Monetary and Fiscal Policy Interactions

Transcription

1 Monetary and Fiscal Policy Interactions IMF Institute Eric M. Leeper Indiana University January 2011

2 Sketch of Course 1. General view of tasks of monetary & fiscal policies 2. Two expositions of the fiscal theory of the price level 3. Observational equivalence of monetary & fiscal determination of inflation 4. Long-term debt and inflation dynamics 5. Applications of the fiscal theory 6. Recurring policy regime change 7. Fiscal limits 8. Wrap up 9. Research agenda

3 What Monetary & Fiscal Policy Do Macroeconomic policies have two tasks to perform 1. control inflation 2. stabilize government debt Control inflation means ensure inflation process unique eliminate self-fulfilling inflation expectations rule out arbitrarily large deviations of inflation from target Stabilize government debt means maintain value of debt prevent debt from growing unsustainably line up market value of debt with its expected backing

4 A Beautiful Symmetry Monetary & fiscal policy perfectly symmetric with regard to these two tasks Two different policy mixes or assignments can accomplish these tasks Regime M: conventional assignment MP targets inflation; FP targets real debt Regime F: alternative assignment MP maintains value of debt; FP controls inflation Regime M: normal state of affairs Regime F: can arise in crises or states of fiscal stress Regime F arises in two ways 1. Sargent & Wallace s unpleasant monetarist arithmetic 2. fiscal theory of the price level

5 Unpleasant Monetarist Arithmetic Best-known case of alternative assignment of tasks FP sets primary surpluses independently of debt & inflation MP passively adjusts money growth so seigniorage revenues service & stabilize debt Higher current debt from fiscal deficits or open-market sales requires higher future money growth quantity theory future inflation rises Fisher relation current nominal interest rates rise lower money demand now inflation may rise now Emphasizes money market equilibrium via M t V t ( ) = P t Y t (QE) Monetary policy loses control of inflation

6 Fiscal Theory of the Price Level FTPL requires nominal government debt Most debt issued by advanced economies qualifies: U.S. (90%); U.K. (80%); over 90% in Australia, Canada, New Zealand, Sweden; most EMU-member debt in euro; most Japanese bonds in yen FP is as in unpleasant arithmetic; MP different FP sets primary surpluses independently of debt & inflation MP prevents nominal rates from rising strongly with debt & inflation Emphasizes debt revaluation effects via M t 1 + B t 1 P t = Expected PV (Surpluses + Seigniorage) (IEC) Monetary policy loses control of inflation

7 The Models Endowment economy, MIUF, g t 0 Representative household maximizes { ( E 0 β t U c t, M ) } t P t t=0 subject to sequence of flow budget constraints M t + E t [R t,t+1 (W t+1 M t )] W t + P t y t T t P t c t Wt+1 M t : nominal value in t + 1 of HH s bond holdings at end of t Et [R t,t+1 (W t+1 M t )]: nominal market value of state-contingent claims Rt,t+1 : stochastic discount factor Note: W s t = Mt 1 s + (1 + i t 1)B s t 1 So 1 + it = E t [R t,t+1 ] 1

8 The Models HH s flow b.c. & borrowing limit intertemporal b.c. T=t [ E t R t,t P T c T + i ] T M T W t i T HH s FOCs yield U m (c t, m t ) U c (c t, m t ) = U c (c t, m t ) U c (c t+1, m t+1 ) = i t 1 + i t And intertemporal b.c. at equality β E t R t,t [P T y T T T ] T=t P t R t,t+1 P t+1

9 Models Equilibria Impose market clearing on liquidity preference ) U m (y t, Ms t P t i ) t = U c (y t, Ms t 1 + i t P t we can write this as M s t P t = L(y t, i t ), L y > 0, L i < 0 Impose market clearing on Fisher relation (assume U separable in c and m) R t,t+1 = β U c(y t+1 ) U c (y t ) { [ 1 + i t = β 1 Uc (y t+1 ) E t U c (y t ) P t P t+1 P t P t+1 ]} 1

10 Models Equilibria In equilibrium, transversality condition implies β T t U c (y T ) E t U T=t c (y t ) Wt s + P t T=t [ y T + β T t E t U c (y T ) U c (y t ) i ] T M T = 1 + i T P T [ y T T ] T P T Simplify to yield the intertemporal equilibrium condition Wt s [ = β T t E t Λ t,t s T + i ] T M T P t 1 + i T P T T=t (IEC) s t T t /P t, primary surplus; Λ t,t β T t U c (y T )/U c (y t ), real discount factor

