Convenience Yields and Financial Repression
Jonathan Payne
PrincetonBálint Szőke
FED Board

IMF-CARF-TCER-Waseda University Conference
June 7, 2024
Disclaimer: The views expressed here are those of the authors and do notnecessarily represent the views of the Federal Reserve Board or its staff.

US government has enjoyed a large funding advantage since 1860
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
Greenback

FED

Gold Standard

FDR

New Deal

Financialderegulation

Bretton
Woods

Fiat
Money

DoddFrank

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High-Grade Corporate - Government Yield Spread

Convenience Yields vs Debt/GDP — exploitable “demand function”?
3.0

National Banking Era (1868-1914)
WWII and its aftermath (1940-1965)
Interwar period (1915-1940) and (1966-2007)
Crisis, Dodd-Frank Act and QE (2008-2022)

2.5
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Payne, Szőke

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Market Value of Government Debt/GDP
Convenience Yields and Financial Repression

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This Paper: Endogenizes the Convenience Yield▶ We build a model where the convenience yield emerges through financial regulation.
▶ Government debt is not inherently special, but financial repression can make it so▶ Convenience premium comes from hedging aggregate risk (Acharya and Laarits, 2023)▶ Environment has a risky financial sector:▶ Banks create on-demand assets + intermediation between savers and borrowers▶ . . . but prone to costly default and “fire sale” dynamics ⇒ hedging is valuable▶ We study a government that wants to finance spending:▶ Cannot change taxes (has a pre-specified “fiscal rule” from the political process)▶ But can impose restrictions on bank portfolios (“regulation” or “repression”)

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Results
1. Portfolio restrictions make government debt a hedge with “convenience-yield”.
▶ Restrictions bind more in bad times and so bank demand increases in bad times.
▶ Regulatory parameters relate to “exogenous” bond demand elasticities.

2. High convenience yields come at the “cost” of financial instability (and crowding out)
3. Fiscal irresponsibility erodes the convenience yield.
4. Exogenous bond demand (bond-in-utility, bond-in-advance, . . . ) miss 2 & 3.

Takeaway: Convenience yield is a choice, not invariant to regulation or fiscal policy

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Table of Contents
Introduction
Illustrative 3-Period Model
Environment
Financial Repression: Costs and Benefits
Is the Convenience Yield Invariant to Fiscal Policy?
Cross Section of Convenience Yields in the Eurozone
Conclusion

Preferences (“Diamond-Dybvig” Style)(λ, s)
t=0

t=1

t=2

(m0 , k0 , q0b b0 )u(c1 ) w.p. λu(c2 ) w.p. 1 − λ▶ Continuum of islands each with unit measures of households and banks▶ One consumption good; households are endowed with one unit at t = 0▶ Two “layers” of idiosyncratic preference shocks at the start of t = 1:
▶ household-specific: households value t = 1 consumption with prob. λ▶ island-specific: probability λ ∼ F is random across islands.

▶ Banks issue on-demand deposits d0 and equity e0 to households on the same island▶ Deposits can be withdrawn for 1 good at t ∈ {1, 2}, unless bank defaults ⇒ δ d < 1
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Household Problem▶ Taking prices as given, household solves:max

d0 ,e0 ,chZEλu(c1 (λ)) + (1 − λ)u(c2 (λ))dF (λ)

i

s.t.

q0d d0 + q0e e0 ≤ 1
and the t = 1 “deposit-in-advance” constraint for early consumers:c1 (λ) ≤ δ d (λ)d0 ,where δ d (λ) = 1, if bank solvent

and the t = 2 budget constraint for late consumers:c2 (λ) ≤ δ2e (λ)e0 + δ d (λ)d0 − T2
Liquidity premium on bank deposit:
only on-demand assets can be used for consumption at t = 1
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Technology and Markets(λ, s)
t=0

t=1

t=2

(m0 , k0 , q0b b0 )(z1 (s), q1k (s), q1b (s))(0, z2 , δ2b (s))▶ Time 0: Three investment opportunities exposed to aggregate risk s ∈ {sL , sH }:▶ Short asset (m0 ), transforms one good at t = 0 to z1 (s) goods at t = 1▶ Capital (k0 ), transforms one good at t = 0 to z2 > z1 (s) goods at t = 2▶ Bond (b0 ), for price q0b (primary market), it promises to pay δ2b (s)b0 at t = 2▶ Time 1: Secondary markets for bonds (at q1b ) and capital (at q1k ):“Fire sale pricing” in inter-bank asset markets at t = 1:
No bank equity issuance and no short selling ⇒ q1k (s) < z2 , q1b (s) < δ2b (s)Payne, Szőke

