Stabilization versus Sustainability: Macroeconomic Tradeoffs Huixin Bi, Eric Leeper & Campbell Leith Bank of Canada, Indiana University & University of Glasgow March 2011 (Preliminary) Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
This Paper Motivation: ◮ Sovereign debt crisis in Europe Question: ◮ Do routine monetary & fiscal policy actions taken to achieve stabilization goals. . . ◮ . . . have different macroeconomic effects in economies facing sustainability issues than in economies not facing such issues? This is an interim report on progress toward answering this increasingly relevant question. ◮ Closed economy with nominal debt ◮ Allow the possibility of sovereign debt default & risk premia Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Paper’s Findings ◮ Specification of monetary policy rule is central to link between default and inflation ◮ If sustainability an issue, monetary policy may lose control of inflation even if it always obeys Taylor principle ◮ If sustainability an issue, expansionary fiscal consolidations are possible over the long run, but not in the short run Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
This Talk ◮ Simple analytics in an endowment economy with exogenous default ◮ New-Keynesian model with state-dependent default (nonlinear) Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Simple Analytics: Endowment Economy ◮ Exogenous sovereign default rate ∆ t ∈ [0 , 1] ◮ Active monetary policy & passive fiscal policy ◮ Household problem: � ∞ β t u ( c t ) max E 0 t =0 P t c t + B t s . t . + P t T t = (1 − ∆ t ) B t − 1 + P t y t R t 1 − ∆ t +1 1 Risky rate: = β E t R t π t +1 1 1 Risk-free rate: = β E t R f π t +1 t ◮ Government: B t (1 − ∆ t ) B t − 1 + P t T t = R t β − 1 − 1 � � (1 − ∆ t ) B t − 1 T t − T = γ − b ( γ > ) 1 − E t ∆ t +1 P t − 1 Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Simple Analytics: Risk-Free Instrument ◮ Monetary instrument risk-free rate � 1 � 1 = 1 − 1 R + α α/β > 1 R f π t π t ◮ Yields dynamic equation for inflation � � 1 − 1 π = β 1 − 1 α E t π t π t +1 π ◮ Unique bounded solution: inflation always on target π t = π ◮ With passive fiscal policy, default causes no problems for monetary policy’s control of inflation (Ricardian) Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Simple Analytics: Risky Instrument ◮ Monetary instrument risky rate � 1 � 1 = 1 − 1 R + α π t π R t ◮ Yields dynamic equation for inflation � 1 − ∆ t +1 � 1 − 1 π = β − 1 α E t π t π t +1 π ◮ Unique bounded solution: inflation always away from target � � β � � i i ∞ 1 = 1 1 − β � � 1 + E t (1 − ∆ t + j ) π t π α α i =1 j =1 ◮ With passive fiscal policy, inflation rises with expected default Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Risky Instrument ◮ Monetary policy accommodates default even without changing policy rate ◮ Risky rate rule implies (with fixed default rate) � 1 � 1 1 − 1 = R + α R t π t π � 1 � 1 �� 1 1 α δ − → = R + − π − R f 1 − δ π t α R t ◮ Higher δ : raises the effective inflation target from π to π 1 − δβ/α ◮ bonds lose value, raises aggregate demand & inflation Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
So Far... ◮ Simple analytics in an endowment economy with exogenous default ◮ New-Keynesian model with state-dependent default (nonlinear) Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Numerical Model ◮ Off-the-shelf new Keynesian model ◮ elastic labor, fixed capital, costly price adjustment ◮ tax on labor income, nominal debt, exogenous spending & transfers ◮ interest rate rule for monetary policy ◮ tax rule for fiscal policy ◮ default rule: model-based “fiscal limit” (Bi (2010)) ◮ Solve full non-linear model ◮ find fixed point in decision rules over discretized state space ◮ calibrate—loosely—to Greek fiscal data Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Numerical Model: Household Household problem: ∞ � β t u ( c t , n t ) max E 0 t =0 + B f P t c t + B t t = (1 − ∆ t ) B t − 1 + B f s . t . t − 1 + (1 − τ t ) ( W t n t + P t Υ t ) + P t z R f R t t ◮ FOC: − u n ( t ) = w t (1 − τ t ) u c ( t ) 1 � 1 − ∆ t +1 u c ( t + 1) � = β E t π t +1 u c ( t ) R t 1 � 1 u c ( t + 1) � = β E t R f π t +1 u c ( t ) t Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Numerical Model: Firm ◮ Final goods firm: competitive firm with CES production form ◮ Intermediate goods firm: Rotemberg adjustment cost � � p t ( i ) � � 2 ∞ p t ( i ) y t ( i ) − mc t P t y t ( i ) − φ 1 � π − 1 max R 0 , t P t Y t 2 p t − 1 ( i ) t =0 � p t ( i ) � − θ s . t . y t ( i ) = Y t P t FOC: � π t � π t +1 � π t � π t +1 u c ( t + 1) Y t +1 (1 − θ ) + θ mc t − φ π − 1 π + βφ E t − 1 = 0 . u c ( t ) π π Y t Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Numerical Model: Government Government budget: B t (1 − ∆ t ) B t − 1 + P t g t + P t z + τ t ( W t n t + Υ t ) = R t � �� � P t T t 1 − ∆ t → b t − + T t = b t − 1 + g t + z R t π t ◮ Unenforceable bond contract: t ∼ N ( b ∗ , σ 2 0 if b t − 1 < b ∗ b ∗ b ) t with � �� � ∆ t = Model-based fiscal limit δ if b t − 1 ≥ b ∗ t Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Numerical Model ◮ Fiscal rule: � � τ t − τ = γ (1 − ∆ t ) b t − 1 − b � �� � b d t ◮ Monetary rule: R t − R = α ( π t − π ) + ε R ε R t ∼ N (0 , σ 2 R ) t ◮ Stochastic government spending: ln g t g = ρ e ln g t − 1 + ε g ε g t ∼ N (0 , σ 2 g ) t g ◮ Stochastic technology: ln A t A = ρ u ln A t − 1 + ε A ε A t ∼ N (0 , σ 2 A ) t A Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Fiscal Limit Following Bi (2010), ◮ Peak of Laffer curve a natural fiscal limit, given spending ◮ A function of exogenous state & model parameters τ max = τ max ( A t , g t , Θ) t T max = T max ( A t , g t , Θ) t ◮ Fiscal limit ≡ expected present value of future maximum surpluses (inflation & transfers at steady state) ∞ β t u max ( A t , g t ) � β p c ( T max ( A t , g t ) − g t − z ) B ∗ = E t u max ( A 0 , g 0 ) c ���� t =0 political factor Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Fiscal Limit ∞ β t u max ( A t , g t ) � c β p ( T max ( A t , g t ) − g t − z ) B ∗ = E t u max ( A 0 , g 0 ) c ���� t =0 political factor ◮ Political risk: β p t ∈ { β p L , β p H } ∼ Markov chain ◮ uncertainty about whether maximum surpluses will be forthcoming ◮ β p < 1 necessary to generate risk premia at plausible debt-GDP levels ◮ Compute unconditional distribution of fiscal limit, f ( B ∗ ) 6 5 4 3 2 1 0 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 Debt over steady−state GDP Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Default Rule ◮ Literature of optimal, strategic default: generates default at implausibly low debt levels ◮ Effective fiscal limit is b ∗ t drawn from N ( b ∗ , σ 2 b ) ◮ choice of effective fiscal limit is random ◮ determined by political considerations: willingness to meet obligations ◮ fiscal limit f ( B ∗ ): ability to meet obligations ◮ Default rule: � δ if b t − 1 > b ∗ t (Above Effective Fiscal Limit) ∆ t = 0 if b t − 1 ≤ b ∗ t (Below Effective Fiscal Limit) ◮ With partial default, debt outstanding at beginning of period t is b d t = (1 − ∆ t ) b t − 1 Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
Nonlinear solution Monotone mapping method (Coleman(1991), Davig(2004)): ◮ Grid points the state space, ψ t = ( b d t ), using Tauchen t , A t , g t , ε R (1991); ◮ Initial guess of the decision rule � � b t = f b 0 ( ψ t ) , π t = f π 0 ( ψ t ) , w t = f w 0 ( ψ t ) ; � � ◮ Update the decision rule by b t = f b j ( ψ t ) , π t = f π j ( ψ t ) , w t = f w j ( ψ t ) iterating over the equilibrium conditions until converge ( ǫ = 1 e − 6). Numerical integration: Newton-Cotes formulas. Huixin Bi, Eric Leeper & Campbell Leith Stabilization versus Sustainability: Macroeconomic Tradeoffs
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