11 Policy Behavior in Model 1 MP: pegs price of one-period bond {i t } exogenous FP: sets {s t } exogenously All government debt riskless, one-period, nominal Total government liabilities at beginning of t: Wt s = Mt 1 s + (1 + i t 1)B s t 1 Law of motion for government liabilities [ Wt+1 s = (1 + i t ) Wt s P t s t i ] t Mt s 1 + i t Need to ensure that hypothesized policies satisfy this law of motion: can solve the model recursively

12 Equilibrium in Model 1 W s t P t = T=t [ E t Λ t,t s T + i ] T L(y T, i T ) 1 + i T News that E t s T implies P t (anticipated fiscal expansions are inflationary) Although M s t to clear money market, this is a passive response induced by pegging i t M is not causing P Both P t and M s t rise before fiscal changes are realized This is not the usual monetization of deficits, as in unpleasant arithmetic Anticipated surpluses & seigniorage symmetric: i lower E t s T or E T t 1+i T L(y T, i T ) both inflationary (highly irregular)

13 The Economics How can changes in lump-sum taxes affect P? Answer: wealth effect Suppose E t s T HH feels wealthier (lower expected future taxes) able to afford more ct, so demand for goods (at initial prices) because supply of goods fixed, Pt P reaches new eqm by reducing real value of nominal assets held by HH P rises to point where value of nominal assets = PV expected primary surpluses b/c then HH can afford to buy exactly the quantity of goods produced P adjusts until intertemporal eqm condition restored in eqm, no change in wealth from lower anticipated taxes

14 Model 2 Generalize policy behavior with a conventional parametric representation Allow us to characterize the MP/FP behavior that is consistent with existence & uniqueness of eqm Cost of generality: focus on local dynamics within a neighborhood of steady state, rather than previous global results Same model as above

15 Model 2 s Critical Equations [ ] 1 1 Fisher: = βe t 1 + i t π t+1 Money demand: m t = L(i t ) Fiscal Policy: τ t = γ 0 + γb t 1 + ψ t (AR(1) coeff ρ ψ ) Monetary Policy: i t = α 0 + απ t + θ t (AR(1) coeff ρ θ ) GBC: b t + m t + τ t = g + (1 + i t 1)b t 1 + m t 1 where: π t = P t /P t 1, m t = M t /P t, b t = B t /P t π t Linearize & reduce to system in (π t, b t ) with exogenous variables (θ t, ψ t ) reflects two tasks: control πt ; stabilize b t Policy parameters (α, γ) critical to existence & uniqueness of equilibrium

16 Solving Model 2 Using Sims s (2001) notation, let x t = (π t, b t ) and z t = (θ t, b t ) and write system as Γ 0 x t+1 = Γ 1 x t + Φ 0 z t+1 + Φ 1 z t + Πη t+1 η t+1 π t+1 E t π t+1 Eigensystem analysis focuses on the transition matrix [ ] Γ 1 0 Γ αβ 0 1 = αβϕ 1 + ϕ 2 β 1 γ Eigenvalues are αβ & β 1 γ With a single forecast error, η t+1, need one unstable root for a unique eqm to exist this anchors expectations

17 Policy Regimes in Model 2 Four regions of policy parameter space are of interest I : αβ 1 and β 1 γ < 1 Unique Eqm III : I I : I V : αβ < 1 and β 1 γ 1 Unique Eqm αβ < 1 and β 1 γ < 1 Multiple Eq/Sunspots αβ 1 and β 1 γ 1 No Bounded Eqm Nature of eqm very different across regions Region I: monetarist & Ricardian Region II: non-monetarist & FTPL Region III: non-monetarist & FTPL in all eq Region IV: no eqm unless θt & ψ t correlated perfectly

18 Active & Passive Policy Behavior An active policy authority is free to pursue its objectives, unconstrained by the state of government debt decision rule may depend on past, current, or expected future variables A passive policy authority is constrained by the behavior of the active authority and the private sector and must be consistent with equilibrium decision rule necessarily depends on state of government indebtedness, as summarized by current and past variables Active forward-looking & passive backward-looking consistent with Simon s rule vs. discretion perspective as put forth by Friedman and with Sargent-Wallace s terminology