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Bank Problem▶ Taking prices and household SDF {ξ(λ)}λ as given, the bank maximizes its value:n hZ

max e Em0 ,k,b,d,δ

n

o

i

o

ξ(λ)max 0; δ2e (λ) dF (λ) + q0d d0 − m0 − k0 − q0b b0 s.t.

δ1d (λ)λd0 + ςd0 1d ≤ z1 m0 + q1k (k0 − k1 (λ)) + q1b (b0 − b1 (λ))|{z

Withdrawals

}

|

{z

Short asset + sale of long term assets}δ2e (λ) + δ2d (λ)(1 − λ)d0 ≤ z2 k1 (λ) + δ2b b1 (λ)
0 ≤ b1 (λ), k1 (λ),
Costly bank default:
Deposit contracts are not fully state contingent on (λ, s) + limited liability

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Government▶ Ranks equilibria by: θG + E
λu(c1 (λ)) + (1 − λ)u(c2 (λ)) dF (λ)
where spending G at t = 0 is financed with debt b0 that is repaid using taxes at t = 2:
R



G = q0b b0 ,

δ2b (s)b0 = T2 (s)Exogenous fiscal rule: T2 (s) determined outside the model (political process)▶ Sets restrictions on bank portfolios:
ϱ d(q d0 − m0 ) ≤ κq0b b0 + (1 − κ)k0 ,2 0ϱ
d1 ≤ κq1b b1 + (1 − κ)q1k k1
2
Regulation: ϱ is overall leverage constraint; κ ∈ [1/2, 1] incentivizes debt holding. . . κ = 1/2 “neutral” regulation;

κ = 1 is “pure” repression;(ϱ, κ) ≈ “risk-weights”

Table of Contents
Introduction
Illustrative 3-Period Model
Environment
Financial Repression: Costs and Benefits
Is the Convenience Yield Invariant to Fiscal Policy?
Cross Section of Convenience Yields in the Eurozone
Conclusion

Inter-bank Market Equilibrium (Conditional on t = 0 choices)▶ Equilibrium in inter-bank asset markets require:q1k (s) =z2 (s)e
1 + µ1 (s) − (1 − κ)µr1 (s)q1b (s) =δ2b (s)1 + µe1 (s) − κµr1 (s)▶ µe1 is the Lagrange multiplier on the (time 1) equity raising constraint▶ µr1 is the Lagrange multiplier on the (time 1) regulatory constraint▶ If κ = 1/2 (“neutral regulation”), then banks are indifferent between b1 and k1 :kbR1,2(s) = R1,2(s)

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Inter-bank Asset Prices Move with “Market Liquidity”

Parameters

Inter-bank Market Equilibrium (Conditional on t = 0 choices)▶ If κ > 1/2 (“repression”), asset demand is tilted toward debt:kbR1,2(s) − R1,2(s) = (2κ − 1)µr1 (s) > 0▶ In the bad state, sL , there are fewer resources and so ↑ µr1 (sL ) and ↑ q1b (s)/q1k (s)(i.e. regulation makes banks a “captive market” for government debt in bad times)

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Repression Makes Government Debt a Hedge Against Aggregate Risk

Parameters

Convenience Yield Increases Fiscal Capacity (benefit)▶ Bank demand for government debt at t = 0:"q0b = EξΩ(µe1 , µr1 )|{zdefault}|(1 − κµr0 )−1
1 + µe1 − κµr1

!

