Convenience Yields and Financial Repression∗
Preliminary Draft
Latest version: https://jepayne.github.io/files/PS_CYRepress.pdf
Jonathan Payne†, Bálint Szőke‡May 2, 2024

Abstract
US federal debt plays a special role in the US economy and so gives the US government afunding advantage, often summarized by the “convenience yield” on US debt. Why? One
reason is that government design (and/or repression) of the financial sector influences asset
pricing and helps make long term US federal debt a “safe-asset”. We study the macroeconomic consequences on government borrowing capacity, financial stability, and investment.
We then test our theory using new historical data on US convenience yields going back to
1860.

JEL classification: E31, E43, G12, N21, N41
Key words: Convenience Yields, Government Debt Capacity, Ramsey Problems, Optimal Fiscal
Policy.

∗ We thank Clemens Lehner for outstanding research assistance.
† Princeton University, Department of Economics. Email: jepayne@princeton.edu‡ Federal Reserve Board. Email: balint.szoke@frb.gov

1

Introduction

Many researchers have documented that US federal debt plays a special role in the US economy
and so gives the US government a funding advantage, often summarized by the “convenience
yield”. Macro-finance models have frequently treated this as an immutable feature of the economic
environment and encoded the “benefits” of holding US debt into agent preferences or the market
structure. This means the government can easily “exploit” the convenience yield to increasespending. By contrast, historical studies suggest that the convenience yield emerged as partof a complicated, long-term government program to increase its borrowing capacity. Financial
regulation and/or repression have been key tools in this process, particularly during crises when
the government has needed to raise funding quickly. When viewed in this way, generating andexploiting a convenience yield imposes far reaching impacts on the economy. It links the stabilityof the financial sector to the stability of the government budget constraint. It distorts the portfolioof the financial sector, potentially increasing default and crowding out private liquidity creationand productive investment. In this paper, we study the mechanics and trade-offs involved withcreating financial sector demand for government debt and relate our analysis to historical eras.
We start with an illustrative three period model, in which the banking sector is risky and,absent regulation, there is no special role for government debt. The economy is populated byhouseholds who need bank deposits to be able to consume in the middle period. Banks issue
on-demand deposits and equity to households and invest in short assets, capital, and government
bonds. In this sense, banks provide both liquidity and intermediation services to households.
In the middle period, banks get heterogeneous deposit withdrawal shocks, which potentiallycause them to default because their resource-drawing capacity is constrained and the inter-bankasset markets are characterized by “fire-sale pricing”. The combination of households’ needfor deposits and the possibility of costly default are the “frictions” in the economy that break
Modigliani and Miller (1958) by driving a wedge between the stochastic discount factors of thehousehold and banks. The government in our model cares about spending and household welfare
but faces a constraint that taxation is determined by an exogenous political process. Instead,the government can place restrictions on the portfolios of the banks that potentially increase
the price of government debt and expand their spending. We focus on restrictions that require
the banks to maintain a particular ratio of weighted average assets to deposits. We interpret
equal weighting on government debt and capital to be neutral regulation since, absent regulation,
government debt does not play a special role in the economy. We interpret a higher weighting on
government debt to be financial “repression” because it makes government debt a better asset
for satisfying regulatory requirements.
We characterize how repression can generate a convenience yield on government debt both
directly through forced portfolio choice and also indirectly by endogenously making government
debt a “safe-asset” in the economy. The key feature of our model is that the constraint on holding
government debt binds more in the bad state of the world and so the relative price of government
debt appreciates. This makes government debt a good “hedge” against bad shocks. So, forcing

2

banks to hold government debt in the interbank market also makes banks more willing to purchasegovernment debt in the primary market to hedge risk, which opens up a convenience yield on
government debt. In the terminology of the recent empirical finance literature on institutional
asset pricing, the government is using regulation to make bond demand inelastic for banks and so
generate price “under-reaction” in the market for that asset. The tractability of our model allows
us to characterize how the shape parameters in the bond demand functions and convenience yield
expressions depend explicitly on regulation and fiscal policy. In this sense, our model offers arich understanding of how the convenience yield emerges from government policy.
We first use our model to show that generating a higher convenience yield comes at thecost of higher bank default, less bank liquidity creation, and lower investment into capital. The
higher rate of bank default appears because financial repression inflates the debt price in theinterbank market but also decreases the portfolio return for solvent banks and so makes themarginal bank more likely to default. The lower investment rate appears because government
borrowing crowds out bank capital creation, as is standard in many macroeconomic models. In
this sense, the government faces a trade-off between optimizing their fiscal capacity and having
a well functioning financial sector. We characterize this trade-off and show that the optimal
government policy requires some degree of repression. This result is different to some recent
papers (e.g. Chari et al. (2020)) because we have placed restrictions on the tax process andbecause the banks in our model play roles as both liquidity providers and intermediaries.
We then show that government fiscal irresponsibility erodes the convenience yield. There
are a number of reasons for this. First, government default in bad states of the world restricts
the banking sector’s ability to use government debt to hedge aggregate risk, which makes it
harder for repression to ensure that government debt plays the “safe-asset” role in the economy.
Second, repression ties the solvency of the banking sector to the solvency of the government. So,
increasing government default makes government debt a worse hedge at the same time that it
makes banks more concerned about finding a good hedge. Ultimately, this leads to a decreasein the convenience yield. This is very different to models with bond-in-the-utility or bond-inadvance. In these cases, the role of government debt is exogenous and its marginal usefulness
increases as the market value of government debt declines. This means that as the government
starts to default, the convenience yield increases. Or put another way, in these models the agents
get utility from giving resources to the government so when the government starts to default,then they want more government debt. This highlights the importance of starting from a model
where government is not exogenously important.
We “test” our model using a new data set containing prices and cash flow information fora large collection of corporate bonds from 1850-1940. To infer term structures of yields on US
high grade corporate bonds, we deploy the techniques from Payne et al. (2022), which use a nonlinear state space model with drifting parameters and stochastic volatility. We combine theseestimates with existing bond indices for the modern period and estimates of the government yield
curve from Payne et al. (2022) to calculate a term structure of spreads between government andcorporate bonds form 1850-2022. We follow Krishnamurthy and Vissing-Jorgensen (2012) and3

refer to this spread as the “convenience yield” of government debt and interpret it as reflecting
the special role of government debt in the economy.
We infer a collection of stylized facts about relative government debt prices and how they are
related to changes in financial regulation. First, we find there are low frequency movement in average convenience yields. During the late nineteenth century there was tight financial repression,high convenience yields, and frequent bank defaults, as predicted by our model. The relationshipis very different after FDR introduces deposit insurance in the 1930s and the banking sector isstabilized. Second, we find that the elasticity of the convenience yield to government debt supply
varies with regulation. In the late nineteenth century and the decades following World War II(times with high restrictions on the financial sector and bank balance sheets skewed towards
government debt), the elasticity is close to zero while in the 1920s, 70s, and 80s (times with lessrestriction on the financial sector), the elasticity is strongly negative. This is consistent with ourmodel, which suggests that the elasticity of the convenience yield is not a stable exploitable demand function but instead a reflection of particular regulations and government policies. Similar
to the Phillips curve, the relationship breaks down as governments try to exploit it.

1.1

Related Literature [Incomplete]

Our equilibrium model of safe asset creation is part of a long literature attempting to understandhow the financial sector and government can create safe assets (e.g. Holmstrom and Tirole (1997),
Holmström and Tirole (1998), Gorton and Ordonez (2013), Gorton (2017), He et al. (2016), Heet al. (2019)) and the macroeconomic implications of safe asset creation (e.g. Caballero et al.
(2008), Caballero et al. (2017), Caballero and Farhi (2018)). Our focus is on trying to characterize
how safe asset creation impacts fiscal capacity, financial stability, and investment.
Our government design problem is part of a literature studying optimal fiscal policy ineconomies with financial frictions and tax distortions (Calvo (1978), Bhandari et al. (2017b),
Bhandari et al. (2017a), Chari et al. (2020), Bassetto and Cui (2021), Sims (2019), Brunnermeier
et al. (2022)). In this paper we take the stand that the government follows a fiscal policy rule
governed by political constraints. We do not address the question of whether a Ramsey plannerwithout any political constraints would want to use financial repression. We believe that thehistorical evidence is clear that the government does use financial repression. We leave the questions of working out financial and political constraints could make this optimal for further work.
Instead, our focus is on studying how the government chooses price processes in a economy witha financial sector.
Our historical comparisons extend existing studies on the convenience yield (e.g. Krishnamurthy and Vissing-Jorgensen (2012), Choi et al. (2022)) back to the mid nineteenth century.
This makes us part of a literature attempting to connect historical time series for asset prices
to government financing costs (e.g. Payne et al. (2022), Jiang et al. (2022a), Chen et al. (2022),
Jiang et al. (2022b), Jiang et al. (2021b), Jiang et al. (2021a), Jiang et al. (2020)).

42Model of Convenience Yields

In this section, we outline a three-period version of our model to illustrate how financial sector
regulation can create a convenience yield on government debt.

2.1

Environment

Setting: The economy lasts for three periods: t ∈ {0, 1, 2}. We interpret t = 0 as a primary asset
market, t = 1 as a morning inter-bank market, and t = 2 as the afternoon competitive market.
There is one consumption good. There is a continuum of islands, j ∈ [0, 1], each with a unit
measure of household members, indexed by h ∈ [0, 1], and a unit measure of competitive banks,
indexed by i ∈ [0, 1]. Each household can only participate in the financial market on their island.
There are two production technologies in the economy: one that transforms m0 goods at time
t = 0 to z1 (s)m0 goods at time t = 1 (short-term asset) and another one that transforms k0
goods at time t = 0 to z2 (s)k0 goods at time t = 2 (capital), where s is the aggregate state thathas distribution Π(s) and is realized at the beginning of t = 1.
Assets and Markets: We use goods as the numeraire. At t = 0, the government issues bondsin the primary market at price q0b that pay δ2b at time t = 2. At time t = 1, banks trade
government bonds, at price q1b , and claims on capital, at price q1k , in the inter-bank market. We
show production and bond payoffs and the timing of shocks graphically in Figure 1.
t=0(m0 , k0 , q0b b0 )(λ, s)t=1

t=2(z1 (s), q1k (s), q1b (s))(0, z2 (s), δ2b (s))

Figure 1: Timing of Payoffs
At t = 0, each bank issues demand deposits, d0 , and equity, e0 , to the households on their island
at prices q0d and q0e , respectively.1 Bank equity pays δ1e at time 1 and δ2e at time 2 and is not
tradable after t = 0. Households can withdraw deposits at time t ∈ {1, 2} for resources δtd , whereδtd = 1 if the bank is solvent and 1 > δ2d ≥ δ1d if the bank is insolvent, where inequality is set so
there is no run.
Government: The government ranks allocations according to:θG + U
where G is the provision of public goods by the government and U is the aggregate lifetime
household utility under equal Pareto weights. Parameter θ is interpreted as the relative value of
1 The deposit and equity prices are the same on each island because islands are ex-ante identical.

