Empirical evidence on the monetary-fiscal policy mix and macroeconomic (in)stability in the US

THE GREAT INFLATION

Inflation analogies by Cochrane (2025)

THE GREAT INFLATION(S)?

Inflation analogies by Cochrane (2025)

WHO DETERMINES INFLATION?

“Inflation is always and everywhere a monetary phenomenon.”
Milton Friedman

“Persistent high inflation is always and everywhere a fiscal phenomenon, in which the central bank is a monetary accomplice.”
Thomas J. Sargent

The policy rules

Monetary policy rule

\[ R_t \,=\, \color{blue}{\phi_{\pi}} \pi_t + g_m(x_t ; \rho_R, \color{blue}{\phi_{x}} ) + \epsilon_{R, t} \]

\[ \pi_t \equiv \frac{P_t}{P_{t-1}} \]

Fiscal policy rule

\[ \tau_{t}= \color{blue}{\psi_{b}} b_{t-1} + g_f(x_t ; \rho_{\tau}, \color{blue}{\psi_{x}} ) + \epsilon_{\tau, t} \]

\[ \begin{align} \tau \equiv \frac{T_t}{P_t Y_t} & \,\,\,\,\,\,\,\ b_{t} \equiv \frac{B_t}{P_t Y_t} \\ \end{align} \]

The government budget constraint

\[ \begin{align} R_t \,&=\, \color{blue}{\phi_{\pi}} \pi_t + g_m(x_t ; \rho_R, \color{blue}{\phi_{x}} ) + \epsilon_{R, t} \\ \tau_{t} &= \color{blue}{\psi_{b}} b_{t-1} + g_f(x_t ; \rho_{\tau}, \color{blue}{\psi_{x}} ) + \epsilon_{\tau, t} \end{align} \]

The govt budget constraint is

\[ b_{t} \approx (1 - \color{blue}{\psi_{b}}) b_{t-1} + (\mathbb{E}_{t-1} \pi_{t} - \pi_t) - \epsilon_{\tau, t} + \ldots \]

If \(\psi_b > 0\), debt level is stable
If \(\psi_b < 0\), \(\pi_t\) has to “accomodate”
- Budget constraints are always satisfied!

Equilibrium depends primarily upon \(\phi_{\pi}\) and \(\psi_{b}\).

4 possible cases (regimes).

Why do we care about regimes?

\[ b_{t} \approx (1 - \color{blue}{\psi_{b}}) b_{t-1} + (\mathbb{E}_{t-1} \pi_{t} - \pi_t) - \epsilon_{\tau, t} + \ldots \]

MONETARY (AM-PF, \(\psi_{b} > 0\)) - Inflation is stable and unique (expectation are anchored) - \(\uparrow R \Rightarrow \downarrow \pi\) (Taylor principle) because fiscal policy accomodates the higher interest bill.

INDETERMINACY (PM-PF, \(\psi_{b} > 0\))

The central bank violates the Taylor principle,
while the Treasury is committed to debt stabilization
Many inflation levels satisfy the budget constraint: Self-fulfilling equilibria

FISCAL (PM-AF, \(\phi_{\pi}<1\), \(\psi_{b} < 0\))

To satisfy budget constraint, inflation has to go up when the interest bill for the Treasury goes up.
Inflation is stable and unique (expectation are anchored)
Fiscal policy does not accomodates the higher interest bill
Under fiscal regime: \(\uparrow R \Rightarrow \uparrow \pi\)
- \(\uparrow R\) implies more money printing by the Tresury and thus raises nominal aggregate demand by bondholders
- Alternateviyl, if the CB sells more bonds (soaks up cash today), with no changes in fiscal policy, the nominal price of those bonds \(Q_0\) falls (no real monetary contraction)
The central bank destabilises the economy!