{z

}

regulation

#

δ2b

>

h i

q0s := E ξ▶ µr0 , direct effect of repression: forcing the bank to hold debt in the primary market▶ µr1 , indirect effect through captive demand in the secondary market (and default)

Convenience Yield: (often) defined as

Payne, Szőke

 

 

χ := log q0b − log q0s

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Decreasing “Risk-Aversion” Increases Financial Instability (cost)▶ Equilibrium in inter-bank asset markets requires:q1k (s) =z2 (s)e
1 + µ1 (s) − (1 − κ)µr1 (s)q1b (s) =δ2b (s)1 + µe1 (s) − κµr1 (s)▶ High µe1 (sL ) makes banks more “risk-averse” (by increasing endogenous default cost)▶ High µr1 (sL ) alleviates excess risk-aversion (by giving banks a hedging asset)⇒ Banks choose less short asset m0 at t = 0 exposing them to increased default risk

Financial instability: repression leads to more (less) default in bad (good) times
National Banking Era (1862-1913): high repression (κ ≈ 0.9), frequent bank crises
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Optimal κ balances fiscal capacity, financial stability, and investment

Table of Contents
Introduction
Illustrative 3-Period Model
Environment
Financial Repression: Costs and Benefits
Is the Convenience Yield Invariant to Fiscal Policy?
Cross Section of Convenience Yields in the Eurozone
Conclusion

Role of a Fiscal Rule — Risky Government Debt
▶ For risky δ2d (s) we need “risk-adjusted convenience yield” (measure of specialness): χ = log q0b − log E[ξδ2b ]
|



{z









+ log E[ξδ2b ] − log E[ξ]}|risk-adjusted convenience yield{z}

risk penalty. . . that can be further decomposed into
 













e = log q0b − log E[ξΩδ2b ] + log E[ξΩδ2b ] − log E[ξδ2b ]χ|{zdirect effect of regulation

}

|

{z

indirect hedging premium▶ Experiment: compare equilibria indexed by T2 (sL ) ↘ 0}⇒ δ2b (sL ) ↘ 0▶ Extension: banks can pay a fixed fee at t = 1 and escape regulatory constraint

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Fiscal Irresponsibility Erodes the Convenience Yield

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Two Alternative Environments with “Exogeneous Demand”
1. Bond-in-utility (BIU): private sector solves:max

b0 ,k0 ,c1

υ(q0b b0 ) + βE[u(c2 )]s.t.

q0b b0 + k0 ≤ 1
c2 ≤ z2 k0 + δ2b b0 − τ

2. Bond-in-advance with uninsurable idiosyncratic risk (BIA): private sector solves:max
b0 ,m0 ,k0 ,b1 ,cE[λu(c1 ) + (1 − λ)u(c2 )]s.t.

q0b b0 + m0 + k0 ≤ 1
c1 ≤q1b b0
c2 ≤ z2 k0 + δ2bPayne, Szőke

zm0 + q1b b0 − c1q1bConvenience Yields and Financial Repression−τJune 6, 2024

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Three Bond Demand Equations
Bond-in-utility:υ ′ (q0b b0 )q0b = E[ξδ2b ] 1 −
µc0

!−1

Bond-in-Advance:

q0b = E ξδ2b

µb
1− ′1
λu (c1 )!−1 Repression Model:"q0b = E ξδ2b Ω(µe1 , µr1 ) 1 + µe1 − κµr1

Payne, Szőke

#
−1 

1 − κb µr0

Convenience Yields and Financial Repression

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Similar Bond Demand Functions For a Fixed Fiscal Rule

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But Very Different Responses When Fiscal Irresponsibility Increases

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Table of Contents
Introduction
Illustrative 3-Period Model
Environment
Financial Repression: Costs and Benefits
Is the Convenience Yield Invariant to Fiscal Policy?
Cross Section of Convenience Yields in the Eurozone
Conclusion

Do Fiscal Troubles Erode the Convenience Yield in the Data?