5

public goods. At t = 0, the government finances public good provision by issuing B0 bonds atprice q0b leading to the t = 0 budget constraint:G ≤ q0b B0(2.1)

At time 2, the government raises taxes T2 (s) from households at t = 2, which it uses to repayδ2b (s) per unit of bonds according to:δ2b (s)B0 ≤ T2 (s)(2.2)

where δ2b (s) < 1 is interpreted as “partial default” or “dilution” when the government decreases
the real value of the bond principle. We refer to T2 (s) as the government “fiscal rule” and treat
it as an exogenous outcome of an unmodelled political process. The exogenous T2 (s) pins down
an upper bound on B0 , which means that the only way the government can increase G at time
t = 0 is by inflating the value of its debt q0b B0 . Motivated by this feature of our model, we refer
to G as the government’s “fiscal capacity”. The government can try to increase its fiscal capacity
by imposing portfolio restrictions on each bank at end of period 0 and period 1:
ϱ(q0d di0 ) ≤ q0b bi0 + (1 − κ)k0i

(2.3)



ϱdi1 (λ) ≤ q1b (s)bi1 (λ, s) + (1 − κ) q1k (s)k1i (λ, s)(2.4)

where (di0 , di1 ) denote bank i’s initial deposit issuance at t = 0 and remaining deposit at the endof period 1, respectively, and similarly for the holdings of government debt (bi0 , bi1 ), and capital(k0i , k1i ). The pair (ϱ, κ) is a set of regulatory parameters: ϱ restricts the bank’s deposit-to-asset
ratio, while κ is the relative “weight” on capital in the calculation of regulatory asset value, that
we interpret as an extent of repression. κ = 0 refers to a regulatory regime that treats government debt and capital symmetrically and just restricts bank risk taking. κ > 0 incentivizes
the holding of government debt over capital as regulatory collateral, while κ < 0 corresponds tothe opposite case. One historically relevant set of regulatory parameters is (ϱ, κ) = (ϱ, 1), whichcorresponds to forcing to back each deposit by 1/ϱ fraction of government debt, similar to what
was done during the National Banking Era (1862-1913). For contemporary regulation, we canalways find a combination of (ϱ, κ) such that 1/ϱ and (1 − κ)/ϱ are the Basel III “risk weights”
for calculating weighted bank assets.
Household problem: Households are uncertain about their own preferences. There are two “layers”
of uncertainty: individual- and island-specific, both of which are resolved at the start of t = 1.
On each island j, with probability λj agents are early consumers, who only value the good atperiod 1, and with probability 1 − λj they are late consumers, who only value the good at period
2. The probability λj is island-specific and it follows the distribution λ ∼ F (λ). For convenience
we drop the j superscript and index islands by λ. We denote the state of being an early consumer6

by ζ h ∈ {0, 1}. At time 0, households rank allocations according to:
U := E ζ h u(ch1 (λ, s)) + (1 − ζ h )u(ch2 (λ, s)) ,(2.5)

where cht (λ, s) denotes consumption of household h on island λ in period t ∈ {1, 2} when aggregate
state is s. Each household is endowed with one unit of goods at t = 0 and zero goods in the otherperiods. All agents have the time 0 budget constraint:
q0d dh0 + q0e eh0 ≤ 1(2.6)

where dh0 and eh0 are household h’s deposit and equity holdings. Early consumers (ζh = 1) only
consume at t = 1 and face the deposit-in-advance constraint:2
ch1 ≤ δ1d (λ, s)dh0 .
Late consumers (ζh = 0) do not consume at t = 0 (leave all their deposits in their bank)3 andface the following budget constraint in periods 1 and 2:
δ1d (λ, s)dh1 ≤ δ1d (λ, s)dh0 + δ1e (λ, s)eh0(2.7)

ch2 ≤ δ2e (λ, s)eh0 + δ2d (λ, s)dh1 − τ (s)where τ (s) denotes (per capita) lump-sum taxes.
Bank problem: Each island has a representative bank owned by the households on that island.
The bank’s object is to maximize its market value at t = 0:hnoi
E ξ(λ, s) max 0, δ1e + δ2e +q0d di0 − mi0 − k0i − q0b bi0
{z
}
|

(2.8)

=q0e (price of equity at t=0)

where ξ(λ, s) denotes the representative household’s stochastic discount factor on island λ when
the aggregate state is s. At t = 0, the bank chooses deposit issuance, di0 ≥ 0, short asset
holdings, mi0 ≥ 0, initial capital, k0i ≥ 0, and initial government debt holding, bi0 ≥ 0, subject tothe regulatory constraint (2.3) at t = 0. At t = 1, it chooses whether to default on its deposit
2 For convenience, we assume that the equity of the early consumers is lost. This assumption is without loss ofgenerality for the qualitative direction of our results.
3 Late consumers have no incentive to run because the deposit contract payouts are restricted to give the lateconsumer at least as much as the early consumer.

7

(by paying δ1d , δ2d < 1), and chooses new asset holdings bi1 ≥ 0 and k1i ≥ 0, subject to:δ1e + δ1d λdi0 + q1k (s)k1i + q1b (s)bi1 ≤ z1 (s)mi0 + q1k (s)k0i + q1b (s)bi1 − ςdi0 1{δ1d < 1},
0 ≤ bi1 ,0 ≤ k1i ,δ2e + δ2d (1 − λ)di0 ≤ z2 (s)k1i + δ2b (s)bi1 ,0 ≤ δ1e(2.9)(2.10)

0 ≤ δ2e ,(2.11)

δ1d ≤ δ2d ,where λdi0 and (1 − λ)di0 represent early withdrawal and rolled over deposit, respectively, δ1e andδ2e are bank dividends paid at t = 1 and at t = 2, while k1i and bi1 denote the bank holdingsof capital and government debt at the end of period t = 1—both of them are subject to shortselling constraints. In addition, banks face the regulatory constraint (2.4) at t = 1.
The bank problem involves three key frictions. First, the deposit payout at t = 1, δ d , cannot
be freely conditioned on the state (λ, s). Second, banks cannot issue equity at t = 1 in the sensethat
0 ≤ δ1e ,(2.12)

which—combined with (2.9)-(2.10)—implies that at t = 1 banks cannot get extra resources fromthe household: they cannot raise equity and must cover their early withdrawals either by using
their short asset holdings or by selling their long assets. This means that banks may potentiallyend up defaulting on deposits. The ability to do so is guaranteed by the third friction, namely,that banks have limited liability, in the sense that they cannot force negative dividends on theirshareholders at t = 2:
0 ≤ δ2e .
If the limited liability constraint binds and the bank defaults, then it incurs a real dead-weight
cost ς at t = 1 (proportional to its total outstanding deposit di0 ) and is contractually obligatedto pay the maximum amount δ1d to its early withdrawers subject to that it is able to pay at least
as much to its late withdrawers at t = 2 (so that late consumers have no incentive to run). The
dead-weight cost ς may include the loss of firm specific information, the destruction of consumer
networks, etc. Banks take ς as given but in equilibrium it is determined as an increasing functionof the fraction of defaulting banks, that is, the cost of default is higher when a lot of banks
default at the same time.

2.2

Equilibrium

Definition 1 (Budget-feasible government policy). Given a fiscal rule T2 (s) and bond price q0b ,a budget-feasible government policy is a tuple (G, B0 , δ2b ) s.t. (2.1) and (2.2) are satisfied withT2 (s) = (1 − Λ)τ (s)8where Λ :=R

λdF is the expected aggregate withdrawal rate.

Definition 2 (Competitive Equilibrium). Given a fiscal rule T2 (s), regulation (ϱ, κ), and a 

budget-feasible government policy (G, B0 , δ2b ), a competitive equilibrium is a set of prices q0d , q0e , q0b






and q1k (s), q1b (s) , payoffs δ1d (λ, s), δ2d (λ, s), δ2e (λ, s) , household policies dh0 , eh0 , ch1 (λ, s), ch2 (λ, s) ,and bank policies di0 , mi0 , k0i , bi0 and k1i (λ, s), bi1 (λ, s) , such that
• Households maximize (2.5) subject to (2.6)-(2.7),• Banks maximize (2.8) subject to (2.3)-(2.4) and (2.9)-(2.11),• Markets clear:
G + mi0 + k0i = 1,
dh0 = di0 ,eh0 = 1,bi0 = B0 ,Z
ZZ
bi1 (λ, s)dF = B0
k1i (λ, s) = k0i
λch1 (λ, s)dF = z1 (s)m0 − ς(λ∗ )d0ZZh(1 − λ)c2 (λ, s)dF = z2 (s)k0 − λδ2e (λ, s)dF (λ)
We characterize equilibrium in the following way. First, we solve the optimization problemof the household in subsection 2.2.1. Second, we combine household and bank optimization withinter-bank asset market clearing to characterize equilibrium in the t = 1 market for given t = 0
choices in subsection 2.2.2. Finally, we characterize equilibrium in the t = 0 market and discuss
convenience yields in subsection 2.2.3.
2.2.1

Household Problem

We characterize the solution to the household problem in Proposition 1. The households choose
their asset portfolio once and for all at t = 0, so that the choices satisfy the Euler equations (2.13)
and (2.14). Given the household portfolio, (dh0 , eh0 ), early consumption c1 and late consumption
c2 are determined as functions of asset payoffs (δ1d , δ2d , δ2e ) and idiosyncratic and aggregate shocks.
Proposition 1 (Characterization of Household Problem). The household portfolio choices at
t = 0 satisfy:hiq0d = E ξ(λ, s) 1 + ν(λ, s) δ1d (λ, s)hiq0e = E ξ(λ, s)δ2e (λ, s)(2.13)(2.14)We use the following notation for the stochastic discount factor (SDF) and the liquidity premium:ξ(λ, s) :=(1 − λ)u′ (ch2 (λ, s)),µc0ν(λ, s) :=9λu′ (ch1 (λ, s))(1 − λ)u′ (ch2 (λ, s))where µc0 > 0 is the households’ Lagrange multiplier on their period t = 0 budget constraint andtheir consumption choices arec1 (λ, s) = δ1d (λ, s)dh0 ,c2 (λ, s) = δ2e (λ, s)eh0 + δ2d (λ, s)dh0 − τ (s).

and(2.15)

Proof. See Appendix A.1.
Demand deposits provide liquidity services at t = 1 to the early consumers, which introduces
a wedge (1 + ν) into the household’s deposit Euler equation. The presence of this asset-specificwedge implies that households are willing to hold demand deposits at a discount, which leads toa “funding advantage” to the providers of such assets.
2.2.2

Equilibrium in the inter-bank markets (t = 1)

Proposition 2 characterizes equilibrium in the inter-bank markets at time t = 1 for given initialasset holdings (m0 , k0 , b0 , d0 ). This involves combining household optimization with bank optimization and inter-bank market clearing, the later two of which are complicated by the possibility
that banks can default. For the characterization of this default decision, it will be useful to define
the banking sector’s net worth at t = 1 (after withdrawal) as:a(λ, s) := z1 (s)m0 + q1k (s)k0 + q1b (s)b0 − δ d (λ, s)λd0 ,and the share of government debt in the banking sector’s period t = 1 portfolio as:φ(λ, s) :=q1b (s)b1 (λ, s).
a(λ, s)At the beginning of time t = 1, the island-specific withdrawal shock, λd0 , leads to ex post
heterogeneity among banks: those with low λ will have excess resources, z1 (s)mi0 − λdi0 > 0,that they can use to purchase assets in the inter-bank markets, while those with λ such thatz1 (s)mi0 − λdi0 < 0 will be forced to sell assets to cover early withdrawals at t = 1.
Proposition 2 (Equilibrium at t = 1). Let ψ1e (s) ≥ 0 and µr1 (s) ≥ 0 denote the Lagrange
multipliers on the t = 1 equity raising constraint (2.12) and the t = 1 regulatory constraint (2.4),
respectively. The following hold:(i) Portfolio choice: If κ = 0 (symmetric regulatory penalty), then government debt and capitalare perfect substitutes, with relative prices satisfying:δ b (s)q1b (s)= 1kk
q2 (s)z2 (s)(2.16)

If κ ̸= 0 (asymmetric regulatory penalty), then the time t = 1 regulatory constraint binds
so for κ > 0 (κ < 0) the banks hold the minimum bonds (capital) required to satisfy the10constraint. In both cases, this implies the portfolio shares:

φ(λ, s) =1 − φ(λ, s) =ϱδ d (λ, s)(1 − λ)d0 − (1 − κ) a(λ, s) − ς 1{δ d < 1}d0κa(λ, s)−ϱδ d (λ, s)(1 − λ)d0 + a(λ, s) − ς 1{δ d < 1}d0κa(λ, s)and the relative prices satisfy:
δ2b (s)q1b (s).
= kk
q1 (s)z2 (s) − κµr1 (s)q1k (s)(2.17)(ii) Default decision: The equity raising constraint at t = 1 always binds, ψ1e > 0, and bankdividends at t = 2 have the form:n oδ2e (λ, s) = max 0, 1 + ψ1e (s) − µr1 (s) + κµr1 (s)(1 − φ(λ, s)) a(λ, s) − (1 − λ)d0 (2.18)
Banks default at t = 1 iff they get a withdrawal shock with λ > λ∗ , where the default cutoff
is determined by δ2e (λ∗ , s) = 0.
If κ ̸= 0, we can use (2.17) and the definitions Rb := δ2b /q1b and Rk := z2 /q1k for the returns
on bonds and capital from t = 1 to t = 2, to show that in equilibrium the term in theparentheses in (2.18) must be equal to the return on the bank’s asset portfolio:
1 + ψ1e (s) − µr1 (s) + κµr1 (s)(1 − φ(λ, s)) = Rb (s) + (Rk (s) − Rb (s))(1 − φ(λ, s)) (2.19)(iii) Equilibrium prices: Inter-bank market prices (q1b (s), q1k (s), µr1 ) satisfy the aggregate resource
constraint at t = 1:
Z 
Z 


b
k
q1 (s)b1 (λ, s) + q1 (s)k1 (λ, s) dF =a(λ, s) − ςd0 1{δ d < 1} dF
with one of the asset market clearing conditions at t = 1 and either (2.16) (if κ = 0) or(2.17) (if κ ̸= 0).
Proof. See Appendix A.2.
For a given parameterization of the model, Figure 2 illustrates numerically how the idiosyncratic and aggregate shocks affect the banks’ default decision and implied asset payoffs.4 The
vertical dashed lines depict default cutoffs λ∗ , assuming that aggregate available resources z1 (s)m0
are high (“good state”, blue color) or low (“bad state”, orange color). A negative shock to theavailable aggregate resources at t = 1 leads to falling prices in the inter-bank asset markets, adecline in bank net worth, and therefore, a fall in λ∗ and an increase in the number of defaulting
4 We can use (2.15) to transform these asset payoffs into household consumption.

