Time-Consistent Fiscal Guarantee for Monetary Stability Gaetano - PowerPoint PPT Presentation

Time-Consistent Fiscal Guarantee for Monetary Stability Gaetano GABALLO Eric MENGUS Banque de France HEC Paris Paris School of Economics CEPR Second Annual Workshop ESCB Research Cluster on Monetary Economics Rome 11-12 October 2018

The views expressed here do not necessarily reflect the ones of Banque de France or the Eurosystem.

Intro Does monetary stability requires a fiscal authority?

Intro Does monetary stability requires a fiscal authority? ◮ Fiscal authority: who can impose transfers at will ( � = capitalized )

Intro Does monetary stability requires a fiscal authority? ◮ Fiscal authority: who can impose transfers at will ( � = capitalized ) ◮ Monetary stability: money is used + price is uniq. determined

Intro Does monetary stability requires a fiscal authority? ◮ Fiscal authority: who can impose transfers at will ( � = capitalized ) ◮ Monetary stability: money is used + price is uniq. determined Existing literature (extreme redux): ◮ Sargent & Wallace (1981): it is a danger

Intro Does monetary stability requires a fiscal authority? ◮ Fiscal authority: who can impose transfers at will ( � = capitalized ) ◮ Monetary stability: money is used + price is uniq. determined Existing literature (extreme redux): ◮ Sargent & Wallace (1981): it is a danger ◮ Obstelf & Rogoff (1983,2017): no need

Intro Does monetary stability requires a fiscal authority? ◮ Fiscal authority: who can impose transfers at will ( � = capitalized ) ◮ Monetary stability: money is used + price is uniq. determined Existing literature (extreme redux): ◮ Sargent & Wallace (1981): it is a danger ◮ Obstelf & Rogoff (1983,2017): no need ◮ Sims (1994), Woodford (1995): must commit to surpluses

Intro Does monetary stability requires a fiscal authority? ◮ Fiscal authority: who can impose transfers at will ( � = capitalized ) ◮ Monetary stability: money is used + price is uniq. determined Existing literature (extreme redux): ◮ Sargent & Wallace (1981): it is a danger ◮ Obstelf & Rogoff (1983,2017): no need ◮ Sims (1994), Woodford (1995): must commit to surpluses This paper: ◮ Essential active off-equilibrium role ◮ no fiscal surpluses along the equilibrium

Intro Does monetary stability requires a fiscal authority? ◮ Fiscal authority: who can impose transfers at will ( � = capitalized ) ◮ Monetary stability: money is used + price is uniq. determined Existing literature (extreme redux): ◮ Sargent & Wallace (1981): it is a danger ◮ Obstelf & Rogoff (1983,2017): no need ◮ Sims (1994), Woodford (1995): must commit to surpluses This paper: ◮ Essential active off-equilibrium role ◮ no fiscal surpluses along the equilibrium ◮ textbook Samuelson (1958)/Sims (2013) model of fiat money ◮ discretionary policy=f*(portfolio choice)

1. Model

OLG Model: consumption-saving problem ◮ Discrete time: t ∈ { 0 , 1 , ... } ◮ Overlapping generations of agents living for two periods. ◮ Representative agent born at time t maximizes: U t ≡ log C t , y + log C t +1 , o ◮ subject to: C t , y + M t young : + S t + T t , y = W P t C t , o = M t − 1 old : + θ S t − 1 + T t , o P t where: ◮ individual endowment W , lump sum taxes/transfers T t , y , T t , o ; ◮ agents choose consumption C and composition of savings: ◮ either in real cash holdings M / P ◮ or in freely available storage S with a return θ < 1 ◮ At date 0, M − 1 = ¯ M .

OLG Model: the authority At date-t, the authority’s objective is: log C y , t + log C o , t + λ log G t , G t : government expenditures, and λ > 0. Its budget constraint is: T t , y + M g , t − 1 = M g , t + T t , o + G t . P t P t with M g , t + M t = ¯ M .

OLG Model: the authority At date-t, the authority’s objective is: log C y , t + log C o , t + λ log G t , G t : government expenditures, and λ > 0. Its budget constraint is: T t , y + M g , t − 1 = M g , t + T t , o + G t . P t P t with M g , t + M t = ¯ M . A policy at time t is P t ≡ ( T t , y , M g , t , G t , T t , o ).

OLG Model: the authority At date-t, the authority’s objective is: log C y , t + log C o , t + λ log G t , G t : government expenditures, and λ > 0. Its budget constraint is: T t , y + M g , t − 1 = M g , t + T t , o + G t . P t P t with M g , t + M t = ¯ M . A policy at time t is P t ≡ ( T t , y , M g , t , G t , T t , o ). As in Obstfeld-Rogoff (1983): the authority can be net buyer of money.

