How tough should you be Inflation targeting, fiscal feedbacks, and multiple equilibria Alexandre Schwartsman Unibanco

The model structure Model consists of 2 blocks The reaction function block A “minimalist” inflation targeting model 1.Phillips Curve 2.“IS” function 3.Loss function The fiscal/arbitrage block Explicit modeling of: 1.Arbitrage between sovereign and risk –free debt instruments 2.Relationship between domestic interest rates, fiscal policy and probability of default

Transmission mechanisms and efficacy usually associated to parameters  The reaction function block - 1 Phillips curve “IS” function Loss function

The reaction function block - 2 Modeling the exchange rate requires 2 assumptions Uncovered interest parity Mean reversal Thus, the current exchange rate behavior is given by

The reaction function block - 3 Reduced form for the Central Bank’s reaction function

The fiscal/arbitrage block Assume 2 other assets, in addition to the local bond Risk-free bond with yield i US Risky sovereign bond with yield i* Risk neutral agents equate expected return where (1- ) is the probability of default

Modeling the default risk Primary surplus is random variable with support [s L, s H ] 2. Default rule: if primary surplus is higher than real debt service [s  (i-  )b], pay; otherwise total default Zero probability of default 100% probability of default

Modeling the default risk - 2 Repayment probability can be expressed as a function of domestic interest rate

Arbitrage The arbitrage equation then becomes

Multiple equilibria and stability

Comparison to standard case Interest rates are higher than in standard case (exogenous i*) Fiscal feedback reduces efficiency of monetary policy instrument

Comparative statics Fiscal policyRisk-free rate Shocks Usual transmission channels

Existence For simplicity assume primary surplus uniformly distributed

Implication of inflation “floor” Setting the inflation target below the critical threshold implies no possible equilibrium

Determinants of inflation “floor” Inflation floor depends essentially on 3 determinants 1. Primary surpluses 2. Public debt 3. Size of supply and demand shocks

Unstable equilibrium properties “Bad” equilibrium associated to weaker currency due to higher interest rate differential

Bizarre shock responses Responses to fiscal policy and shocks at odd with the data

Saddlepath properties? Model does not have saddlepath properties, that is, Central Bank behavior is myopic (converges to stable equilibrium) If Central Bank were to choose the equilibrium, why would it choose the “bad” one?

Extension Possibility of further equilibria, depending on primary surplus distribution (if second order condition fails) Stable high-interest rate equilibrium (C)

Concluding remarks 1. Multiple equilibria, at least in this setting, do not seem to be the cause behind high real interest rate 2. Fiscal feedbacks, nonetheless, imply higher interest rates than standard exogenous interest rate case 3. Feedbacks depend on sensitivity of default likelihood to domestic interest rates, which is an empirical issue. Other forces may be at work (global “risk aversion”) 4. Future direction of research: Central Bank reaction when output gap enters loss function; possibility of further equilibria depending on the primary surplus distribution