11

banks. The left panel in Figure 2 shows how dead-weight default losses ς introduce a discontinuity in the deposit payoff at λ∗ . The right panel, depicting bank dividends at t = 2, defined in(2.18), illustrates how banks with low withdrawal shocks λ are benefited from falling inter-bankasset prices in the bad aggregate state.
The bottom two plots of Figure 2 depict bank deposit and equity payouts when financial
repression (κ) is increased. Evidently, an increase in financial repression leads to more default
in the bad state and less default in the good state. To understand this, recall from part (ii) of
Proposition 2 that banks default when the combination of withdrawals and asset sales force thedividend at t = 2 to be negative. From equations (2.18)-(2.19), we can see that higher financial
repression forces the bank portfolio share in bonds to increase. This increases their return inthe good state of the world because Rk (sH ) > Rb (sH ), which increases the default cut-off λ∗ .
However, it decreases their return in the bad state because Rk (sL ) < Rb (sL ), which decreases thedefault cut-off λ∗ . Or put another way, financial repression leads to redistribution from solvent
to insolvent banks in the good state but redistribution from insolvent to solvent banks in the badstate.

Figure 2: Equilibrium at t = 1: asset payoffs as functions of λ and s. The yellow vertical dashedline depicts λ∗ in the bad state and the blue vertical dashed line depicts λ∗ in the good state.
The bank portfolio decisions and the market clearing conditions in Proposition 2 characterizeasset prices (q1k , q1b ) in the inter-bank market at time t = 1. Evidently, two key features influence
asset prices: the banking sector’s inability to draw resources from the households (as characterized
by the multiplier ψ1e ) and the regulatory constraint (as characterized by the multiplier µr1 ). If
neither of these features were present, then ψ1e = µr1 = 0 and so the prices of bonds and capitalwould be q1b = δ2b and q1k = z2 . We refer to this as the assets being priced at their “fundamental
12value”. Adding the equity raising friction introduces a link between the aggregate proceeds frombank short asset holdings, z1 m0 , and aggregate asset demand, putting downward pressure on
asset prices in the inter-bank market. This shows up as a wedge, ψ1e > 0, between the marginalvalue of income inside versus outside of a particular bank. In equilibrium this wedge manifests
itself as “fire sale pricing” in the inter-bank asset markets in the sense that q1b < δ2b and q1k < z2 ,i.e., assets are traded below their “fundamental value” at t = 1.5 Finally, we can consider thecase with both equity raising frictions and regulation. If regulation is symmetric in its treatmentof bonds and capital, then κ = 0 and the relative price ratio is simply the ratio of t = 2 payoffs(2.16). If regulation advantages government bonds, then κ > 0 and relative price of government
debt is higher and satisfies:
q1b (s)δ2b (s)= kk
q1 (s)z2 (s) − κµr1 (s)q1k (s)In the bad state, sL , there are fewer resources and so µr1 (sL ) increases, which in turn increases
q1b (s)/q1k (s). In this sense, regulation makes banks more “captive buyers” for government debt in
bad times. Both cases are depicted graphically in Figure 3.

Figure 3

2.2.3

Equilibrium at time t = 0

We finish the characterization of equilibrium by studying agent decisions and market clearing at
t = 0 in Proposition 3.
Proposition 3 (Equilibrium at t = 0). The household demand for banks deposit and the bank
5 The finance literature refers to this as “fire sale” Shleifer and Vishny (1992, 2011) or cash-in-the-market pricing
Allen and Gale (1994, 1998). The monetary literature, starting with Lucas (1990), refers to this as “liquidity effect”
which was taken up by the limited participation literature (Christiano and Eichenbaum, 1992, 1995).

13

supply of deposit are determined by the Euler equations:hiq0d = E ξ(λ, s) 1 + ν(λ, s) δ d (λ, s)hiq0d (1 − ϱµr0 ) = E ξ(λ, s)Ω(λ, s)Γ(λ, s)δ d (λ, s)where µr0 ≥ 0 is the Lagrange multiplier on the t = 0 regulatory constraint (2.3), ν is the liquidity
premium defined in Proposition 1 and Ω and Γ satisfy:Ω(λ, s) :=Γ(λ, s) :=

1 + ψ1e×ξ(λ∗ )(1+ν(λ∗ ))f (λ∗ )
(1+ν(λ))(1+ψ1e )λ+(1+ϱµr1 )(1−λ) + ς
ξ(λ)Rℓ(1−F (λ∗ ))1ℓ(s)/δ d (λ, s)

λ > λ∗r (1+ψ1e (s))λ+(1+ϱµ1 (s))(1−λ)
erλ ≤ λ∗(1+ψ1 (s))(1−ϱµ0 )λ > λ∗λ ≤ λ∗The bank asset choices satisfy:hi
1 = E ξ(λ, s)Ω(λ, s)z1 (s)
h
i
h


i
1
1 − (1 − κ)µr0 = E ξ(λ, s)Ω(λ, s)q1k (s) = E ξ(λ, s)Ω(λ, s)z(s)2
1 + ψ1e (s) − (1 − κ)µr1 (s)
"
#
"
#


1
q0b (1 − µr0 ) = E ξ(λ, s) Ω(λ, s; ψ1e , µr1 )q1b (s) = E ξ(λ, s) Ω(λ, s; ψ1e , µr1 )δ b (s)|{z}|{z} 1 + ψ1e (s) − µr1 (s) 2{z}|default
default
regulation

From Proposition 3, we can see the two key features of the bank problem. First, the costly
default wedge Ω effectively makes the banking sector act as more “risk-averse” than the household
sector even though they use the household’s SDF. Second, the optimal bank leverage choice at
t = 0 trades off earning the liquidity premium on deposits, as measured by ν, against the cost of
having a higher default probability, as captured by Ω. In this sense, the combination of deposit
liquidity services and costly default break Modigliani-Miller style results. We plot Ω in Figure 4,
where the left hand plot has symmetric treatment of assets and the right hand plot has financial
repression.
Corollary 1. If the government fiscal rule fully repays the debt, δ2b (s) = 1, then the regulatory
Lagrange multiplier binds at t = 1 (µr1 > 0) but not at t = 0 (µr0 = 0).
The multiplier µr0 reflects the impact of forcing the banks to buy government debt in the
primary market. This can be thought of as the “direct” impact of financial repression. The
multiplier µr1 reflects the impact of creating a captive secondary market for government debt in
the interbank market. Ultimately, this changes the price process for government debt and makes
government debt a “safe-asset” that banks want to hold at t = 0, which means that the constraint
in the primary market no longer binds. Corollary 1 shows that the safe asset benefit is sufficiently
14

Figure 4
strong that the banks want to purchase more government debt in primary market than is requiredby regulation. That is, the bank have additional precautionary motive for holding government
debt that further increases the convenience yield.
A key feature of our model is that the default cut-off λ∗ and default wedge Ω depends upon
the policy parameters of the government: (ϱ, κ, δ b ). This means that regulation and fiscal irresponsibility not only directly change demand but also change the precautionary role for holding
government debt. Taken together, our expression for Ω(λ, s; ψ1e , µr1 , δ b )/(1+ψ1e −µr ) characterizes
how government policy can create endogeneous demand for government debt by distorting theSDF of the banks.
2.2.4

Convenience Yields

We close this section by characterizing the convenience yield. The convenience is often defined
to be the percentage deviation between the asset price and the expectation of stochastic discountfactor:χ := log(q0b ) − log(E[ξ(λ, s)]).
However, for risky assets, this definition includes both the role of the asset and risk premium onthat asset. In this sense, it helpful to break up the convenience yield into:
χ = log(q0b ) − log(E[ξ(λ, s)δ b (s)]) + log(E[ξ(λ, s)δ b (s)]) − log(E[ξ(λ, s)])where we refer to the first term as the “risk-adjusted” convenience yield:χ
e := log(q0b ) − log(E[ξ(λ, s)δ b (s)])

15which is the difference between the price of government debt and an asset with the same cash flows
as government debt that is not government debt. We interpret the “risk-adjusted” convenience
yield as the value that households place on the special role that government debt plays. If we
expand out covariances, then we get the following approximate expression for the risk adjusted
convenience yield:
 

r
χ
e ≈ µ0 + log E Ω(λ, s)

1
1 + ψ1e − µr1

ξ(λ)δ2b,+ Cov E[ξ(λ)δ2b ] 
1Ω(λ, s) ψe −µrh 1 1 i 1E Ω(λ, s) ψe −µr
11From this expression we can see that the convenience yield is partly the direct impact comingfrom forced purchases of government debt in the primary market and the indirect impact comingfrom the that repression helps the government to hedge risk.

2.3

Costs of Generating Convenience Yields

In this subsection, we use our microfounded model to understand the costs of generating a
convenience yield. Figure 5 plots the equilibrium outcomes at t = 0 for different values of financial
repression. Evidently, an increase in financial repression leads to a higher convenience yield andmore fiscal capacity, as measured by the amount of government spending. However, it also leads
to more bank default in the bad state of the world and lower bank investment into capital. The
higher rate of bank default appears because financial repression inflates the debt price in theinterbank market and so also decreases the portfolio return for solvent banks, which makes themarginal bank more likely to default. The lower investment rate appears because government
borrowing crowds out bank capital creation, as is standard in many macroeconomic models.
Together these effects lead to lower household consumption. In this sense, the government facesa trade-off between optimizing their fiscal capacity and having a well functioning financial sector.
For our numerical example, we find that some degree of repression is optimal. This result isdifferent to some recent papers (e.g. Chari et al. (2020)) because we have placed restrictions on
the tax process and because the banks in our model play roles as both liquidity providers andintermediaries.

2.4

Comparison to Exogenous Bond Demand Functions

In this section, we consider two alternative model of bond demand that are frequently used in
the macroeconomics literature: bond-in-the-utility and bond-in-advance.

16

Figure 5: Equilibrium at t = 0 for Different Levels of Repression.
Bond-in-the-utility: In this model, the household solves:max

b0 ,k0 ,c1

ν(q0b b0 ) + βE[u(c2 )]s.t.

q0b b0 + k0 ≤ 1
c2 ≤ z2 (s)k0 + δ2b (s)b0 − τ (s)where ν(q0b b0 ) denotes the utility benefit from holding the real value of government debt.
Bond-in-advance: In this model, the household solves:
max

h h h
bh
0 ,m0 ,k0 ,b1 ,cE[λu(ch1 ) + (1 − λ)u(ch2 )]s.t.

q0b bh0 + mh0 + k0h ≤ 1
ch1 ≤q1b bh0
ch,i
PM ≤

δ2b b h(q b + zm0 − ch1 ) + z2 k0h − τ (s)q1b 1 0where the constraint ch1 ≤q1b bh0 says that the household need to use bonds to purchase consumption goods at t = 1.
The corresponding Euler equations for government debt the bond-in-the-utility (BIU) and17

bond-in-advance (BIA) are given by:−1ν ′ (q0b b0 )1−
E[ξδ2b (s)]
µ0
" 
#
−1
µb1 (s)bbq0 = E ξ 1 − ′δ2 (s)λu (c1 (s))
q0b =



. . . (BIU). . . (BIA)

By contrast, the repression model has the Euler equations:"q0b = (1 − µr0 )−1 E ξ(λ, s) Ω(λ, s; ψ1e , µr1 ) 1 + ψ1e (s) − µr1 (s)−1#δ2b (s)Ultimately, we can see that the repression model “nests” the bond-in-the-utility and bondin-advance models in the sense that we get terms that look similar to the bond-in-the-utility
and bond-in-advance wedges. To illustrate this, in Figure 6 we plot the government bond demand functions from each model and show that they can have similar slopes. In this sense, theregulatory parameters map to the shape parameters in the reduced form bond demand functions. However, there are two important differences in our formulation: (i) we have an additional
wedge coming from government default, and (ii) all our wedges are explicit functions of government policy. We use our microfoundation in the next section to show that convenience yield in
our repression model reacts very differently to government default.

