Monetary Financing
Without Inflation
Gregor Boehl
University of Bonn
Job hearing
Magdeburg University
Link to slides:
https://gregorboehl.com/revealjs/job_talk
Can central banks
monetize fiscal spending?
Consensus: No!
- Monetary financing is inflationary
- Central bank looses its independence (provoking persistent fiscal deficits)
- "Unpleasant Monetarist Arithmetic" (Sargent & Wallace, 1981)
This paper: Yes!
Motivation: Central Bank profits
- Central Banks run operational profits
- Profits are remitted to the treasury
-
Profits vary significantly
(more data)
Motivation: Central Bank reserves
- Balance sheet size $\approx$ CB reserves
- Minimal reserves as lower bound
- since 2008/2009 crisis: balance sheet as policy tool (QE)
-
CB has several tools
(more data)
This paper
What are the general equilibrium effects of monetary operations?
- CB operates indirecty through the banking sector
- CB has several tools
- CB can independently control inflation & profits
- CB profits act like a redistributive tax
Cental banks wield powerful fiscal tools!
Framework:
IO banking sector with liquidity demand...
...embedded in heterogeneous agents NK model
Mechanism
Households:
consumption/saving based on
savings return
$\color{Goldenrod}r\color{white} \: \Rightarrow C \: \Rightarrow \: \pi$
Banks:
borrowing/lending based on liquidity
$(J, \color{springgreen}r^J\color{white}, \psi) \: \Rightarrow (\color{Goldenrod}r\color{white}, \color{Lavender}r^A\color{white})$
Central Bank:
provides liquidity to control inflation
$\text{set }(J, \color{springgreen}r^J\color{white}, \psi)$
remits profits to treasury
$\Pi = (\color{Lavender}r^A\color{white} - \color{springgreen}r^J\color{white})J$
Mechanism
Households:
$\color{Goldenrod}r\color{white} \: \Rightarrow C \: \Rightarrow \: \pi$
Banks:
$(J, \color{springgreen}r^J\color{white}, \psi) \: \Rightarrow (\color{Goldenrod}r\color{white}, \color{Lavender}r^A\color{white})$
Central Bank:
$\text{set }(J, \color{springgreen}r^J\color{white}, \psi)$
$\Pi = (\color{Lavender}r^A\color{white} - \color{springgreen}r^J\color{white})J$
$\Pi = (\color{Lavender}r^A\color{white} - \color{springgreen}r^J\color{white})J$
Recipe for
monetary financing
monetary financing
- Use reserves $J$ to control inflation $\pi$
- Set IOR rate $\color{springgreen}r^J$ very low
- Use regulatory tools $\psi$ to max out asset returns $\color{Lavender}r^A$
Model:
An IO model of the banking sector
Banking sector: bank $i$'s problem
-
banks hold assets and reserves, backed by deposits:
$$ \definecolor{sgreen}{RGB}{78, 126, 100} \definecolor{sred}{RGB}{231, 75, 75} \definecolor{sblue}{RGB}{112, 174, 255} A_{i,t} + J_{i,t} = D_{i,t} \color{sgreen} - \Delta D_{i,t} $$$$ \color{sred}A_{i,t} \color{white} + J_{i,t} = D_{i,t} \color{sgreen} - \Delta D_{i,t} $$$$ \color{sred}A_{i,t} \color{white} + J_{i,t} = D_{i,t} \color{sblue} - \Delta D_{i,t} $$
- assets are fixed at the beginning of each period
- deposits subject to random transfers (prob. $\chi$)
Banking sector: bank $i$'s problem
- deposits subject to random transfers (prob. $\chi$) $$ \color{sred}A_{i,t} \color{white} + J_{i,t} = D_{i,t} \color{sblue} - \Delta D_{i,t} $$
- $\Delta D_i$ compensated by reserves $J_i > 0$ $$ \color{sred}A_{i,t} \color{sblue} + J_{i,t} \color{white} = D_{i,t} - \Delta D_{i,t} $$
- any unit $\Delta D_i > J_i$ incurs a cost $\gamma$ $$ \color{sred}A_{i,t} \color{sblue} + J_{i,t} \color{white} = D_{i,t} - \Delta D_{i,t} $$
- any unit $\Delta D_i > J_i$ incurs a cost $\gamma$ $$ \color{sred}A_{i,t} \color{sblue} + J_{i,t} \color{white} = D_{i,t} - \Delta D_{i,t} $$