19 Active MP & Passive FP: Regime M Equilibrium is π t = β αβ ρ θ θ t i t = ρ θ αβ ρ θ θ t η t = β αβ ρ θ ε θt Inflation entirely a monetary phenomenon What is FP doing? adjusts future surpluses to cover interest plus principal on debt any shock that changes debt must create the expectation that eventually future surpluses will adjust to stabilize debt s value for MP to target inflation, fiscal expectations must be anchored on FP adjusting to maintain value of debt

20 Active MP & Passive FP: Regime M Equilibrium sequences of {τ t, b t } are determined by the (stable) difference equation in debt and the tax rule Taxes & debt irrelevant for inflation equilibrium exhibits Ricardian equivalence Tax policy stabilizes debt E t 1 b t = (β 1 γ)b t 1 E t 1 ψ t + terms in θ t, θ t 1 Higher debt induced by fiscal or monetary shocks is expected to bring forth higher taxes that retire debt back to steady state Although taxes appear to be irrelevant, tax policy provides essential support to monetary policy

21 Passive MP & Active FP: Regime F Focus on the special case in the FT literature Assume α = γ = ρθ = ρ ψ = 0 α = 0 the nominal interest rate is exogenous γ = 0 the net-of-interest surplus exogenous Equilibrium is i t = ε θt π t = ϕε ψt + βε θt 1, ϕ < 0 b t = δε θt, δ > 0 Features of the equilibrium tax cuts raise inflation open-market sales raise future inflation fiscal shocks do not change value of debt open-market sales raise value of debt

22 Passive MP & Active FP: Regime F Why don t tax shocks change the value of debt? Surprise tax cut at t financed with new nominal debt Monetary policy pegs i t no change in expected inflation (and seigniorage) FP does not allow future taxes to change (γ = 0) At pre-shock prices, a cut in taxes without an increase in expected taxes, makes households feel wealthier Higher wealth leads households to try to raise their consumption paths Higher aggregate demand raises goods prices Price level rises until the wealth effect disappears (B t /P t back to initial value) In equilibrium, no change in real wealth and the tax cut raises current inflation

23 Passive MP & Active FP: Regime F Why does an open-market sale raise future inflation? π t = ϕε ψt + βε θt 1 ϕ < 0 Open-market sale: raises Bt ; contracts M t but Bt = M t total nominal liabilities unchanged so Pt cannot change Monetary contraction: raises B t /P t & i t Higher value of debt supported by higher expected seigniorage revenues Same phenomenon as in unpleasant arithmetic

24 For Completeness: Other Regimes Passive MP & Passive FP Eqm is indeterminate and admits bounded sunspot solutions Both MP & FP are stabilizing debt Neither policy is controlling inflation This is the policy regime in Sargent-Wallace s result about indeterminacy under an interest rate peg Active MP & Active FP No eqm exists with bounded debt Both MP & FP are controlling inflation Neither policy is stabilizing debt An unsustainable policy mix

25 An Observational Equivalence Result Let X t denote the vector of observed (endogenous) time series with joint probability distribution f (X t ) and let ξ t denote the vector of unobserved (exogenous) driving processes with joint probability distribution g(ξ t ). Proposition If g(ξ t ) generates the equilibrium f (X t ) under an active monetary/passive fiscal regime (AM/PF), then there exists another distribution function for the driving processes, h(ξ t ), that also generates the equilibrium f (X t ), but under a passive monetary/active fiscal regime (PM/AF).

26 Observational Equivalence Reasoning Any equilibrium satisfies both conditions M t V t ( ) = P t Y t Wt s = P t T=t E t Λ t,t [ s T + i ] T L(y T, i T ) 1 + i T (QE) (IEC) cannot use these conditions alone to discern regime Solution to any structural model can be written as function of only exogenous shocks but PM/AF regime has structural policy equations that are functions of only exogenous shocks Classic identification problem writ large Problems not well understood by the profession