Figure 618

2.5

Government Default

We now use our model to explore how government fiscal irresponsibility impacts the convenience
yield Figure 7 shows the convenience yield as the government defaults more in the bad state.
Evidently, in the repression model, an increase in government default leads to a decrease in theconvenience yield. There are a number of reasons for this. First, government default in bad statesof the world restricts the banking sector’s ability to use government debt to hedge aggregate risk,
which makes it harder for repression to ensure government debt plays the “safe-asset” role in
the economy. Second, repression ties the solvency of the banking sector to the solvency of thegovernment. So, increasing government default makes government debt a worse hedge at thesame time that it makes banks more concerned about finding a good hedge. Ultimately, thisleads to a decrease in the convenience yield.
This is very different to the models with bond-in-the-utility or bond-in-advance, where an
increase in government default leads to a higher convenience yield. Why? In these models,
the role of government debt is exogenous and its marginal usefulness increases as the market
value of government debt declines. This means that as the government starts to default, theconvenience yield increases. Or put another way, in these models the agents get utility fromgiving resources to the government so when the government starts to default, then they want
to give more resources by buying government debt. This highlights the importance of making
government debt endogenously important to the economy.

Figure 7
Figure has the corresponding plot for the fiscal capacity of the government. In this case government defaults leads to fall in government fiscal capacity whereas in the bond-in-utility modelthe decrease is much more muted and in bond-in-advance model government default actuallyleads to higher capacity, which is a counter intuitive result.
19Figure 8

3

Empirical Connection

In Section 4.4 we saw that our model made sharp predictions for what how the design of thefinancial sector impacted the convenience yield. We close the paper by studying whether we see
evidence for these relationships in the historical data.

3.1

Data and Methodology

In a previous paper, Payne et al. (2022), we assembled prices and cash flows for the universeof government bonds and estimated the zero-coupon yield curve on US federal debt. For thispaper, we assemble a companion data-set with a large collection of corporate bonds between 1860
and 1940. We describe the original sources and the details of the data collection in Appendix
C. We use the classification system from Macaulay et al. (1938) to identify a collection of low
risk corporate bonds (primarily railroad bonds) for the period before 1900 when there is no
Moody’s rating system. We estimate the historical yield curve on low risk corporate debt using
the empirical approach developed in Payne et al. (2022). We then combine our estimates forhistorical US Treasury yields and our estimates for historical corporate bonds, with existing
modern series.

3.2

Stylized Facts

We use our estimates of historical yields to construct a collection of stylized facts about thehistorical pricing of government debt.
Fact 1: Low frequency movements in average convenience yields: Figure 9 shows the time series
20for the 10-year corporate yield, the 10-year treasury yield, and the “convenience yield”, as measured by the corporate yield minus the treasury yield. We can see that throughout the National
Banking Era (1860-1917), the convenience yield was typically relatively high, around 1.5%. The
convenience yield then drops down significantly to close to zero around WWII before spiking
again during the 1970s.
10-year corporate greenback yield - government spread
10-year corporate gold yield - government spread
AAA-Treasury Spread (long term) from KVJ

3
2
1
0
1

National Banking Era
Inconvert
GreenbackGold Standard

FED
FDR

New Deal

Financialderegulation

Bretton
Woods

Fiat
Money

DoddFrank

2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202
Figure 9: Government Yields, (high-grade) Corporate Yields, and the Convenience Yield: 18602020

Fact 2: Low frequency movements in the elasticity of the convenience yield with respect to government debt supply. Figure 10 shows a scatter plot with with the ratio of the market value ofgovernment debt/GDP on the x-axis and the convenience yield on the y-axis. We can see thatwithin the National Banking Era (1868-1914) and around WWII (1940-1965), the elasticity of
the convenience yield is very low, even though the level of the convenience yield is very different.
These are both periods, where the government intervened very directly in financial markets to try
and create a market for government debt. The Period with the much studied downward sloping“demand curve is really the period in the interwar period and the period of financial deregulation.
These are both periods, where the government relaxes demand for government. In the interwar
period, Fed takes over money creation from the national banks and so banking sector does notneed to hold as much government debt. In the last third of the 20th century, the government
deregulates the financial sector. Ultimately, we interpret this plot as suggestive evidence thatthe elasiticity has very different properties under different financial regulation regimes.

21

High-Grade Corporate - Government Yield Spread

3.0

National Banking Era (1868-1914)
WWII and its aftermath (1940-1965)
Interwar period (1915-1940) and 1966-2008

2.5
2.0
1.5
1.0
0.5
0.0
0.0

0.2

0.4

0.6
0.8
1.0
Market Value of Government Debt/GDP

1.2

1.4

1.6

Figure 10: Convenience Yield vs Debt/GDP: 1868-2008

Fact 3: Short rate “disconnect” for most of the sample. In Figure 11, we use our statisticalmodel to examine whether a so called “short-rate disconnect” existed during the 19th century.
The pale blue dots depict the difference between model-implied and observed yield-to-maturities
for bonds with less than one year to maturity. Because we estimate our yield curve models
using bonds with maturity greater than 1 year, these dots represent an “out-of-sample” fit at
the short end of the yield curve. The solid blue line depicts the 15-year centered moving averageof these blue dots. The orange solid line depicts the 15-year centered moving average of thedifference between model-implied and observed yield-to-maturities for bonds with more than one
year to maturity. Evidently, pricing errors average out for bonds with long maturities but aresystematically positive for extended periods for bonds close to maturity. In particular, until
the 1880s, bonds close to maturity traded with a premium in a range of 0.5 to 1.0 percentage
points. The premium effectively disappeared from the 1880s until the First World War before
reappearing in the 1920s. We interpret this as strong evidence that there has been a short rate
disconnect through most US history, with a period towards the end of the 19th century when
the short rate disconnect disappeared.

22

3.0

15-year moving average (maturity less than 1 year)
15-year moving average (maturity more than 1 year)

2.5
2.0 First B.U.S.

Second B.U.S. ''Free banking''

National Banking Era

FED

Yield error

1.5
1.0
0.5
0.0
0.5

Suspension ofConvertibility

1.0Gold Coins,
State Bank Notes

Inconvertible
GreenbackGold Standard

1.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
179 180 181 182 183 184 185 186 187 188 189 190 191 192 193
Figure 11: Short Rate Disconnect.
Pale blue dots depict the difference between model-implied and observed yield-to-maturities for bonds with lessthan one year to maturity. The solid blue line depicts the 15-year centered moving average of these dots
excluding yield errors with magnitude greater than 4 (to handle potential outliers from data issues). The orange
solid line depicts the 15-year centered moving average of the difference between model-implied and observed
yield-to-maturities for bonds with more than one year to maturity. The light gray intervals depict recessions,and the light red intervals depict wars.

4

Infinite Horizon Macroeconomic Model

The previous sections illustrated how the regulation of bank balance sheets can generate a convenience yield. In this section, we move to an infinite horizon general equilibrium model. We
show that the impact of financial repression depends on “stickiness” of deposit demand. We use
the model to explore how the government can use the financial sector to smooth borrowing costs
across bad shocks.

4.1

Environment

Setting: Time is discrete in infinite horizon. There is one consumption good. The economy ispopulated by a representative household that directly or indirectly owns all claims to production. The economy also contains a representative firm, a representative financial intermediary,
and a government, all of which issue securities. The firm issues equity claims and creates capital23

to produce consumption goods. The intermediary issues deposits and equity. The government
issues geometrically decaying long-term bonds that pay repay a fraction ζ of the principal eachperiod. The high level relationship is given in figure 12.

Figure 12: Agent balance sheets

Representative household: ranks allocations according to:
E0

"∞
X

#
β t u(ct ) + ν(dht + ζbht ) − Ψt+1 (aft+1 )eht − Ωt+1 (τt+1 )

t=0where ct is household consumption at time t, dht is the household holdings of financial intermediary deposits, bht is household holdings of government debt, aft+1 is the net-worth of the financial
intermediary, eht is household equity holdings, and τt+1 is the tax rate. The function ν(·) is
increasing and captures the non-pecuniary benefit of holding “safe-assets”. The function Ψ(·)
is decreasing and captures the cost of bank “insolvency”. The function Ω(·) is increasing andcaptures the distortion from raising taxes. The household also faces the short selling constraints
dht ≥ 0, sht ≥ 0, and bht ≥ 0, where sht is household holdings of shares in the firm. At time 0, thehousehold is endowed with capital, k0 , and sells it to the representative firm. Each period, thehousehold is endowed with a unit of labor, lt = 1.
Representative firm: has a Cobb-Douglas production technology subject to stochastic productivity zt :αy = zt kt−1lt1−αlog(zt ) = (1 − η) log(z̄) + η log(zt−1 ) + ϵtwhere lt is labor hired by the firm and kt−1 is firm capital stock. The evolution of capital stock24

is given by the constant-return-to-scale technology:
kt = (1 − δ)kt−1 + Φ (ιt−1 ) kt−1
is the investment-capital ratio and Φ(·) is an “adjustment” function.
where ιt−1 := kit−1
t−1
Representative financial intermediary: On the liability side of their balance sheet, the intermediary issues “safe-assets”, dft , that each pay 1 good at t + 1 and equity, eft , that pays a dividendeδt+1
at t + 1. On the asset side, they purchase shares in the firm, sft , and government debt, bft .

The intermediary faces a regulatory collateral constraint that at any point in time, a proportion
κb of the maturing safe asset must be backed by the market value of government debt:(ζ + (1 − ζ)qtb )bft ≥ κb dft
where qtb is the price of government debt.
Government: Each period, the government raises lump sum taxes, τt , issue bonds, bt , andundertakes spending gt = g(zt )yt that is a function of the aggregate state, where g(·) is adecreasing function. Bonds are issued at par and repay a fraction ζ of the principal each period.
They face the inter-temporal budget constraint that:gt + ζbt−1 ≤ τt + qtb (bt − (1 − ζ)bt−1 ).
Following Bohn (1998) and Bai and Leeper (2017), we impose that the government sets a budget
feasible tax policy to target a long run debt to GDP ratio:τ̂t − τ̂ ∗ = γ b̂t−1 − b̂∗
where τ̂t := τt /yt and b̂t−1 := bt−1 /yt−1 . The government also chooses regulatory portfolio restriction κb ≥ 0.
Markets: All markets are competitive. Let qts denote the firm equity price. Let qtb denote thegovernment bond price. Let (qte , qtd ) denote the time-t price of equity and safe assets issued by
the financial intermediary. We use upper case R for the gross return and r for the yield. Let
wt denote the wage rate. We are focusing on the case when ζ is a parameter and to simplify
notation we define q̃tb := ζ + (1 − ζ)qtb .
Functional Forms: We imposeu(c) = log c,

ν = log(exp(−rtd )dht+1 + ζbht+1 )25

capital adjustment costΦ(ι) = ϕ0 +ϕ̄ 1−ϕι
1−ϕDiscussion of environment frictions: This environment is characterized by two key distortions. The first distortion is that the households get additional utility from holding safe assets
through the ν function. The second is distortion is that the the financial intermediaries, whohave the technology to create safe assets, face the cost function, Ψt+1 , when they become insolvent. This effectively makes the safe asset issuers less willing to take on risk than the households.
Although we are not modelling the microfoundations for these distortions, we believe the model
captures the key friction in macro-finance models.
Discussion of government policy rule: We interpret our government tax and spending policies as arising from unmodelled political frictions that induce the government to run deficits
during recessions and then surpluses in expansions to return to a target long-run debt-to-GDP
ratio. This policy potentially imposes welfare costs if running surpluses induces the government
to move the tax rate around. We are going to study how financial regulation and changes in
the convenience yield on government debt influence the welfare cost of running such a fiscal policy.
Discussion of regulatory constraints: In addition to the environmental frictions, the environment also contains regulatory constraints that restrict the portfolio choices of agents and sochange asset demand elasticities. The key constraint is the collateral requirement that the market value of government debt cannot fall below κb dt . Effectively, this constraint means that the
government only allows the financial sector to use their financial technology to issue safe-assets
to households if they hold government bonds. In this sense, the government is repressing thefinancial sector to create demand for their debt and so drive up the price of their debt when
the collateral constraint binds. The other regulatory constraint is that the household may nothold government bonds and firm equity. This segments the market for government debt so thatthe only agents trading government debt are the financial intermediaries facing the collateral
constraint requiring them to hold government bonds. Ultimately, these regulatory constraints
will allow the government to indirectly tax the value that the financial intermediaries generate
through safe asset creation.