OLG Model: the authority At date-t, the authority’s objective is: log C y , t + log C o , t + λ log G t , G t : government expenditures, and λ > 0. Its budget constraint is: T t , y + M g , t − 1 = M g , t + T t , o + G t . P t P t with M g , t + M t = ¯ M . A policy at time t is P t ≡ ( T t , y , M g , t , G t , T t , o ). As in Obstfeld-Rogoff (1983): the authority can be net buyer of money. ◮ In the FTPL: price set indirectly by agents affected by tax decisions.

OLG Model: the authority At date-t, the authority’s objective is: log C y , t + log C o , t + λ log G t , G t : government expenditures, and λ > 0. Its budget constraint is: T t , y + M g , t − 1 = M g , t + T t , o + G t . P t P t with M g , t + M t = ¯ M . A policy at time t is P t ≡ ( T t , y , M g , t , G t , T t , o ). As in Obstfeld-Rogoff (1983): the authority can be net buyer of money. ◮ In the FTPL: price set indirectly by agents affected by tax decisions. ◮ Still, fixing a redemption price does not imply agent trading money

OLG Model: the authority At date-t, the authority’s objective is: log C y , t + log C o , t + λ log G t , G t : government expenditures, and λ > 0. Its budget constraint is: T t , y + M g , t − 1 = M g , t + T t , o + G t . P t P t with M g , t + M t = ¯ M . A policy at time t is P t ≡ ( T t , y , M g , t , G t , T t , o ). As in Obstfeld-Rogoff (1983): the authority can be net buyer of money. ◮ In the FTPL: price set indirectly by agents affected by tax decisions. ◮ Still, fixing a redemption price does not imply agent trading money ◮ at the core of time-consistency

2. Benchmark: No Policy

Optimal choices of agents No policy benchmark: P t = (0 , 0 , 0 , 0). Savings D t ≡ S t + M t = W P t 2 for any expected return (property of log-utility) ρ t = θ S t + M t / P t +1 D t Portfolio allocation: Π t +1 < 1 M t = D t and S t = 0 if θ, P t Π t +1 = 1 M t + S t = D t if θ, P t Π t +1 > 1 and M t S t = D t = 0 if θ, P t where Π t +1 ≡ P t +1 / P t is the inflation rate from time t to time t + 1.

No policy leads to indeterminacy Π t S t M t /P t 1.2 pure monetary asymptotic autarky 1 1 asymptotic autarky pure autarky 0.8 0.8 1.1 0.6 0.6 0.4 0.4 1 0.2 0.2 0 0 0.9 1 10 20 30 1 10 20 30 1 10 20 30 time Figure : Equilibria without policy intervention for θ = 0 . 9 , W = 2 and ¯ M = 1.

3. Optimal policy with fiscal power

Optimal policy with fiscal power At any t , an optimal policy is a P ∗ t = ( T ∗ y , t , M ∗ g , t , G ∗ t , 0) that solves: P t , G t { log C y , t + log C o , t + λ log G t } , max subject to T y , t + M g , t − 1 = M g , t + G t P t P t taking into account agents’ decision process on consumption: M t + S t = W − T y , t = C y , t 2 P t M t − 1 = + θ S t − 1 C o , t P t and market clearing conditions, with S 0 = 0 and M 0 ≤ ¯ M . ◮ WLoG: no transfers to old.

Optimal policy with fiscal power We can rewrite the problem of the authority as        � � � M t − 1 �    W − G t − M t − 1 max log − S t + log + θ S t − 1 + λ log G t P t P t P t , G t       � �� � � �� �   = C y , t = C o , t whose solution is � (2+ λ ) M t − 1 G t = λ C y , t , P t = with C y , t ≥ C o , t W − (1+ λ ) θ S t − 1 − S t G t = λ C y , t , P t → ∞ otherwise.

Optimal policy with fiscal power We can rewrite the problem of the authority as        � � � M t − 1 �    W − G t − M t − 1 max log − S t + log + θ S t − 1 + λ log G t P t P t P t , G t       � �� � � �� �   = C y , t = C o , t whose solution is � (2+ λ ) M t − 1 G t = λ C y , t , P t = with C y , t ≥ C o , t W − (1+ λ ) θ S t − 1 − S t G t = λ C y , t , P t → ∞ otherwise. The authority likes consumption equality → it fights inflation!

Optimal policy with fiscal power We can rewrite the problem of the authority as        � � � M t − 1 �    W − G t − M t − 1 max log − S t + log + θ S t − 1 + λ log G t P t P t P t , G t       � �� � � �� �   = C y , t = C o , t whose solution is � (2+ λ ) M t − 1 G t = λ C y , t , P t = with C y , t ≥ C o , t W − (1+ λ ) θ S t − 1 − S t G t = λ C y , t , P t → ∞ otherwise. The authority likes consumption equality → it fights inflation! But inflation fixed by arbitrage → more storage is needed for the same inflation rate → at same point it is unfeasible