27 Observational Equivalence Implications For every new Keyesian/Ricardian interpretation of time series, there is an equivalent fiscal theory/ non-ricardian interpretation Bohn (1998)-style regressions not identified Regress st = α + βb t 1 + X t Γ + ε t IEC ˆβ > 0 in every eqm Canzoneri-Cumby-Diba (2001)-style VARs not identified Bivariate {st, b t } VARs reveal dynamics implied also by IEC not policy behavior alone Tests of intertemporal equilibrium condition (IEC) are meaningless if debt is valued, condition must hold expectations unobserved but critical Solution: work much harder to identify policy behavior

28 Maturity of Debt & Inflation Dynamics Long maturity bonds affect inflation dynamics Bonds sold at Q t, issued in t pay φ j dollars j + 1 periods later Bond s duration is (1 βφ) 1 ; consol sets φ = 1 Now W s t = M s t 1 + (1 + φq t)b s t 1 W s t P t = T=t [ E t Λ t,t s T + i ] T L(y T, i T ) 1 + i T W s t no longer predetermined at t news about future st affects both P t & Q t

29 Maturity of Debt & Inflation Dynamics Two no-arbitrage conditions Combining and linearizing i t = βe t 1 π t+1 Q t = i t E t [1 + φq t+1 ] Q t = φ i E t π t+i+1 i=0

30 Maturity of Debt & Inflation Dynamics M s t 1 + (1 + φq t)b s t 1 P t = [ E t Λ t,t s T + i ] T L(y T, i T ) 1 + i T φ i E t π t+i+1 T=t Q t = i=0 Adjustments in value of liabilities come through both P t & Q t Lower Q t pushes inflation into the future Timing: first long-term bond yields move, then short-term, then inflation

31 Long Debt & J.H. Inflation Cochrane / European Economic Dynamics: Review ] (]]]]) ]]] ]]] Cochrane Percent Three Inflation Paths % s shock Shock Date 30 Three Price Level Paths Percent % s shock Shock Date Three reactions to a 10% expected surplus shock. Red triangles: time-t price-level possible reactions to a 10% expected-surpluse shock DS t ¼ðE t E t D Þ R 1 t ¼ 0 e rt s t þt dt. Red triangles display a time-t price-level jum nal inflation. jump Bluefollowed circles displaya by nosteady additional inflationstarting inflation; time bluet. circles: Black triangles steady displaya inflation steady starting inflationat starting time4years t; afterthe alibrated to black an estimate triangles: of the US steady Federal inflation debt maturity starting structure. 4 years (For interpretation after the shock. of the references Calibrated to colour to U.S. in this figure legend the web version of this article.) federal debt maturity structure.

32 the web version of this article.) Long Debt & Inflation Dynamics: Cochrane 12 Bond yield reaction 10 8 s shock Yield Inflation Shock Date ields and inflation, from a 10% shock to expected surpluses DS, when the government sells debt to postpone inflation for 5 years. aturity ofbond the bond yields yields. and Theinflation vertical line fromindicates a 10% theshock date oftothe expected surplus shock. surpluses, I assumewhen a 2% constant the real rate. government sells debt to postpone inflation for 5 years. Numbers indicate the maturity of the bond yields. The vertical line indicates the date of the surplus shock.

33 Application: Fiscal Stimulus M t 1 +B t 1 P t = E PV(Surpluses from t onward) News that future surpluses will be smaller state governments cannot meet pension payments, turn to federal government ($3.2 trillion) 2001 & 2003 tax cuts extended Fannie & Freddie costs higher than anticipated increase in willingness to take on risk flight from quality (raises real discount rates) political clout of tea party rises Each of these reduces market value of debt Increases aggregate demand & inflation Fiscal expansion matched by future fiscal contraction does not stimulate

34 Application: Flight to Quality M t 1 +B t 1 P t Flight to quality = E PV(Surpluses from t onward) shift from risky assets to government bonds sharp reduction in real discount rates increase in E PV(Surpluses) large & sudden revaluation in debt drop in aggregate demand lower inflation & economic activity now and in future Possible source of deflation fears? Ultimate source of demand is fiscal news beyond central bank s control