4.2

Competitive Equilibrium

In this subsection, we set up the agent problems and characterize the competitive equilibrium.

26

4.2.1

Household Problem

We set up the household problem recursively. The (individual) state variable for the household
is aht , which denotes the wealth of the household at the start of period t. The household solves
problem (4.1) below:
Vt (aht ) =

max

h h h
ct ,dht ,bt ,et ,st

n


o
u(ct ) + ν dht + ζbht − Et Ψt+1 eht + Ωt+1 + βVt+1 (aht+1 )s.t. ct + qte eht + qts sht + qtb bht + qtd dht ≤ aht

(4.1)

e
e
s
s
b
aht+1 = (δt+1+ qt+1)eht + ((1 − τt+1 )δt+1+ qt+1)sht + q̃t+1
bht + dht

0 ≤ dht ,0 ≤ bht ,0 ≤ sht

Taking first order conditions and imposing the envelope condition gives the “asset-demand”
equations:λdt
ν ′ (dht + ζbht )+u′ (ct )u′ (ct )h′ h
ν (dt + ζbt )λbtbqtb = E[ξt,t+1 q̃t+1]+ζ+u′ (ct )u′ (ct ) Et [Ψt+1 ]ee
qte = E ξt,t+1 (δt+1+ qt+1) −u′ (ct )λsss
qts = E ξt,t+1 ((1 − τt+1 )δt+1+ qt+1) + ′ tu (ct )

[dht ] :qtd = E[ξt,t+1 ] +[bht ] :[eht ] :[sht ] :where ξt,t+1 := βu′ (ct+1 )/u′ (ct ) is the household stochastic-discount-factor (SDF) and whereλdt ≥ 0, λbt ≥ 0, and λst ≥ 0 are the multipliers on the household portfolio constraints on dht ,bht , and sht . Observe the Euler equations for dht and bht have been “distorted” by the household
demand for safe assets, ν. Observe that the Euler equation for bank equity can be rewritten as:
qte = Et




Ψt+1
e
e
ξt,t+1 δt+1 + qt+1 − ′u (ct+1 )so we can see that the insolvency costs distort the price of price of bank equity.

27

4.2.2Financial Intermediary Problem

The financial intermediary chooses a collection of asset portfolio and dividend payouts to maximise its market value by solving problem:
V0 =

max

δ e ,sf ,bf ,df{q0e + q0h h1 − q0s s1 − q0b b1 }s.t.

δte + qts sft + qtb bft − qtd dft = aftsbaft+1 = ((1 − τt+1 )δt+1+ qts )sft + q̃t+1
bft − dft!#"
Ψt+1 (aft+1 )eee
qt = Et ξt,t+1 δt+1 + qt+1 −u′ (ct+1 )bq̃t+1bft ≥ κbt dft

sft ≥ 0The first order conditions gives the following financial intermediary asset demand and supply
equations :[sft+1 ][bft+1 ][dˆft+1 ]








∂eδ Ψt∂ea Ψt+1∂eδ Ψt+1ss
0 = −qts 1 − ′− ′δt+1+ qt+1+ Et ξt,t+1 1 − ′+ µstu (ct )u (ct+1 )u (ct+1 )






∂ea Ψt+1∂eδ Ψt∂eδ Ψt+1b+ Et ξt,t+1 1 − ′− ′+ µbt+1 q̃t+1
0 = −qtb 1 − ′u (ct )u (ct+1 )u (ct+1 )







∂ea Ψt+1∂eδ Ψt∂eδ Ψt+1− Et ξt,t+1 1 − ′− ′+ κbt µbt+1 exp rth
0= 1− ′u (ct )u (ct+1 )u (ct+1 )In equilibrium, market clearing and the regulatory constraint on household portfolio sht ≤ κstwith κst ≥ 0 implies that the short-selling constraint for the financial intermediary never binds(µst = 0).
4.2.3

Firm Problem

Taking prices and the shareholder’s SDF as given, firms solve:
Vt (kt−1 ) = max
ιt ,ltnhioαzt kt−1lt1−α − wt lt − ιt kt−1 + Et ξˆt,t+1 Vt+1 (kt )where ξˆt,t+1 is the weighted average of the household and firm stochastic discount factors andthe firm is subject to the capital accumulation technology:
kt = (1 − δ + Φ(ιt )) kt−128

itis the investment-capital ratio. The first order conditions are:where ιt := kt−1

[wt ] :α0 = (1 − α)zt kt−1
lt−α − wt[ιt ] :

0 = −kt−1 + Et [ξˆt+1 ∂k Vt+1 (kt )Φ′ (ιt )kt−1 ]Guess the form Vt = υt kt−1 , then the first order condition for ιt becomes:Φ′ (ιt ) = Et [ξˆt+1 ∂k Vt+1 (kt )]−1 = Et [ξˆt+1 υt+1 ]−1
The Bellman equation becomes:!
1/α hiαzt (1 − α)ˆt,t+1 υt+1 kt
υt kt−1 =
−
ι
k
+
E
ξ
t
t−1
t
1−α
wt1−α


h
i
yt
− ιt + (1 − δ + Φ(ιt ))Et ξˆt,t+1 υt+1
⇒ υt = αkt−11 − δ + Φ(ιt )yt− ιt +⇒ υt = αkt−1
Φ′ (ιt )

ytt)
Let r̂tY := α kt−1
be the marginal return to capital (from production) and r̂tK = ΦΦ(ι′ (ι ) − ιt be thetmarginal return to capital (from reducing future adjustment costs6 ). Then, the value function
becomes:
Vt = (r̂tY − ιt )kt−1 +kt′
Φ (ιt )
(1 − δ)kt−1
Φ′ (ιt )|{z}= (r̂tY + r̂tK )kt−1 +{z}|return on capital

capital stock after production

and so the dividend and ex-dividend price are:
δts = (r̂tY − ιt )kt−1
qts =

kt
Φ′ (ιt )4.3

Financial Repression and Asset Pricing

4.4

Fiscal Capacity Over the Business Cycle

Government funding advantage in our model:“Convenience yield” = Et [ξt,t+1/ζ ]−1 − ζ log(1/qtb )6 This is the capital goods producer’s return.

29

Figure 13: Inelastic Deposit Demand: κ makes z-shock gov. debt demand shock

In our model, the “convenience yield” on long-term government debt can potentially come (i)regulation (the constraint ϱb ) leading banks to buy more debt in recessions and (ii) the government reducing bond supply in recessions. However, the empirical fiscal policies shut down thissecond channel. To understand how this plays out in equilibrium, we simulate economy under
different regulatory policies and plot:
Et [ξt,t+1/ζ ]−1 − ζ log(1/qtb )
{z
}
|

∼

Convenience yield / “funding advantage”

q b bt+1 /yt|t {z }

Market Value of Debt to GDP

We then show how convenience yield moves along the equilibrium path.
We plot the results in Figure (15). The top line shows the simulated relationship between themarket value of debt-to-GDP and the convenience yield in an economy without regulation. The
middle line shows the simulated relationship with loose regulation and elastic demand. The final
line shows the simulated relationship with tight regulation and inelastic demand. Evidently, theshape of the relationship between the convenience yield and debt-to-GDP changes from downward
sloping to flat once tight regulation is introduced. To understand this, consider the impact ofa recession in the model. A decrease in productivity, ↓ z, lead the government to increase
debt/GDP. But the decrease in productivity also causes the regulatory constraint to bind and soincreases bank demand for government debt. Thus, under tight regulation, the government canincrease the debt/GDP ratio without facing an increasing interest rate.

30

Figure 14: Elastic Deposit Demand: κ makes q b more procyclical

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34

A

Details on the Model in Section 2

Notation: There is a continuum of islands, i ∈ [0, 1], each with a unit measure of household
members, indexed by h ∈ [0, 1], and a unit measure of competitive banks, indexed by f ∈ [0, 1].
Index h can be replaced by the binary idiosyncratic shock ζ ∈ {0, 1} (the probability of which isisland-specific), while i can be replaced by the idiosyncratic shock λ.

A.1

Household problem

Taking prices (q0d , q0e ) and payoffsnoδ d (λ), δPe M (λ)
as given, the household solves (each ofthem being able to buy assets from only one bank):

λ

h
i
h,i
E ζh,i u(ch,iAM ) + (1 − ζh,i )u(cP M )d0 ,e0 ,c0 ,c,dq0d dh0 + q0e eh0 ≤ 1 = ah0 = δ0e + q0e eh−1
max

d,i h
ch,i
AM ≤ δ d0

∀i

h,i
e,i h
d,i h
ch,i
AM ≤ δ (d0 − dAM ) + δAM e0chP M ≤ δPe,iM eh0 + δ d,i dh,iAM − τP Mh,ih,ih
0 ≤ ch,i
AM , cP M , d0 , dAM

∀i

s.t.


µc,h
0


h,i
ψAM


µc,h,i
AM


µc,h
PM


j,h
µt

At time t = 0, the household sells its initial consumption goods ah0 = z−1 k−1 to the two typesof capital goods producers (for price of one). For a given island i, the FOCs of an individual
household h are[chAM ]c,hh
0 = ζh u′ (chAM ) − µc,hAM − ψAM + µAM[chP M ]c,h0 = (1 − ζh )u′ (chP M ) − µc,h
P M + µP M

[dhAM ]d,hd c,h0 = −δ d µc,hAM + E[δ µP M ] + µAM

For early consumers (ζ = 1), the marginal value of income in the PM is zero: µcP M (1) = µcP M (1) =0, while the marginal utility of consumption is equal to the marginal cost of consumption whichin the AM is equal to the marginal value of income adjusted by the extra cost from the CIA
constraint: u′ (cAM (1)) = µcAM (1) + ψ(1). This implies that early households want to sell allof their assets in the AM, µdAM (1) > 0 and dAM (1) = 0. Their supply is inelastic irrespectiveof which island they are on. The CIA constraint binds ψAM > 0 and the income constraint issatisfied with dAM (1) = 0, nevertheless µdAM (1) = µcAM (1) = 0. In this sense, CIA constraint
is equivalent with the households’ inability to trade assets in the AM. In other words, we could“drop” the CIA constraint from the above problem. The key for this is that early households
don’t care about the potential continuation value in the portfolio-adjustment sub-period. If they
do care about the PM period, we need to keep the explicit CIA constraint.

35

For late consumers (ζ = 0), the marginal value of income in the PM equals to the marginal utility of consumption, µcP M (0) = u′ (cP M (0)). It follows from their FOCs for deposit that their
marginal utility of income in the AM must be strictly positive as well, µcAM (0) = E[µcP M (0)] > 0
and µdAM (0) = µeAM (0) = 0, due to the fact that they can use idle AM income to save for the PM.

