easing, while unconstrained firms and single-constraint firms show more symmetric responses. This asymmetry persists throughout the 12-quarter horizon, supporting the paper's main hypothesis.
Figure 10: Sensitivity Analysis: Impulse Responses of Aggregate
Investment.
(a) with \(\epsilon = 0.5\)
(b) with \(\epsilon = 1.5\)
(c) with \(\mu_{1} = 0.16\)
(d) with \(\mu_{1} = 0.36\)
Notes: Impulse responses to a monetary tightening
and a monetary easing of \(25\) basis
points. The sign of the responses to the monetary easing is flipped to
facilitate comparison between the two cases.
This is a 2×2 grid of line charts showing sensitivity analysis of aggregate investment responses to monetary policy under different parameter values. Each panel plots responses over 12 quarters, with the y-axis showing percentage changes from -2.5% to 0%. Each panel contains two lines representing responses to monetary tightening and easing (with sign flipped for comparison). Panels (a) and (b) vary the interest-rate elasticity parameter ε, with ε=0.5 and ε=1.5 respectively. Panels (c) and (d) vary the population share parameter μ₁, with μ₁=0.16 and μ₁=0.36 respectively. Across all specifications, the tightening response (solid line) is consistently stronger than the easing response (dashed line), though the magnitude of asymmetry varies with the parameter values. This demonstrates the robustness of the paper's main finding that contractionary policy has stronger effects than expansionary policy.