35 Recurring Policy Regime Change Regime change: realizations of params in policy rule i t = α 0 (S t ) + α π (S t )π t + α x (S t )x t + σ i (S t )ε i t τ t = γ 0 (S t ) + γ b (S t )b t 1 + γ x (S t )x t + σ τ (S t )ε τ t S t evolves stochastically by a known process Many researchers have estimated policy rules to find parameters changed over time Taylor, Clarida-Galí-Gertler, Auerbach, Lubik- Schorfheide, Sala, Favero-Monacelli, Davig-Leeper Fixed-regime theory: problematic interpretation ex-ante agents put probability 0 on change ex-post agents put probability 1 on new regime Cooley-LeRoy-Raymon: this is logically inconsistent

36 Recurring Regime Change: Analytical Example Canzoneri, Cumby, Diba (2001): Ricardian equilibria are more general than non-ricardian if responses of taxes to liabilities is positive infinitely often however small and infrequent then eqm exhibits Ricardian equiv because fiscal response does not stabilize debt, these are potentially equilibria with unbounded debt-output ratios Our example satisfies CCD s assumptions, but delivers a unique eqm in set with bounded debt-output ratios this eqm is non-ricardian important conclusions hinge on unboundedness assumption of CCD

37 Recurring Regime Change: The Model MIUF, constant endowment, log prefs, constant g Fisher equation 1 1 = βe t I t π t+1 Money demand [ ] 1 It 1 m t = c Monetary policy I t Tax policy I t = exp (α 0 + α(s t )ˆπ t + θ t ) τ t = γ 0 + γ(s t )(b t 1 + m t 1 ) + ψ t (θ t, ψ t ) exogenous policy shocks; ˆπ = ln π

38 Recurring Regime Change: The Model S t an N-state Markov chain with transition probs P[S t = j S t 1 = i] = p ij Define expectation error (and use Fisher equation) η t+1 1/π t+1 E t [1/π t+1 ] = β I t π t+1 Then the inflation process is given by ˆπ t+1 = α(s t )ˆπ t + α 0 + θ t ˆη t+1 + ln β Let l t = b t + m t, real govt liabilities Use tax rule & money demand in govt budget constraint [ ] It 1 l t = γ(s t ) l t 1 I t 1 c + D ψ t π t π t D = g γ 0

39 Recurring Regime Change: Solution Assume that i E t [γ t+1 ] = γ ii γ satisfies 1/β γ > 1 iii inflation process is stable in expectation (i.e., there exists a 0 < ξ < such that E t π t+k < ξ for all k (i)-(ii): on average FP active; (iii): on average MP passive Iterate on l equation, take E t 1, apply law of iterated expectations E t 1 [l t+k ] = (1/β γ) [l k+1 t 1 c ( ) 1/β D/c +c 1/β γ 1 Stability requires that l t 1 = c positive if D/c < 1/β ( 1/β D/c 1/β γ 1 ( )] 1/β D/c 1/β γ 1 ), which is

40 Recurring Regime Change: Solution The value of η t is obtained from the budget constraint after substituting in the value of l η t = β (1 + γ(s t)) (1/β D/c) (D/c) (1/β γ 1) 1 + γ D/c + β ( ) 1/β γ 1 ψ t c 1 + γ D/c The unique eqm mapping from ψ t and γ(s t ) to forecast error in inflation η t process yields unique solution for inflation Unique bounded eqm is a fiscal theory eqm tax shocks & parameters affect inflation monetary policy shocks do not affect current inflation

41 Recurring Regime Change: Example Two regimes, N = 2, and policy parameters take on the distinct values in each regime Suppose α(1) and α(2) are sufficiently small such that the inflation process is stable in expectation E[γ t+j S t = 1, Ω t ] = γ(1)p 11 + γ(2)p 12 = E[γ t+j S t = 2, Ω t ] = γ(1)p 21 + γ(2)p 22 γ If either γ(1) or γ(2) is positive, then the model satisfies CCD s premise that taxes adjust to debt infinitely often But negative tax shocks generate wealth effects that raise inflation The only eqm with bounded debt is one in which Ricardian equiv breaks down: counterexample to CCD

42 Recurring Regime Change: Fiscal Theory Always Operative Percentage of time in AM/PF regime in a new Keynesian model % 25% 50% Δ y (%) % 100% Tax Shock 200 Δ π (basis pts) Tax Shock