Their deposit roll-over decision depends on the relative returns on deposit vs alternative invest-

ment opportunities between the AM and PM (we assume that there is none). Strictly positive
value of AM income and the lack of utility from AM consumption implies that late consumers
set cAM (0) = 0 and so ψ(0) = 0. As a result, being “cash constrained” is equivalent with being
an early consumer (ζ = 1).
The FOCs with respect to period t = 0 choices are[dh0 ]

Z  
ccd
λ µAM (1, λ) + ψAM (1, λ) + (1 − λ)µAM (0, λ) δ (λ)dF (λ)
Z 


′
′
d
=E
λu (cAM (1, λ)) + (1 − λ)E[u (cP M (0, λ))] δ (λ)dF (λ)
Zhiλu′ (cAM (1, λ))  d=E(1 − λ)E[u′ (cP M (0, λ))] 1 +
δ
(λ)dF
(λ)
(1 − λ)µcAM (0, λ)|{z}q0d µc0 = E=:1+ν(λ)



i
hZ
d
ξAM (λ) 1 + ν(λ) δ d (λ)dF (λ)
q0 = E[eh0 ]hZ 

q0e µc0 = EieλµcAM (1, λ) + (1 − λ)µcAM (0, λ) δAM(λ)dF (λ)
hZ 

i
+E
λµcP M (1, λ) + (1 − λ)µcP M (0, λ) δPe M dF (λ)

hZ
i
e
=E
(1 − λ)µcAM (0, λ)δAM(λ)dF (λ)
hZi
(1 − λ)u′ cP M (0, λ) δPe M (λ)dF (λ)
+E
hZ

i

ξP M (λ) eeeδP M (λ) dF (λ)
q0 = EξAM (λ) δAM(λ) +ξAM (λ){z}|=:VAM (λ)

where we used the notations for the stochastic discount factorξAM (λ) :=(1 − λ)E[u′ (cP M (0, λ))]µc0

ξP M (λ) :=36(1 − λ)u′ (cP M (0, λ))µc0The individual consumption choices arecAM (0, λ) = 0
cP M (0, λ) = δPe M (λ)eh0 + δ d (λ)dh0 − τP M

cAM (1, λ) = δ d (λ)dh0
cP M (1, λ) = 0

Remark: A (“shadow”) asset that promises to pay a risk-free unit of goods in the PM but
otherwise plays no special role in the AM market would be priced as
q0s = E

ZξP M (λ)dF (λ) = E

Z

ξAM (λ)dF (λ)

Comparing this expression with the deposit Euler equation, we can define the liquidity premiumon bank deposit as sh ξ (λ) ir0 − r0dAM=
q0d (q0s )−1 − 1 = E
1 + ν(λ) δ d (λ) > 0dE[ξAM (λ)]
1 + r0In yield terms we can write this condition as(cost of deposit financing)r0d < r0s

(cost of equity financing)This is the source of “funding advantage of bank deposit”: in equilibrium the household’s required(risk-adjusted) return on bank equity is r0s , while the required (pecuniary) return on bank deposit
is r0d . However, it is also clear that as δ d gets lower (due to bankruptcy) the liquidity premiumis also decreasing.

A.2

Bank problem

Default is costly for two reasons: (i) there are deadweight costs of default (proportional tooutstanding deposit d0 ) and denoted by ς. While banks take ς as given, in equilibrium ς is anincreasing function of the fraction of defaulting banks that leads to “too much deposit issuance”(individual costs < social costs); (ii) forced selling results in the sale of assets at prices below
their “fundamental value” because of market illiquidity. This is a transfer of value from the seller
to the buyer, so it leads to “too little deposit issuance” (individual costs > social costs). Takingbprices (qAM
, qPb M ) as given, the bank solvesmax

d0 ,m0 ,k0 ,b0

n
hZ


io
δ0e + EξAM (λ)VAM d0 , m0 , k0 , b0 ; λ, s dF (λ)
s.t.

δ0e + m0 + k0 + q0b b0 ≤ q0d d0
ϱ(q0d d0 ) ≤ κm m0 + κb (q0b b0 ) + κk k0
0 ≤ d0 , m0 , k0 , b0hZiq0d = EξAM (λ) 1 + ν(λ) δ d (λ)dF (λ)

37where

o



n
ξP M (λ)
e
δPe M
s.t.
VAM d0 , m0 , k0 , b0 ; λ, s = max 0, δAM+E
E[ξP M (λ)]
e
k
b
k
b
δAM
+ qAM
kAM + qAM
bAM ≤ zAM m0 + qAM
k0 + qAM
b0 − δ d λd0 − ςd0 1{δ d < 1}

δPe M ≤ zP M kAM + δPb M bAM − δ d (1 − λ)d0e0 ≤ δAM, kAMϱ δ d (1 − λ)d0|{z}rolled-over deposit≤

q b bAM|AM{z }

k+(1 − κ)(qAMkAM )ϱ ≥ 0, κ ≤ 1

market value of debt

Function ς(·) denotes real dead-weight losses from default that may include the loss of firm
specific information, the destruction of capital/consumer networks, etc. The ς(·) function is afeature of the environment that the government cannot overcome per se, but they can internalize
the externality that it represents.
Parameters (ϱ, κ) are regulatory parameters:• ϱ restricts the banks’ deposit-to-asset ratio (“leverage constraint”). ϱ = 0 corresponds tothe case of no financial regulation. We call ϱ the regulation parameter.
• κ measures the amount of repression. κ = 0 corresponds to symmetric regulatory treatmentof the two assets, while κ ̸= 0 introduces asymmetric treatment. When κ is positive,
government debt is preferred to capital, when κ is negative capital is preferred relative to
debt. κ = 1 corresponds to the extreme case when capital is excluded completely.
A.2.1

Portfolio choice in the AM and default

Given period t = 0 choices (m0 , k0 , b0 , d0 ) and the aggregate shock, there is a bank-specificwithdrawal shock of size λd0 . Because of financial frictions, liquidity is limited in the AM:e(i) there is no equity injection δAM≥ 0, and (ii) there is no un-collateralied debt issuancebAM , kAM ≥ 0 (i.e., banks are borrowing constrained). Market illiquidity introduces a wedge
between the asset’s market price and “fundamental value” which makes AM asset sales costly.
Nevertheless, because of (i) and (ii), withdrawals must be financed either by cash-on-hand orby costly asset sales/borrowing, both of which affect the shareholders’ dividend payment in the
PM. Shareholders of the bank have limited liability, so when the bank value in the AM becomes
negative, they choose to default.
To see how the wedges between asset prices and fundamental value appear in the AM, we

38study the FOCs with respect to AM choices:
e
[δAM
]

[bAM ][kAM ]eµAM = 1 + ψAM





u′ (cP M (0, λ))rbbδqAM µAM − µAM = E
E[u′ (cP M (0, λ))] P M





u′ (cP M (0, λ))krqAM µAM − (1 − κ)µAM = E
zP M
E[u′ (cP M (0, λ))]

(A.1)
(A.2)

e
where ψAM
≥ 0 is the Lagrange multiplier on the equity raising constraint, µAM ≥ 0 is themultiplier on the period t = 1 budget constraint and µrAM ≥ 0 is the multiplier on the t = 1 regulatory constraint. The RHS of (A.1) and (A.2) represent the two long-term assets’ fundamental
value from the AM point of view. When there is no aggregate risk in the PM, the expressions
become δPb M and zP M , respectively.
(I).

No equity raising + No regulation:

Consider the case with ϱ = 0, when µrAM = 0 andthe two long-term assets are perfect substitutes. When the AM equity raising constraint binds,e(s) > 0, the “liquidity shortage” makes AM asset prices lower than what the household wouldψAMkb(s) < zP M (s).
(s) < δPb M (s) and qAM
be willing to pay for them (“fundamental value”), i.e. qAM

In fact, the presence of the idiosyncratic shock λ makes the equity raising constraint always bindin the AM: low-λ banks would raise equity to buy assets cheaply, high-λ banks would raise equity
to avoid costly default.7 We can use the t = 1 Euler equations and combine the t = 1 and t = 2
budget constraints to get
e
δAM
+



δPe M
zP M k0 + δPb M b0
1−λ
d
=
z
m
+
−
δ
λ
+
d0 −ςd0 1{δ d < 1}
AM 0
e
e
e
1 + ψAM
1 + ψAM
1 + ψAM|{z}
exposure to λ shock

which shows how the “missing morning markets” causes troubles for the banks to move resources
between the AM and PM. Effectively, it changes the banks’ inter-temporal marginal rate ofesubstitution between the AM and PM (recall that shareholders want to maximize δAM+ δPe M ,i.e. their IMRS is one). It also shows that without the equity raising friction, shareholder
value would not depend on λ. We can rearrange this “consolidated” budget constraint to write
dividends in the PM as:



e
k
b
e
δPe M = 1 + ψAMzAM m0 + qAM
k0 + qAM
b0 − δ d λd0 − ςd0 1{δ d < 1} − δAM− δ d (1 − λ)d0
7 The relationship works vice versa: without equity raising friction the idiosyncratic shock λ has no bite.

39

The bank defaults when this term becomes negative assuming δ d = 1. This leads to the cutoff

λ∗ :=
=

e
1 + ψAMkbzAM m0 + qAM
k0 + qAM
b0 − d 0eψAM
d0zAM m0 zAM m0 + zP M k0 + δPb M b0 − d0
+
e
d
ψAM
d0
| {z0 }=λ0

This expression (that we got by substituting out prices using the t = 1 Euler equations) clarifies
that the reason why λ is an issue and certain banks default is the equity raising friction. In theevent of default, λ > λ∗ , deposit payout is




e
k
b
1 + ψAMzAM m0 + qAM
k0 + qAM
b0 − ςd0e
1 + ψAM(λ∗ − ς) − ςhiδ d (λ) ==e
1 + ψAMλe
1 + ψAMλ + (1 − λ) d0
We can use the expression for the default cutoff to write dividends in the PM asn oδPe M = max 0, ψPe M λ∗ − λ d0
which shows that the source of positive dividend (and a non-zero q0e is the equity raising frictionin the morning).
(II).

e≥ 0 conFree equity raising + Regulation: Consider the case without the δAMe= 0 and there is no default. Looking at the Euler equations reveals thatstraint, when ψAMa binding t = 1 regulatory constraint has an opposite effect on AM asset prices to the equitybkabove their fundamental values. However,and qAMraising constraint, i.e., µrAM > 0 raises qAM

it is not clear that the t = 1 regulatory constraint binds. To see this, plug the t = 1 budget
constraint into the regulatory constraint:eϱ(1 − λ)d0 ≤ zAM m0 + (1 − µrAM )−1 zP M k0 + δPb M b0 − λd0 − δAM
which shows that banks can always avoid the t = 1 regulatory constraint by raising equity. In thiseconomy, the λ shock has no bite, so for all purposes, this looks like one with a t = 0 regulatory
constraint without a morning market.
(III).

No equity raising + Regulation:

This is the case when the two non-negative mul-

tipliers might appear together with opposite effects on AM asset prices. In other words, the factthat banks cannot easily avoid the regulatory constraint makes µrAM > 0 more likely. Following
the same logic as before, we can use the consolidated budget constraint to write PM divideds as



e
k
b
δPe M = 1 + ψAM− µrAM qAM
kAM + qAM
bAM − δ d (1 − λ)d040

and the default cutoff as

λ∗ :=
=

e
1 + ψAM− µrAMkbzAM m0 + qAM
k0 + qAM
b0 − d0e
ψAM− µrAM d0zAM m0 zAM m0 + zP M k0 + δPb M b0 − d0


+
d
e
ψAM
− µrAM d0| {z0 }
=λ0ewhich shows that for a given initial balance sheet, (d0 , m0 , k0 , b0 ), and a given ψAM, a bindingt = 1 regulatory constraint can help reduce the probability of default. This works through avaluation effect: by linking asset trading in the morning markets to the bank’s (fixed) outstanding
liabilities, regulation can keep morning asset prices relatively high. However, in equilibrium higherefalls.
morning asset prices mean that the equity raising constraint is less of a problem and ψAM

Similarly, higher morning prices mean that the regulatory constraint binds less. Plugging thet = 1 budget constraint into the regulatory constraint leads toδ d λd0 + ϱ(1 − λ)d0 ≤ zAM m0 +

zP M k0 + δPb M b0e
1 + ψAM− µrAM

so it is unclear if the t = 1 regulatory constraint can be “stronger” than the t = 0 constraint. In
the event of default, λ > λ∗ , deposit payout ise− µrAM (λ∗ − ς) − ς
1 + ψAMδ d (λ) =e
1 + ψAM− µrAM λWe can use the expression for the default cutoff to write dividends in the PM as
n 

 o
e
δPe M = max 0, ψAM− µrAM λ∗ − λ d0
which shows that the effect of regulation on PM dividends is ambiguous. The increasing λ∗ isbeneficial, but the “return” on morning resources is lower.
(IV).