▶ We use data on Eurozone debts during the Sovereign Debt Crisis as a laboratory. . . following closely Jiang, Lustig, van Nieuwerburgh, and Xiaolan (2024)▶ Risk-adjusted convenience yield differentials (2004-2024)▶ relative to Germany to control for the common risk-free rate
▶ use CDS spreads to control for compensation for default risk
▶ 5-year tenor (most liquid)

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Fiscal Troubles Tend To Erode the Convenience Yield
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Fiscal Troubles Tend To Erode the Convenience Yield
0.2
Difference in Risk-Adjusted Convenience Yield to Germany

High CDS Countries
Netherlands
FinlandFranceAustria

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Difference in Risk-Adjusted Convenience Yield to Germany

Low CDS Countries

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Payne, Szőke

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CDS Spread

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Table of Contents
Introduction
Illustrative 3-Period Model
Environment
Financial Repression: Costs and Benefits
Is the Convenience Yield Invariant to Fiscal Policy?
Cross Section of Convenience Yields in the Eurozone
Conclusion

Conclusion▶ Historical yield curves suggest government can exert high influence on government
bond demand through financial sector regulation.
▶ We build a model to understand the trade-offs.
▶ Q. Can the government choose the convenience yield with financial repression? Yes!
▶ Q. Should the government create a large convenience yield? Maybe!
▶ Q. Is the convenience yield invariant to fiscal policy? No!
▶ Work in progress: infinite horizon model with (i) long-term government debt, (ii)mean-reverting aggregate shocks, and (iii) an empirically plausible fiscal rule

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Thank You!

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Literature: Integration of Public Finance and Macro-Finance▶ Macroeconomic models of financial sector and government safe asset creation
Holmstrom and Tirole (1997), Holmström and Tirole (1998), Gorton and Ordonez (2013), Gorton (2017), Heet al. (2016), He et al. (2019), Caballero et al. (2008), Caballero et al. (2017), Caballero and Farhi (2018)▶ This paper: Taxation distortions and “shadow costs” of financial sector regulation.

▶ Historical asset pricing, market segmentation, and inelastic demand
Krishnamurthy and Vissing-Jorgensen (2012), Daglish & Moore (2018), Choi et al. (2022), Payne et al.
(2022), Jiang et al. (2022a), Chen et al. (2022), Jiang et al. (2022b), Jiang et al. (2021b), Jiang et al.
(2021a), Koijen and Yogo (2019)▶ This paper: Government strategically chooses inelastic demand.

▶ Ramsey planners and government policy
Calvo (1978), Bhandari et al. (2017b), Bhandari et al. (2017a), Chari et al. (2020), Bassetto and Cui (2021),
Sims (2019), Brunnermeier et al. (2022), Angeletos (2002), Buera and Nicolini (2004), Lustig et al. (2008)▶ This paper: Focuses on regulation in risky economy rather than debt issuance decision.
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1 / 31Competitive Equilibrium
Given a fiscal rule T2 , regulation (ϱ, κ), and a budget-feasible
government
policy


b
d
e
b
k
b
(G, b0 , δ2 ), a competitive equilibrium is a set of prices q0 , q0 , q0 , q1 , q1 and policies








dh0 , eh0 , c1 (λ), c1 (λ) and d0 , m0 , k0 , b0 , λ∗ , k1 (λ), b1 (λ) s.t.
1. Households and banks optimize
2. Markets clear:
dh0 = df0 ,eh0 = 1,Z

bf0 = b0 ,Z

b1 (λ)dF = b0 ,Z

λc1 (λ)dF = z1 m0 − ς (λ∗ ) d0Zλδ e (λ)dF

k1 (λ)dF = k0 ,Z

Payne, Szőke

G + m0 + k0 = 1,

(1 − λ)c2 (λ)dF = z2 k0 −Convenience Yields and Financial Repression

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Quantitative Illustration▶ Aggregate shock is a (common) TFP shock to the two types of capital:zAM (s) = zAM s,Parameter
γ
θ
zAM
zP M
TP M
(α, β)
ςzP M (s) = zP M s
Value
2
0.75
1
1.5
0.15
(4, 4)
1 − F (λ∗ )withs ∈ {1, 0.95} s.t. P[s = 0.95] = 0.05

Description
Risk aversion
Weight on fiscal capacity
TFP in the AM (good state)
TFP in the PM (good state)Tax in the PM
Withdrawal distribution, λ ∼ Beta(α, β)Deadweight default costWhy do other papers get a different result?
▶ We have default prone banks that play two roles in our model:
1. Liquidity provision, and
2. Investment into capital▶ Financial repression can help liquidity provision because it creates a “safe-asset”.
(connection to Gorton and Ordonez (2013), Gorton (2017))▶ But financial repression also hurts the economy:▶ Crowds out investment into capital (Chari et al. (2020))▶ Worsens frictions in the inter-bank market at time 1.
▶ Ultimately, increases bank default in the bad times.