43 Fiscal Limits Many advanced economies are heading to an era of fiscal stress populations are aging governments have promised many more benefits... than they have made provisions to finance Several European countries Greece, Ireland, Portugal are facing sovereign debt crises even before demographic effects hit Raises the possibility that countries will run against their fiscal limit a point beyond which taxes & spending cannot be adjusted to stabilize debt Regime F becomes relevant at the fiscal limit Just the prospect of a fiscal limit can be sufficient for Regime F effects to arise in current equilibrium

44 U.S. Unfunded Liabilities 35 Percentage of GDP Social Security Source: CBO Long-Term Budget Outlook (June 2009)

45 U.S. Unfunded Liabilities 35 Percentage of GDP Medicare and Medicaid Social Security Source: CBO Long-Term Budget Outlook (June 2009)

46 U.S. Unfunded Liabilities Percentage of GDP 35 Other Federal Non-interest Spending 30 Medicare and Medicaid Social Security Source: CBO Long-Term Budget Outlook (June 2009)

47 Worldwide Unfunded Liabilities Country Aging-Related Spending Australia 482 Canada 726 France 276 Germany 280 Italy 169 Japan 158 Korea 683 Spain 652 United Kingdom 335 United States 495 Advanced G-20 Countries 409 Net present value of impact on fiscal deficit of aging-related spending, in percent of GDP. Source: IMF

48 Rolling Projected Deficits into Debt Alternative Scenario 2010 Alternative Scenario 2009 Percentage of GDP Baseline Scenario 2009 Baseline Scenario Source: CBO Long-Term Budget Outlook (2009 & 2010)

49 Fiscal Limits Spending promises without financing plans create unresolved fiscal stress Raises likelihood that agents will begin to speculate about when and if the economy will hit its fiscal limit Natural questions to ask: 1. What are the effects of unresolved fiscal stress & the prospect of hitting a fiscal limit? 2. What are the impacts of alternative possible resolutions? 3. Even if we knew long-run policies, what might happen along the transition to the long run?

50 Analytic Intuition: Simple Model Consider a flexible price, cashless, endowment economy (as before) The consumption Euler equation reduces to the Fisher equation ( ) 1 Pt = βe t I t P t+1 Transfers grow at rate µ financed by lump-sum taxes and debt z t = (1 µ)z + µz t 1 + ε t, µ < 1/β Government s Budget Constraint: B t P t + τ t = z t + I t 1B t 1 P t

51 Analytic Intuition: Policy Specification At time T economy reaches fiscal limit Monetary Policy I 1 t Regime 1 t = 0, 1,..., T 1 ( ) = I 1 + α Pt 1 P t 1 π Tax Policy τ t = τ + γ ( Bt 1 P t 1 b )

52 Analytic Intuition: Policy Specification At time T economy reaches fiscal limit Monetary Policy I 1 t Regime 1 Regime 2 t = 0, 1,..., T 1 t = T, T + 1,... ( ) = I 1 + α Pt 1 P t 1 π Tax Policy τ t = τ + γ ( Bt 1 P t 1 b ) I 1 t = I 1 τ t = τ max Fiscal limit may be economic (peak of Laffer curve) or political (intolerance of taxation)

53 Analytic Intuition: Polar Case 1 If Regime 1 were absorbing state (No Fiscal Limit) ( α β E Pt t 1 ) = P t 1 1 (Regime 1) P t+1 π P t π ( ) ( ) Bt E t 1 b = E t 1 (z t z ) + (β 1 Bt 1 γ) b P t P t 1 α/β > 1, β 1 γ < 1 Equilibrium π t = π A Standard Monetary Equilibrium

54 Analytic Intuition: Polar Case 2 If Regime 2 were absorbing state ( ) Pt E t = 1 P t+1 βi = 1 (Regime 2) π ( ) B t β = τ E t P t 1 β α = 0, γ = 0 Actual Inflation j=1 β j z t+j P t = ( 1 1 β I t 1 B ) t 1 τ E t j=0 βj z t+j A Standard Fiscal Equilibrium

55 Fiscal Limit: Reneging Monetary Policy I 1 t t = 0, 1,..., T 1 t = T, T + 1,... ( ) = I 1 + α Pt 1 P t 1 π Tax Policy τ t = τ + γ ( Bt 1 P t 1 b ) same τ t = τ max Transfer Policy z t λ t z t E t 1 [B t /P t ] + τ max = E t 1 λ t z t + (β 1 γ)(b t 1 /P t 1 ) λ t adjusts to stabilize debt π t = π A Standard Monetary Equilibrium