EXPLOSIVE (AM-AF, \(\phi_{\pi}\)>1, \(\psi_{b} < 0\))

the monetary authority is resolute in its commitment to stabilize inflation, but it does not have the necessary …fiscal backing
non-coordinated policy rules, the economy is in a regime of indeterminacy (also conflict)
no stable rational expectations equilibria exists \(\rightarrow\) change in regime

EMPIRICAL ISSUES: Lack of consensus

Endogeneity and weak identification

\[ R_t \,=\, \color{blue}{\phi_{\pi}} \pi_t + \epsilon_{R, t} \]

Instrumental variable estimator:
- Instrument: \(\pi_{t-1}\).
- Weak identification: \(\pi_{t}\) moves little
  - For example: \(\pi_t \rightarrow \pi^*\)

An additional instrument

\[ \begin{align} R_t \,&=\, \color{blue}{\phi_{\pi}} \pi_t + \epsilon_{R, t} \\ \pi_t &= \rho \pi_{t-1} + \gamma R_t + \varepsilon_{\pi, t} \end{align} \]

An additional instrument

\[ \begin{align} R_t \,&=\, \color{blue}{\phi_{\pi}} \pi_t + \epsilon_{R, t} \\ \pi_t &= \rho \pi_{t-1} + \gamma R_t + \varepsilon_{\pi, t} \end{align} \]

An additional instrument

\[ \begin{align} R_t \,&=\, \color{blue}{\phi_{\pi}} \pi_t + \epsilon_{R, t} \\ \pi_t &= \color{red}{\rho}_t \pi_{t-1} + \gamma R_t + \varepsilon_{\pi, t} \end{align} \]

Structural breaks as instruments

\[ \begin{align} R_t \,&=\, \color{blue}{\phi_{\pi}} \pi_t + \epsilon_{R, t} \\ \pi_t &= \color{red}{\rho}_t \pi_{t-1} + \gamma R_t + \varepsilon_{\pi, t} \end{align} \]

\(\pi_{t-1}\)
\(\mathcal{1}_{\{t>50\}} \pi_{t-1}\)

Structural breaks free up information

What if we don’t know the break dates?

Do hypothesis testing.
- Fix \(H_0: \color{blue}{\phi_{\pi, 0}}\) and test whether \(\hat{\epsilon}_{R, t}\) is sufficiently stable.
- The test has power if \(\rho\) shifts
- If \(\rho\) does not shift, you will know it!

Identification by stability restrictions

Exploit instabilities in subsamples for identification (Magnusson and Mavroeidis 2014).

Let \(\color{blue}{\mathbf{\theta_0}} \equiv \left[ \phi_{\pi}, \phi_x, \psi_{b}, \psi_{x}\right]\) be possible candidate parameter values.
Fix the parameters under the null \[ H_0 : \color{blue}{\mathbf{\theta}} = \left[ \phi_{\pi, 0}, \phi_{x,0}; \psi_{b, 0}, \psi_{x, 0} \right] \]
Compute “residuals” and the S and generalised-S test statistic.
Keep \(\color{blue}{\mathbf{\theta_0}}\) if the test statistic is below the critical value.
Rinse and repeat (grid search)

A confidence set comprises all \(\color{blue}{\mathbf{\theta_0}}\) that do not reject \(H_0\).

DATA

Before Volcker: 1961 Q1 to 1979 Q2 (74 observations)
After Volcker: 1984 Q1 to 2008 Q4 (100 observations)

\(R\)	effective Federal Funds rate	\(\tau\)	current tax receipts + social insurance contributions
\(\pi\)	CPI	\(b\)	market value of privately held gross federal debt
\(x\)	Output gap as estimated by CBO	\(Y\)	Gross Domestic Product (GDP)

Source is FRED.

CONFIDENCE SETS: before Volcker

S set

90% confidence sets Indeterminacy, monetary, fiscal. 1961q1 - 1979q2.

CONFIDENCE SETS: before Volcker

genS-qLL set

90% confidence sets Indeterminacy, monetary, fiscal. 1961q1 - 1979q2.

CONFIDENCE SETS: after Volcker

S set

90% confidence sets Indeterminacy, monetary, fiscal. 1984q1 - 2008q4.

RESULTS: after Volcker

genS-qLL set

90% confidence sets Indeterminacy, monetary, fiscal. 1984q1 - 2008q4

ROBUSTNESS: Alternative policy rules

AR(2) monetary policy smoothing

Forward-looking monetary policy rule