US Financial Eras: with Varying “Restrictions” on Financial Sector▶ 1791-1862: State banks: Federal gov. issued coins; state banks issued paper money▶ 1862-1913: National Banking System: of federally regulated one branch banks▶ National banks issued bank notes backed by long term US Federal bonds.
▶ Looks very similar to our model with (κk , κb ) = (0, κ)▶ 1913+: Federal Reserve System established as lender of last resort.
▶ 1934+: Federal Deposit Insurance, Banks make LT mortgages & Glass-Steagall Act▶ 1942-1951: Yield curve control: treasury and Fed fix long rate at 2.5%
▶ 1944-1971: Bretton Woods: exchange rates fixed to dollar; dollar convertible to gold
▶ 1972-2007: Financial deregulation: interstate banking, repeal of Glass-Steagall Act▶ 2010-2023: Basel III accord, Dodd-Frank Act, and QE.
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Estimation: Corporate Bond Yields▶ Data: new database of price & cash-flows for US corporate bonds (1850-1940)(Companion to our database for US Federal bonds (1790-1940))▶ Sources: NYT, CFC, Merchant’s Magazine, US Treasury Circulars,
Bayley (1882), Sylla (2006), Razaghian (2002), Macaulay (1838).

▶ Statistics: Deploy methodology from Payne-Szoke-Hall-Sargent (2024):▶ Similar challenge: long time series but sparse cross-section at many dates.
Response: statistical model with drifting parameters that interpolates gaps.
▶ New challenge: no corporate bond ratings pre-1900.
Response: Extract pre-1900 “AAA” bonds using Macaulay (1838) + pricing errors.

▶ Output:▶ Zero-coupon yield curve on “AAA” US corporate bonds for 1860-1940.
▶ Convenience yield = “AAA” US corporate yield - US Federal yield for 1860-2022▶ We interpret convenience yield as measuring “funding advantage” of government
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6 / 31An exploitable demand function?
▶ Previous plot has sometimes been interpreted as exploitable stable demand function.
▶ Many macro models capture this using an exogenous bond demand function.
▶ But our model suggests that:▶ This curve reflects many regulatory shifts/skews in the bond demand function,▶ There are complicated costs with changing the shape of the demand function,▶ Ultimately reflects and equilibrium path of debt issuance in response to shocks.

▶ We integrate our illustrate model into dynamic macroeconomic model to study this.

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Why do BIU and BIA Get Different Results?
▶ Bond-in-Utility (BIU) and Bond-in-Advance (BIA) have the features:▶ “Specialness” of government debt is exogenous and▶ . . . its marginal usefulness increases as market value of government debt decreases▶ So, as the government devalues its debt it becomes more “useful”.
(the agents “like” to fund the government even more).

▶ In our Repression Model:▶ Government debt is not exogenously special▶ Government debt’s “safe-asset” role emerges from how regulation changes price process.
▶ Repression ties the solvency of the banking sector to the solvency of the government.
▶ ⇒ ↑ default (ultimately) leads to ↓ convenience yield

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Low Frequency Movements in Convenience Yield
16
14

10-year corporate greenback yield (high grade)
Moody's seasoned AAA corporate bond yield
10-year Treasury greenback yield
10-year Treasury gold yield
Long-term Treasury yield from KVJ

12
10
8
6
4
2

National Banking Era

FED

New Deal

Financialderegulation

DoddFrank

0
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

0Assets Composition (%)
.2
.4
.6
.8

1

Bank Asset Holdings

1896 1906 1916 1926 1936 1946 1956 1966 1976 1986 1996 2006 2016
year
B. OtherB. Fed Funds

B. Vault Cash

B. Reserves

B. Other Loans

B. Consumer Loans

B. Interbank

B. Mortgages

B. Other Sec.

B. Treasuries

Setting, Agents, and Production▶ Discrete time, infinite horizon, one consumption good.
▶ Representative firm produces goods by y = zt ktα lt1−α , where lt is labor,▶ zt is productivity; has evolution log(zt ) = (1 − η) log(z̄) + η log(zt−1 ) + ϵt ,▶ kt is firm’s capital stock; has evolution kt+1 = (1 − δ)kt + Φ(ιt )kt ,▶ Representative bank with financial technology:▶ Assets: purchases firm equity, sft and government bonds, bft .
e▶ Liabilities: deposits, dft , pay 1 good at t + 1, and equity, eft , pay δt+1
at t + 1.