No equity raising + Repression: It is clear from the Euler equations, that κ ̸= 0

introduces a wedge between the AM asset returns. Asymmetric regulatory treatment makes
the otherwise perfectly substitutable assets different. This implies that banks will have a clear
preference which asset they want to hold and make morning trades so that the t = 1 regulatory
constraint always binds. In particular,
zP M
δPb M
+ κµrAM = k
b
qAM
qAM

⇔

41

b
qAM
δPb M
=
k
k
qAM
zP M − κµrAM qAM

The binding regulatory constraint implies the following “asset demand functions”:


b
b
k
κqAM
bAM = ϱδ d (1 − λ)d0 − (1 − κ) qAM
bAM + qAM
kAM
and


k
b
k
κqAM
kAM = −ϱδ d (1 − λ)d0 + qAM
bAM + qAMkAM= −ϱδ d (1 − λ)d0 + ℓAM − δ d λ d0
The consolidated budget constraint can be used to express dividend in the PM



e
k
b
k
δPe M (λ) = 1 + ψAM− µrAM qAM
kAM + qAM
bAM + κµrAM qAM
kAM (λ) − δ d (1 − λ)d0





e
= 1 + ψAM
ℓAM − δ d λ d0 − 1 + ϱµrAM δ d (1 − λ)d0
where the orange term highlights the effect of the asymmetric regulatory treatment of assets.
The second equality uses the binding regulatory constraint to substitute out the orange term.
The default cutoff is (where 1 denotes the event {κ ̸= 0}):e
− µrAM + 1µrAM ℓAM − 1 + 1ϱµrAM
1 + ψAM


λ∗ :=
e
ψAM
− µrAM + 1(1 − ϱ)µrAM


In the event of default, λ > λ∗ , deposit payout ise
1 + ψAM− µrAM + 1µrAM ℓAM − ςδ d (λ) = e
1 + ψAM− µrAM + 1µrAM λ + 1 + 1ϱµrAM (1 − λ)We can use the expression for the default cutoff to write dividends in the PM as
n 

 o
e
δPe M = max 0, ψAM− µrAM + 1(1 − ϱ)µrAM λ∗ − λ d0
A.2.2

Market clearing in AM asset marketsbk(i) κ = 0: (δPb M /qAM
= zP M /qAM): The portfolio shares are indeterminate, but the two asset

markets must clear at the aggregate:
Z


k
b
qAM
∆k + qAM∆b dF = 0Z λ∗(zAM m0 − λd0 ) dF = −

42

Z
λ∗


zAM m0 − ςd0 − δ d (λ)λd0 dF

(ii) κ ̸= 0: Market clearing on the debt market requiresRbAM = b0 which becomes:Z ϱδ d (λ)(1 − λ) − (1 − κ) ℓAM − ς 1{δ d < 1} − δ d (λ)λκ
Market clearing on the capital market requires

R

b
qAM
b0
d0

kAM = k0 which becomes:Z −ϱδ d (λ)(1 − λ) + ℓAM − ς 1{δ d < 1} − δ d (λ)λ
κ
A.2.3

dF =

dF =

k
qAM
k0
d0

Aggregate resource constraints

The banks aggregated budget constraints in the AM can be written as (where we also use
RR∆kdF = ∆bdF = 0:
"Z
|

λ∗

λdF (λ) +Zλ∗#δ (λ)λdF (λ) d0 = zAM m0 − ςd0 (1 − F (λ∗ ))d{zaggregate payout to early households}

where the last term is equal to aggregate consumption (from household BC)
Z

λcAM (1, λ)dF (λ) ="Z ∗λλdF (λ) +Zλ∗#δ (λ)λdF (λ) d0d

The aggregated bank budget constraint in the PM isZ δPe M (λ) + (1 − λ)δ d (λ)d0 dF (λ) = zP M k0 + δPb M b0

while aggregate consumption in the PM (from the household budget constraint) is
Z

Z



(1 − λ) δPe M (λ) + δ d (λ)d0 − τ dF (λ)
Z= zP M k0 + δPb M b0 − λδPe M (λ)dF (λ) − TP M

(1 − λ)cP M (0, λ)dF (λ) =43

A.2.4

Choice of initial portfolio

The FOCs with respect to period t = 0 choices are
∂q0e
∂q0d
d0 +
+ κm µr0
∂m0
∂m0
∂q e
∂q d
0 = − 1 + 0 d0 + 0 + (1 − κ)µr0
∂k0
∂k0
d
∂q
∂q e
0 = − q0b + 0 d0 + 0 + µr0 q0b
∂b0
∂b0


d
e
∂q
∂q
∂q0d
0
0
d
r
d
0 =q0 +d0 +− ϱµ0 q0 +
d0
∂d0
∂d0
∂d0

[m0 ]

0=−1+

[k0 ]
[b0 ]
[d0 ]

Before we get to the partial derivatives of prices, note that for x ∈ {m0 , k0 , b0 , d0 }
∂δ d
=
∂x



∂λ∗
∂x






r
r
e
+
1
(1
−
ϱ)µ
−
µ
ψ
AM
AM

 AM
  δde
1 + ψAM− µrAM + 1µrAM ℓAM − ςand for simplicity, let’s defineeR := ψAM− µrAM + 1(1 − ϱ)µrAM

We use the Leibnitz integral rule several times to obtain for x ∈ {m0 , k0 , b0 , d0 }
1
∂q0e
= cE
∂x
µ0

" Z ∗
λ

!
ξ(λ)dF (λ) R



∂λ∗
∂x



#
d0 +

q0e
1{x=d0 }d0

The partial derivatives of the deposit price w.r.t. x ∈ {m0 , k0 , b0 , d0 } are
∂q0d
∂x


Z
= E



  ∂λ∗ ξ(λ) 1 + ν(λ)∂xλ∗1 + ψeRrAM − µAM +

1

µrAM



ℓAM − ς  δ d (λ)dF (λ) +




i
h  ∂λ∗ ξ(λ∗ ) 1 + ν(λ∗ ) 1 − δ d (λ∗ ) f (λ∗ )+E∂xwhere the last term comes from the discontinuity in the deposit payoff at λ∗ , and1 − δ d (λ∗ ) =

44

ς
ℓAM



Using these objects, we can write x ∈ {m0 , k0 , b0 }





 ∗
nZ
1
+
ν(λ)
∂λ
 dF (λ)+



d0 +
= E
d0 R
ξ(λ)  
∂x
∂x
∂x
e
λ∗
1 + ψAM− µrAM + 1µrAM λ + 1 + 1ϱµrAM (1 − λ)






Z
Z λ∗
o
ξ(λ∗ ) 1 + ν(λ∗ ) 1 − δ d (λ∗ ) f (λ∗ )  dF ++ξ(λ) 
ξ(λ)dF (λ) ξ(λ)Rλ∗1 − F (λ∗ )

∂q0d

∂q0e

and










nZ
1 + ν(λ)
∂q e
∂q d

  δ d (λ)dF (λ)(1 − ϱµr0 )+(1 − ϱµr0 ) 0 d0 + 0 = E (−µAM ℓAM )ξ(λ) 
∂d0∂d0∗
λµAM ℓAM − ςξ(λ∗ ) 1 + ν(λ∗ ) 1 − δ d (λ∗ ) f (λ∗ )  δ d (λ)dF (1 − ϱµr0 )+ξ(λ) 
ξ(λ)δ d (λ)R∗λ∗
1 − F (λ )





Z λ∗
o
µAM λ + 1 + ϱµrAM (1 − λ) dF (λ) +ξ(λ) 
µAM ℓAM


Z

Using
∂λ∗
∂λ∗
∂λ∗
∂λ∗
µAM ℓAMkb
d0 R = µAM zAM ,k0 R = µAM qAM,
d0 R = µAM qAM,
d0 R = −
∂m0
∂k0
∂b0
∂m0
d0
the FOCs becomehi
1 − κm µr0 =E ξ(λ)Ω(λ)zAM


h
i
k
1 − κk µr0 =E ξ(λ)Ω(λ)qAM


h
i
b
q0b 1 − κb µr0 =E ξ(λ)Ω(λ)qAMhideq d =E ξ(λ)Ω(λ)Ω(λ)δ
(λ)

[m0 ]
[k0 ]
[b0 ]
[d0 ]

0

where
Ω(λ) :=

 (1+ν(λ))δd (λ) + µ(ℓAM −ς)AMξ(λ∗ )(1+ν(λ∗ )) ςf (λ∗ )
ξ(λ)RℓAM (1−F (λ∗ ))λ > λ∗λ ≤ λ∗

µ

AM

and


ℓAM /δ d(λ)
eΩ(λ):= µ λ+ 1+ϱµr
AMAM (1−λ)µAM (1−ϱµr0 )45

λ > λ∗λ ≤ λ∗

Looking at the formula for Ω it is pretty clear that it arises from the equity raising cost (see thepresence of µAM ) and regulation has only an indirect affect through λ∗ (and R and δ d ), which
is why this decomposition makes sense (sort of).

46

B

Exogenous Bond Demand Functions

B.1

Exogenous Bond Demand: Bond-in-Advance

B.1.1

Environment

Setting: The economy lasts for three periods: t ∈ {0, 1, 2}. We interpret t = 0 as a primary asset
market, t = 1 as a morning market, and t = 2 as the following period. There is one consumption
good. There are two production technologies in the economy: one that transforms m0 goods attime t = 0 to z1 (s1 )m0 goods at time t = 1 (short-term asset) and another one that transforms
k0 goods at time t = 0 to z2 (s1 )k0 goods at time t = 2 (capital), where s1 is the aggregate statethat has distribution Π(s1 ) and is realized at the beginning of t = 1.
Assets and Markets: We use goods as the numeraire. At t = 0, the government issues bonds inthe primary market at price q0b that pay δ2b at time t = 2. At t = 1, the agents are only able totrade bonds for goods at price q1b . They cannot trade capital.
Government: The government ranks allocations according to:θG + U
where G is the provision of public goods by the government and U is the aggregate lifetime
household utility under equal Pareto weights. Parameter θ is interpreted as the relative value of
public goods. At t = 0, the government finances public good provision by issuing B0 bonds atprice q0b leading to the t = 0 budget constraint:G ≤ q0b B0
At time 2, the government raises taxes T2 (s1 ) from households at t = 2, which it uses to repayδ2b (s1 ) per unit of bonds according to:δ2b (s1 )B0 ≤ T2 (s1 )where δ2b (s1 ) < 1 is interpreted as “partial default” or “dilution” when the government decreases
the real value of the bond principle. We refer to T2 (s1 ) as the government “fiscal rule” and treat
it as an exogenous outcome of an unmodelled political process. The exogenous T2 (s1 ) pins down
an upper bound on B0 .
Household problem: Agents cannot consume their own goods. Instead, they can only consume
goods produced by other agents. All agents rank consumption allocations at t = 1 and t = 247

according to:λu(c1 ) + (1 − λ)u(c2 ).
At time 0, households rank allocations according to:
U := E λu(ch1 ) + (1 − λ)u(ch2 ) ,where ch,it denotes consumption of household h on island i in period t ∈ {1, 2} and the expectationis only taken over s. Each household is endowed with one unit of good at t = 0 and zero goodsin the other periods. All agents have the time 0 budget constraint:
q0b bh0 + mh0 + k0h ≤ 1
where bh0 , mh0 , and k0h are household h’s bond, short asset, and capital holdings. At t = 1, thehouseholds face the budget constraint and the bond-in-advance constraint:
ch1 + q1h bh1 ≤ q0b bh0 + z1 m0
ch1 ≤ q1b bh0
At t = 2, the households face the budget constraint:
b h
h
ch,i
2 ≤ δ2 b1 + z2 k0 − τ (s)B.1.2

Household Problem

Taking prices (q0b , q1b ) as given, the household solves:
max

h h h
bh
0 ,m0 ,k0 ,b1 ,cE[λu(ch1 ) + (1 − λ)u(ch2 )] s.t.

q0b bh0 + mh0 + k0h ≤ 1
ch1 ≤ q1b bh0
ch,i
2 ≤

δ2b b h(q b + zm0 − ch1 ) + z2 k0h − τ (s)q1h 1 0bh0 , mh0 , k0h , bh1 ≥ 0
Lagrangian is (leaving the short selling constraints implicit): b
δ2 (s) bhhh
L = E λu(ch1 (s)) + (1 − λ)u
(q
(s)b
+
z
(s)m
−
c
(s))
+
z
(s)k
−
τ
(s)
1
0
2
0
1
0
q1h (s) 1+ µ0 1 − q0b bh0 − mh0 − k0h+ E µb1 (s) q1b (s)bh0 − ch1 (s)48The first order conditions are following: (Note that this maps to the bank problem if they canchoose δ1d freely as a function of the state).
[ch1 (s)] :[mh0 ] :[k0h ] :[bh0 ] :δ b (s)− µb1 (s)0 = λu′ (ch1 (s)) − (1 − λ)u′ (ch2 (s)) 2b
q1 (s)δ b (s)0 = − µ0 + E (1 − λ)u′ (ch2 (s)) 2b z1 (s)q1 (s)′ h0 = − µ0 + E (1 − λ)u (c2 (s)z2 (s)µb1 (s)q1b (s)b
0 = − µ0 q0b + E (1 − λ)u′ (ch2 (s)) 1 +δ(s)(1 − λ)u′ (ch2 (s)) δ2b (s) 2