- any unit $\Delta D_i > J_i$ incurs a cost $\gamma$ $$ \color{sred}A_{i,t} \color{sblue} + J_{i,t} \color{white} = D_{i,t} - \Delta D_{i,t} $$
- any unit $\Delta D_i > J_i$ incurs a cost $\gamma$ $$ \color{sred}A_{i,t} \color{sblue} + J_{i,t} \color{white} = D_{i,t} - \Delta D_{i,t} $$
- any unit $\Delta D_i > J_i$ incurs a cost $\gamma$ $$ \color{sred}A_{i,t} \color{sblue} + J_{i,t} \color{white} = D_{i,t} - \Delta D_{i,t} $$
- each bank choses $J_{i}$, $D_{i}$ & $A_{i}$ optimally
- given $r$, $r^J$ & $r^A$ (price takers)
- symmetric competitive equilibrium
Aggregation:
MODEL: General equilibrium
- Embed banking sector in heterogeneous agents NK model
-
Key features:
- uninsurable income risk
- demand for liquid assets (bank deposits)
- distribution of wealth
- non-Ricardian behavior
-
Nonlinear solution (using EP framework
![]()
)
(to general policy effectiveness)
Results: excess reserves
Steady states given the level of reserves
Results: excess reserves
Welfare given the level of reserves
Results: MRR
Steady states given minimal reserve requirements
Results: MRR
Welfare given minimal reserve requirements
Results: excess reserves
Distribution of welfare for the transition from current state to optimal excess reserves
Results: comparison
Wealth distributions for different policy frameworks
Conclusion
- CB independently controls inflation & profits
- "Tax" incidence of CB profits:
- With MRR: tax on liquid wealth + tax on lending
- Without MRR: tax on bank profits
- Provide a unifying framework for monetary policy pass-through
Disclaimer
(the end.)
Appendix
Policy Effectiveness
| reserves policy | ||
|---|---|---|
| MRR* binding | high | low |
| MRR* slack | low | high |
(back) (illustration) (math)
Banking sector: Market rates
- Interest on reserves fixed at 1%
- MRR not binding: limited pass-through
- MRR binding: large pass-through
Banking sector: Market rates
- Keeping reserve volume fixed
- MRR not binding: large pass-through
- MRR binding: limited pass-through
Literature (back)
- DSGE literature: Gertler & Karadi (2011,2013), Carstrom et al. (2013), Boehl et. al. (2024)
- Banking literature: Corbae & D'Erasmo (2021), Drechsler et al. (2017), Poole (1968)
- Monetary: Sargent & Wallace (1981), Friedman (1969), Bianchi & Bigio (2022), Piazzesi et al. (2019)
Banking sector (back)
- banks hold assets and reserves, backed by deposits: $$ A_{i,t} + J_{i,t} = D_{i,t} $$
- assets are fixed at the beginning of each period
- deposits subject to random transfers (prob. $\chi$) $$ \Delta {D}_{i,t} \sim \mathcal{N} \left( 0, \frac{{D}_{i,t} D_{-i,t}}{\sum D_{j,t}} (2 \chi - \chi^2)\right). $$
- any transfered unit of deposits not backed by reserves incurs a cost $\gamma$
Banking sector: bank $i$'s problem (back)
- Expected cost for each bank: $$ g(J_{i,t}, D_{i,t}) = h(D_{i,t}) f_h\left(J_{i,t}\right) - J_{i,t} \left[1-F_h\left(J_{i,t}\right)\right], $$
- Banks are subject to a minimal reserve requirement (MRR) $$ \psi D_{i,t} \leq J_{i,t} $$
- Each bank $i$ maximizes profits s.t. balance sheet, expected costs, MRR & competitors actions
Banking sector: aggregation (back)
FOCs:
$$
\small
\definecolor{sgreen}{RGB}{78, 126, 100}
\begin{align}
R = (1-\psi) R^b + \psi R^j &-\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\color{sgreen}
\underbrace{
\color{white}
R^j -
R^b +
\gamma \left[1-
\hat{F}
\right]
}_{MPJ}
&=
\min\left\{
0,
\;
R^j -
R^b +
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
FOCs:
$$
\small
\begin{align}
R = (1-\psi) R^b + \psi R^j &-\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\underbrace{
R^j -
R^b +
\gamma \left[1-
\hat{F}
\right]
}_{MPJ}
&=
\min\left\{
0,
\;
R^j -
R^b +
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
FOCs when MRR slack:
$$
\small
\begin{align}
R
= \color{sgreen}(1-\psi)\color{white} R^b \color{sgreen}+ \psi R^j
\color{white}
&-\gamma
\color{sgreen}
\left(
\color{white}
0.5\hat{f}
\color{sgreen}
-
\psi \left[1-\hat{F}\right]
\right)
\\
\color{white}
\underbrace{
R^j -
R^b +
\gamma \left[1-\hat{F}\right]
}_{MPJ}
&=
\color{sgreen}
\min\left\{
\color{white}
0
\color{sgreen},
\;
R^j -
R^b +
\gamma \left[1-\hat{F}_\psi
\right]
\right\}
\end{align}
$$
FOCs at MRR:
$$
\small
\begin{align}
R = (1-\psi) R^b + \psi R^j &-\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\color{sgreen}
\underbrace{
R^j -
R^b +
\gamma \left[1-
\color{white}
\hat{F}
\color{sgreen}
\right]}_{MPJ}
&=
\color{sgreen}
\min\left\{
0,
\;
R^j -
R^b +
\gamma \left[1-
\color{white}
\hat{F}_\psi
\color{sgreen}
\right]
\right\}
\end{align}
$$
- IOR rate $R^j$, deposit rate $R$, lending rate $R^b$
- $\hat{f} = f\left(\hat{J}| 0, \hat{D}\right)$, $\hat{f}_\psi = f\left(\psi\hat{D}| 0, \hat{D}\right)$, $\hat{F}=...$
- Reserves & deposits scaled by liquidity risk $\hat{J} = \frac{J}{\nu}$
Banking sector: partial equilibrium - lending (back)
$$
\scriptstyle
\begin{align}
\text{demand:}& &{d_A}\left(R^b\right) \; &= \;\hat{D}, \qquad \left\{\hat{J}, R^j\right\} \text{ fixed}\\
\text{supply:}&
&\gamma \left[1-
\hat{F}
\right]
\; &= \;
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
$$
\scriptstyle
\begin{align}
\text{demand:}& &{d_A}\left(R^b\right) \; &= \; \hat{D}, \qquad \left\{\hat{J}, R^j\right\} \text{ fixed}\\
\text{supply:}&
&\color{sgreen}
\gamma \left[1-
\color{white}
\hat{J}
\color{sgreen}
\right]
\; &= \;
\color{sgreen}
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\color{white}
\psi \hat{D}
\color{sgreen}
\right]
\right\}
\end{align}
$$
$$
\scriptstyle
\begin{align}
\text{demand:}& &{d_A}\left(R^b\right) \; &= \; \hat{D}, \qquad \left\{\hat{J}, R^j\right\} \text{ fixed}\\
\text{supply:}&
&\color{white}
\gamma \left[1-\hat{F}\right] \; &= \;
\color{sgreen}\min\left\{
\color{white}
R^b - R^j
\color{sgreen},
\;
\gamma \left[1-\hat{F}_\psi
\right]
\right\}
\end{align}
$$
$$
\scriptstyle
\begin{align}
\text{demand:}& &{d_A}\left(R^b\right) \; &= \; \hat{D}, \qquad \left\{\hat{J}, R^j\right\} \text{ fixed}\\
\text{supply:}&
&\gamma \left[1-
\hat{F}
\right]
\; &= \;
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
partial equilibrium: reserves policy (back)
$$ \scriptsize \begin{align} R &= (1-\psi) R^b + \psi R^j -\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\ \gamma \left[1- \hat{F} \right] &= \min\left\{ R^b - R^j, \; \gamma \left[1- \hat{F}_\psi \right] \right\} \end{align} $$
partial equilibrium: higher elasticity (back)
$$
\scriptsize
\begin{align}
R &= (1-\psi) R^b + \psi R^j -\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\gamma \left[1-
\hat{F}
\right]
&=
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
partial equilibrium: IOR policy (back)
$$
\scriptsize
\begin{align}
R &= (1-\psi) R^b + \psi R^j -\gamma \left( 0.5\hat{f} - \psi \left[1-\hat{F}\right] \right) \\
\gamma \left[1-
\hat{F}
\right]
&=
\min\left\{
R^b -
R^j,
\;
\gamma \left[1-
\hat{F}_\psi
\right]
\right\}
\end{align}
$$
Facts
- Balance sheets are huge
- Debate on operational framework
- CB profits can be significant
(to motivation)