▶ Friction: faces recapitalization “cost” if net-worth, Aft , goes negative.
1−φc

h

1−φd

(d −d)t▶ Representative household; utility u(ct , dht ) = (1 − ν) c1−φ+ ν t 1−φdc.

▶ Competitive deposit, firm, equity, capital markets with prices qtd , qtb , qts , qte , qtk .

Agents and Balance SheetsGovernment▶ Finances spending, g, using output tax, τ̂ , and debt, bt s.t. budget constraint:g + ζbt−1 ≤ τ̂t yt + qtb (bt − (1 − ζ)bt−1 )▶ bt is long-term debt that repays a fraction ζ ∈ [0, 1] of principal each period▶ Budget feasible tax policy: (following Bohn (98), Leeper (15), Bianchi et al. (23))
τ̂t+1
=
τ̂ ∗



yt
yt+1

γy

b̂t
b̂∗

!γb

 z γztz∗,x̂t :=xt,yt

γy , γb , γg ≥ 0▶ Sets restrictions on bank portfolio (modeled as a penalty):
ϱdft−1 ≤κb (ζ + (1 − ζ)qtb )bft−1 + κs (δts + qts )sft−1



⇔

1
µbt =
µ

ϱb dft−1κb (·) + κs (·)!µ▶ ϱ is constraint on risk taking; (κb , κs ) incentivise holding particular assets.
▶ National banking sets κst = 0 to get “collateral need”: dft−1 ≤ κb (ζ + (1 − ζ)qtb )bft−1▶ Basel III (approximately) sets κbt and κst as “risk-weights”,(

Household Problem▶ Household choose paths for consumption {c} and deposits, bank equity, firm shares{dh , eh , sh }, to solve:nmax E0∞Xoβ t u(ct , dht )s.t.

sht ≥ 0,dht ≥ 0,lt = 1,t=0

ct + qte eht + qtd dht + qts sht≤ (δts + qts )sht−1 + (δte + qte )eht−1 + dht−1

Environment friction: “transaction utility” u(·, dht ) enhanced by holding deposits.

Bank Problem▶ Morning: Value of bank assets, Aft := (ζ + (1 − ζ)qtb )bft−1 + (δts + qts )sft−1 :▶ Bank incurs recapitalization cost if Aft < dft (modeled as penalty Ψ(dft , Aft ))▶ Afternoon: Asset markets open. Bank chooses dividends and portfolio{δte , dft , bft , sft }t≥0 to maximize bank market value:
Vt (aft ) =maxδte ,bft ,sft ,dft

n

h

io

δte + Et ξt,t+1 Vt+1 (aft+1 ),

ξt,t+1 is household SDF

s.t. δte + qts sft + qtb bft − qtd dft ≤ aft

aft+1 = Aft+1 − dft − Ψ dft , Aft+1





b
s
s
ϱdft ≤ κb (ζ + (1 − ζ)qt+1)bft + κs (δt+1+ qt+1)sft ,

0 ≤ bft , 0 ≤ sft

Environment friction: Banks face resource cost Ψ(dft , Aft ) when “insolvent”.

Key Features of Environment▶ “Role of banking” is to create a safe deposits▶ “Cost of banking” banks face costly recapitalization, Ψ(·), when low net-worth(The cost of financial instability in our model)▶ Distortions break Modigliani & Miller and make safe deposit creation difficult:▶ Creating safe deposits exposes banks to costly recapitalization.
▶ Generates key distortion that household SDF differs from bank SDF.

▶ Clear welfare criteria because households are residual owners of banks and firms.