If the bond-in-advance constraint binds, then we have that (c1 (s), b1 ) satisfies:
c1 (s) = q1b (s)b0
q1b (s)b1 = z1 (s)m0
If the bond-in-advance constraint doesn’t bind, then we have that (c1 (s), b1 ) satisfies:
λu (ch1 (s)) = (1 − λ)u′
′

 b
 b
δ2 (s) b
δ (s)
h
h
h
(q1 (s)b0 + z1 (s)m0 − c1 (s)) + z2 (s)k0 − τ (s) 2bh
q1 (s)
q1 (s)

q1b (s)b1 = q1b (s)bh0 + z1 (s)m0 − ch1 (s)B.1.3

Market Clearing

The market clearing conditions at t = 0 are:b0 = B0 ,q0b b0 + m0 + k0 = 1

The market clearing conditions at t = 1 are:b1 (s) = B0 ,c1 (s) = z1 (s)m0

The market clearing condition at t = 2 is:c2 (s) = z2 (s)k0
B.1.4

Equilibrium Characterization

We start by considering market clearing at t = 1. Assuming that the bond-in-advance constraint
binds, then the bond market and goods market must satisfy:
q1b (s) =z1 (s)m0,
B0

c1 (s) = z1 (s)m049

In summary, the 9 equilibrium variables (b0 , m0 , k0 , c1 (s), c2 (s), µ0 , µb1 (s), q0b , q1b (s)) satisfy (ifthe bond-in-advance constraint binds):
δ b (s)− µb1 (s)0 = λu′ (c1 (s)) − (1 − λ)u′ (c2 (s)) 2b
q1 (s)δ b (s)µ0 = E (1 − λ)u′ (c2 (s)) 2b z1 (s)q1 (s)µ0 = E [(1 − λ)u′ (c2 (s)z2 (s)]
µ0 q0b = E (1 − λ)u′ (c2 (s)) 1 +µb1 (s)q1b (s)(1 − λ)u′ (c2 (s)) δ2b (s)δ2b (s)b0 = B0
1 = q0b b0 + m0 + k0
q1b (s) =z1 (s)m0
B0

c1 (s) = z1 (s)m0c2 (s) = z2 (s)k0
Combining the equations we get that:δ2b (s)λu (c1 (s)) − (1 − λ)u (c2 (s)) qb (s)µb1 (s)1=1+1+
δ b (s)(1 − λ)u′ (c2 (s))(1 − λ)u′ (c2 (s)) 2b′′

q1 (s)=λu (c1 (s))′δ b (s)(1 − λ)u′ (c2 (s)) q2b (s)1=λu′ (c1 (s))δ b (s)B(1 − λ)u′ (c2 (s)) z12(s)m00

Thus, the bond market Euler equation becomes:µb1 (s)q1b (s)bµ0 q0b = E (1 − λ)u′ (c2 (s)) 1 +δ(s)(1 − λ)u′ (c2 (s)) δ2b (s) 2"#
λu′ (c1 (s))′= E (1 − λ)u (c2 (s))
B0(1 − λ)u′ (c2 (s)) z1 (s)m
0


z
(s)m
1
0
= E λu′ (c1 (s))
B0z1 (s)m0= E λu′ (z1 (s)m0 )B0which seems to be independent of δ2b (s)50B.1.5

Convenience yields

Define the price of the “synthetic asset” by:
µ0 q̃0b := E (1 − λ)u′ (c2 (s))δ2b (s)So, I think the convenience yield is:log(q0b ) − log(q̃0b ) = log


 


z1 (s)m0′− log E (1 − λ)u′ (c2 (s))δ2b (s)E λu (z1 (s)m0 )B0which is decreasing in δ2b because the bond-in-advance constraint makes ends up making q0b
independent of δ2b .

B.2

Bond in Utility

Consider the bond-in-utility model where the household solves:max

b0 ,k0 ,c1

ν(q0b b0 ) + βE[u(c1 )]s.t.

q0b b0 + k0 ≤ 1
c1 ≤ z1 (s)k0 + δ1b (s)b0
Let µ0 be the Lagrange multiplier on time t = 0 budget constraint. The first order conditionsare:
q0b (µ0 − ν ′ (q0b b0 )) = E[u′ (z1 (s)k0 + δ1b (s)b0 )δ1b (s)]µ0 = E[u′ (z1 (s)k0 + δ1b (s)b0 )z1 (s)]Define the price of the synthetic asset by:µ0 q̃0b = E[u′ (z1 (s)k0 + δ1b (s)b0 )δ1b (s)]So the convenience yield is:log(q0b ) − log(q̃0b ) ≈ν ′ (q0b b0 )µ0Again, since q0b is increasing in δ1b (s) and ν ′ (·) is a decreasing function, a decrease in δ1b (s) leads
to an increase in ν ′ (q0b b0 ).

51

C

Data Sources

We combined existing historical databases with transcription from the digital archives of newspapers and government reports. Before 1884, we take bond data from Global Financial Data
(GFD). From 1884 to 1940, we collect digitize and organize data from The New York Times, theCommercial & Financial Chronicle, Merchant’s Magazine, and Macaulay et al. (1938). We use
the risk classifications from Macaulay et al. (1938) to create a collection of high-grade corporate
bonds.

D

Historical Time LineThe text references many changes to monetary and financial regulation. In this section, we collectthose events into a historical timeline, which is shown in table 1. The time line is broken up
into a collection a collection of banking “eras”. The first era is from 1791-1836, during which theFirst and Second Banks of the US operated alongside state banks. The second era is from 18371962, during which state banks could automatically gain bank charters without a congressional
review process, often referred to as the “free banking” era. The third era is from 1863-1913,
during which the federal government charted national banks that issued bank notes backed by
US federal government debt. The fourth era is from 1913-1933, during which the Federal Reserve
Bank was introduced to act as lender-of-last resort to the banking sector. The fifth era is from
1934-1980, during which the New Deal financial regulations were in place. The sixth era is from1980s-2009, during which the New Deal financial regulations were gradually unwound. Finally,
there is the era from 2010 to the present day, during which the Dodd-Frank Act another financial
crisis legislation are in place.
Table 1Time Line of Monetary and Financial Events

1791 • Congress charters the First Bank of the US. The bank is privately owned. It
operates as a commercial bank but also has the special privileges of acting asbanker for the federal government (storing tax revenue and making loans) andbeing able to operate across states. It shares responsibility with state banks
for bank note issuance. It influences state bank money and credit issuance bysetting the rate at which it redeems state notes collected as tax revenue into
gold.
1792 • Coinage Act of 1792. Authorizes the US to issue a new currency, the US gold
dollar.
1811 • Charter of the First Bank of the US expires and is not renewed.
1812-5 • War of 1812. Convertibility to bank notes to gold is suspended. Government
issues Treasury Notes to finance the war.
52

1816 • Congress charters the Second Bank of the U.S.
1819 • Panic of 1819. Cotton prices fall, farms go bankrupt, and banks fail.
1832 • Jackson vetoes bill to recharter Second Bank.
1833 • Jackson removes federal deposits from Second Bank of the US
1834 • Coinage Act of 1834. Changes the ratio of silver to gold from 15:1 to 16:1.
1836 • Charter of the Sector Bank of the US expires and is not renewed. The Second
Bank becomes a private corporation.
1837 • “Free Banking” Era begins. Michigan Act allows the automatic chartering ofbanks (without requiring explicit approval from state legislature) that issuebank notes backed by specie (gold and silver coins). Over the next few years,
other states pass similar laws.
1837 • Panic of 1837. Sharp decrease in real estate prices leads to large bank losses.
In New York, every bank suspends payment in gold and silver coinage. Manybanks fail.
1857 • Coinage Act of 1857. Foreign coins can longer be legal tender.
1857 • Panic of 1857. Railroad company stocks drop sharply. Ohio Life Insurance
and Trust company fails, which prompts a collapse in stock prices andwidespread failures across mercantile firms.
1861-5 • Civil War.
1862 • Legal Tender Act. Authorizes the federal government to use nonconvertible
greenback paper dollars to pay its bills.
1863-4 • The National Bank Acts. The National Currency Act (1863) and The
National Bank Act (1864) establish a system of nationally charted banks andthe Office of the Comptroller of the Currency. National banks can issue
national bank notes up to 90% of the minimum of par and market value ofqualifying US federal bonds. Limit on aggregate national bank note issuanceis $300 million. Banks must pay a 1% annual tax per on outstanding nationalbank notes backed by US federal bonds. State banks must start paying a 2%
annual tax on state bank notes.
1865-6 • Additional National Bank Acts. State banks must start paying a 10% annual
tax on state bank notes.
1870 • Limit on aggregate national bank note issuance increases to $354 million.

53

1873 • Bank panic of 1873. Widespread failure of railroad firms leads to stock
market crash and bank failures. Jay Cooke and Company goes bankrupt.
1875 • Congress repeals limit on aggregate national bank note issuance.
1879 • US Treasury starts to promise to convert greenbacks to dollars one-for-one.
1893 • Bank panic. A combination of falling commodity prices, oversupply of silver,
and a fall in US Treasury gold reserves prompted a run on bank deposits.
1896 • Cross of Gold Speech. Democratic presidential candidate William Jennings
Bryan gives a speech in favor of allowing unlimited coinage of silver intomoney demand (“free silver”).
1900 • Tax on national bank notes backed by US federal bonds paying coupons lessthan or equal to 2% is reduced to 0.5% per annum.
1900 • Gold Standard Act. The gold dollar becomes the standard unit of account(further restricting the possibility of “free silver”).
1907 • Panic of 1907. The Knickerbocker Trust Company collapses prompting abank run. J.P. Morgan organizes New York bankers to provide liquidity toshore up the banking system.
1913 • Federal Reserve Act. Establishment of the Federal Reserve Bank to act as areserve money creator of last resort during financial panics.
1914-8 • World War I.
1917 • 2nd Liberty Loan Act establishes a $15 billion aggregate limit on the amountof government bonds issued.
1929 • Stock market crash and start of the Great Depression.
1929 • US issues first Treasury Bill.
1933 • Banking Act (“Glass-Steagall Act”). Establishes the Federal Deposit
Insurance Corporation (FDIC). Separates commercial and investmentbanking. Introduces cap on deposit interest rate (“Regulation Q”).
1933 • President Roosevelt issues an Executive Order requiring people andbusinesses to sell their gold to the government at $20.67 per ounce.
1934 • Gold Reserve Act.
1934 • National Housing Act. Establishes the Federal Savings and Loan Insurance
Corporation (FSLIC).
1935 • The last national bank notes are replaced by Federal Reserve notes.

541938 • Amendment to the National Housing Act established the Federal National
Mortgage Association (FNMA), commonly known as Fannie Mae.
1939-45 • World War II.
1942 • The Treasury and Federal Reserve agree to fix the yield curve on Treasury
securities.
1944 • Bretton Woods Agreement.
1951 • Treasury-Fed Accord ends the fixed yield curve on Treasury securities andestablishes the Fed’s policy independence from fiscal concerns.
1968 • Housing and Urban Development Act of 1968. Creates the Government
National Mortgage Association (GNMA), commonly known as Ginnie Mae.
1966 • Fed applies Regulation Q to impose deposit rate ceiling for the first time.
1971 • US effectively terminates the Bretton Woods system by ending theconvertibility of the US dollar to gold.
1977 • Congress issues the Fed with the dual mandate to “promote effectively thegoals of maximum employment, stable prices, and moderate long terminterest rates”.
1980 • Depository Institutions Deregulation and Monetary Control Act of 1980
starts to phase out Regulation Q.
1986-1989 • Savings and loan crisis.
1994 • Riegle-Neal Interstate Banking and Branching Efficiency Act. Allows banks
to operate across states.
1999 • Gramm–Leach–Bliley Act. Repeals provisions of the Glass-Steagall Act thatprohibited a bank holding company from owning other financial companies.
2007-9 • Great Financial Crisis.
2010 • Dodd-Frank Wall Street Reform and Consumer Protection Act.

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