Equilibrium
Given a government fiscal rule and initial capital, k0 , a competitive equilibrium is asequence of prices {qtd , qte , qtb , qts }t≥0 , household and bank choices s.t.:
1. Households, banks, and firms solve optimize given prices.
2. Markets clear:dht = dft ,eht = 1,

bht + bft = bt ,yt − Ψt = ct + ιt kt−1 + gt ,3. Government budget constraint is satisfied.

sht + sft = 1,

Asset Pricing Equations: Deposit Market▶ Deposit market:hqtd = Et ξt,t+1

∂d ut+1 i
1+,∂c ut+1|{zHousehold demand}

Safe asset benefithqtd = Et ξt,t+1|

1 − ∂d Ψt+1 + ϱµt+1

i

{z

}

Distortion from solvency
costs and regulation

Bank supply▶ where µt+1 is the penalty on regulation constraint▶ If ν ≡ 0, then banks issue dt only if ∂a Ψt = 0▶ If Ψ ≡ 0 (and bank competition), then banks ↑ dt until ν ′ (d) = 0 and so qtd = E[ξt,t+1 ]▶ Otherwise, ∂Ψt distorts risk pricing of bank and qtd > E[ξt,t+1 ]▶ Ψ generates key distortion that household SDF differs from bank SDF.
Payne, Szőke

Convenience Yields and Financial Repression

June 6, 2024

17 / 31Asset Pricing Equations: Government Debt Market▶ Government debt market:b
qtb ≥ E[ξt,t+1 (ζ + qt+1
(1 − ζ))],"Household demand




#

b
qtb = Et ξt,t+1 1 − ∂A Ψt+1 + κb µt+1 (ζ + qt+1
(1 − ζ))|{z

distortion from solvency
costs and regulation

Bank demand}▶ If regulation penalty µt+1 is large during negative aggregate shocks, then government
debt acts as a good hedge ⇒ qtb is high (and convenience yield appears).
▶ Banks potentially value government bonds more than households because they allowbanks to hedge the cost of equity issuance when zt is low.

Payne, Szőke

Convenience Yields and Financial Repression

June 6, 2024

18 / 31

Parameter Values▶ State variables: (zt , kt , bt−1 , dt−1 , bft−1 , sft−1 )▶ We solve the model globally for following parameters (NOT a calibration):
Parameterβδζ(b∗ , γz )(ρz , σz )(ψ, ψ̄)(µ, µ̄, κb , κs , ϱ)

Value
0.99
0.025
0.025
(45, −0.1)(0.97, 0.05, 0.1)
(2, 0.01)(2, 0.01, κ, 0, 1)

Description
Discount factor
Rate of depreciation
Maturity of government debt (10 years)
Debt policy parameters
Parameters of log(z) (AR(1))
Distortion cost
Regulation penalty▶ We plot policies as function of z at stochastic steady state for other variables.

Impact of Regulation Depends on Bank Adjustment▶ Decrease in output zt ⇒ decrease in government debt and equity prices.
▶ Decrease in prices ⇒ tighter regulatory constraint! Banks can respond by:▶ Decreasing deposit creation (i.e. shrinking balance sheet), or▶ Buying more bonds (to better back their deposits)▶ How bank responds is governed by tradeoff:▶ ↓ deposits means giving up profits from providing liquidity services(governed by curvature in transaction utility u(·, dht ) from deposits)▶ ↓ deposits leads to ↓ leverage, which helps decrease solvency and regulatory costs(governed by curvature in resource cost Ψ(dft , Aft ) when insolvent)▶ If banks respond by re-balancing from firm equity to bonds, then ↑ qtb /qts
The more stable deposit demand in recession ⇒ the larger increase in qtb /qts

Inelastic Deposit Demand: κ makes z-shock gov. debt demand shockElastic Deposit Demand: κ makes q b more procyclicalConvenience Yields and Borrowing Cost Smoothing▶ Government funding advantage in our model:“Convenience yield” = Et [ξt,t+1/ζ ]−1 − ζ log(1/qtb )▶ In our model, “convenience yield” on long-term government debt comes from:▶ Regulation (the constraint ϱb ) leading banks to buy more debt in recessions.
▶ Government reducing bond supply in recessions (fiscal policy doesn’t do this).

▶ 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▶ Show how convenience yield moves along the equilibrium path.

No Regulation

Loose Regulation, Elastic Demand For Deposits

Tight Regulation, Inelastic Demand For Deposits

Intuition▶ The government increases debt/GDP when ↓ z.
▶ But, ↓ z causes regulatory constraint to bind and and so ↑ bank demand forgovernment debt.
▶ So, government can ↑ debt/GDP without facing an ↑ interest rate.

Household Welfare▶ Household welfare in equilibrium:nmax E0∞X

β t u(ct , dht )ot=0

ct = yt − Ψ(dt , At ) − ιt kt−1 − gtτ̂t yt = gt + ζbt−1 − qtb (bt − (1 − ζ)bt )kt Φ(ιt )[Φ′ (ιt )]−1 = qts ,qtb , qts , qtd

satisfy equilibrium conditions

Financial regulation to increase risk weight on government debt κb implies:▶ ↓ E0 [τ̂t yt ] because government faces higher q b when issuing debt.
▶ ? E0 [ιt ] because lower bank demand for equity ↓ qts but lower taxes ↑ qts .
▶ ↓ E0 [Ψ(dt , At )] because risk taking penalized and banks can better use
government debt to hedge risk.
Payne, Szőke

Convenience Yields and Financial Repression

June 6, 2024

25 / 31

Optimal κb balances tax smoothing, stability, and investment

Table of Contents

Data

Dynamic Model

Policy functions and payoffs

Payoffs and Individual Consumption

Payne, Szőke

Convenience Yields and Financial Repression

June 6, 2024

27 / 31Withdrawal distribution

Payne, Szőke

Convenience Yields and Financial Repression

June 6, 2024

28 / 31

SDF Formulas(1 − λ)u′ (cP M (λ))µc0λu′ (cAM (λ))
ν(λ) :=(1 − λ)u′ (cP M (λ))
ξ(λ) :=Ω(λ) :=

 1+ν(λ)+ ∆(λ) λ > λ∗(Rk −1)λ+1(1 − λ)−1 + ∆(λ)

ξ(λ∗ ) 1 + ν(λ∗ )∆(λ) :=

Γ(λ) :=

Payne, Szőkeξ(λ) (Rk − 1)λ∗ + 1kλ ≤ λ∗

kzP M k0 ς
f (λ∗ )

d0

b



!

R λ + 1 + κ(R − R ) (1 − λ)Convenience Yields and Financial Repression

June 6, 2024

29 / 31

Deposit Market at t = 0 [JP: Move to APPENDIX]"

q0d = E#dξ(λ) (1 + ν(λ)) δ (λ) ,|{zHousehold demand}

on-demand benefit#"

q0d = Eξ(λ) Ω(λ)| {z }dΓ(λ) δ (λ)

Bank supply| {z }

default regulation▶ If ν ≡ 0, then banks issue d0 only if Ω = 1▶ If Ω ≡ 0, then banks ↑ d0 until ν = 0▶ Otherwise, positive equilibrium liquidity premium on deposits q0d > E[ξ]λu′ (cAM (λ))▶ 1 + (1−λ)µc(λ) =: 1 + ν(λ)
AM

▶ where(Ω(λ) :=
Payne, Szőke∗∗(1+ν(λ))δ d (λ))) ς
f (λ∗ )+ µAM ξ(λ )(1+ν(λ(ℓAM −ς)ξ(λ)RℓAM (1−F (λ∗ ))λ > λ∗µConvenience
AM
Yields and Financial Repression

λ ≤ λ∗

June 6, 2024

30 / 31

Increasing κ reduces leverage and bank profit

Shareholder value:










k
b
(1 − λ)d0
VAM = Rk ℓ−1
AM − λ d0 − (1 − λ)d0 − κ R − R|{z

net worthkwhere Rk := zP M /qAM,}

| {z }

late depositb
Rb := 1/qAM
,

|

{z

loss from repression

and

}

λ∗ =

k
b
Rk ℓ−1AM − 1 + κ(R − R )

Rk − 1 + κ(Rk − Rb )kbℓAM := d0 /(zAM m0 + qAM
k0 + qAMb0 )