56 Fiscal Limit: No Reneging Monetary Policy I 1 t t = 0, 1,..., T 1 t = T, T + 1,... ( ) = I 1 + α Pt 1 P t 1 π Tax Policy τ t = τ + γ ( Bt 1 P t 1 b ) I 1 t = I 1 τ t = τ max Transfer Policy z t same ( Pt E t 1 ) = α ( Pt 1 1 ), P t+1 π β P t π α β > 1 P t = f (z t ; γ, µ, β, π ) A New Fiscal Equilibrium Before the Limit

57 Fiscal Limit: No Reneging Analytics s t = B 0 P 0 = E 0 β j s j j=1 T 1 = E 0 β j s j + j=1 ( ) T 1 1 E 0 β j s j 1 βγ j=t { τ γ(b t 1 /P t 1 b ) z t, t = 0, 1,..., T 1 τ max z t, t = T,...,

58 Fiscal Limit: No Reneging Analytics Evaluate sum from 1 to T 1 T 1 ( ) j β β j s j = (τ γb z ) 1 γβ E 0 T 1 j=1 j=1 j=1 T 1 ( βµ (z 0 z ) 1 γβ Evaluate sum from T to, letting τ max = τ ) j E 0 j=t ( ) β j BT 1 s j = E 0 = βt P T 1 1 β (τ z ) (βµ)t 1 βµ (z 0 z )

59 Fiscal Limit: No Reneging Analytics Pulling it together... [( ) T 1 B 0 1 β T T 1 = P 0 1 βγ 1 β + ( ) j ] β (τ z ) 1 γβ T 1 ( ) j β γb 1 γβ j=1 [( 1 1 βγ j=1 ) T 1 (βµ) T T 1 1 βµ + j=1 ( ) j ] βµ (z 0 z ) 1 γβ

60 Analytic Intuition: Debt 0.8 Fiscal Limit Regime is Passive Monetary/ Active Fiscal Debt GDP Target Debt in Fixed Regime Passive Monetary/ Active Fiscal

61 Analytic Intuition: Debt 0.8 Debt When Fiscal Limit at T = 50 Fiscal Limit Regime is Passive Monetary/ Active Fiscal Debt GDP Target Debt in Fixed Regime Passive Monetary/ Active Fiscal

62 Analytic Intuition: Inflation Fiscal Limit Regime is Passive Monetary/ Active Fiscal Inflation Target Inflation in Fixed Regime Passive Monetary/ Active Fiscal

63 Analytic Intuition: Inflation Inflation When Fiscal Limit at T = 50 Fiscal Limit Regime is Passive Monetary/ Active Fiscal Inflation Target Inflation in Fixed Regime Passive Monetary/ Active Fiscal

64 Analytic Intuition: Expected Inflation Expected Inflation When Fiscal Limit at T = 50 Inflation When Fiscal Limit at T = 50 Fiscal Limit Regime is Passive Monetary/ Active Fiscal Inflation Target Inflation in Fixed Regime Passive Monetary/ Active Fiscal

65 Stronger Response of Taxes to Debt 1.1 Debt When Fiscal Limit at T = 50 Fiscal Limit Regime is Passive Monetary/ More Aggressive 1 Response of Taxes Active Fiscal to Debt Debt When Fiscal Limit at T = 50 Less Aggressive Response of Taxes to Debt Debt GDP Target Debt in Fixed Regime Passive Monetary/ Active Fiscal

66 Stronger Response of Taxes to Debt Inflation When Fiscal Limit at T = 50 More Aggressive Response of Taxes to Debt Inflation When Fiscal Limit at T = 50 Less Aggressive Response of Taxes to Debt Fiscal Limit Regime is Passive Monetary/ Active Fiscal Inflation Target Inflation in Fixed Regime Passive Monetary/ Active Fiscal

67 Fiscal Limit: Implications Expectations of post-limit policies determine pre-limit equilibrium Inflation and debt not anchored on targets Expectations and equilibrium time varying as approach limit More aggressive inflation or debt targeting pre-limit raises instability Monetary policy loses its ability to control inflation and influence economy in usual ways

68 Wrap Up Monetary & fiscal policies always interact to determine equilibrium In normal times, when FP behaves to stabilize debt, we tend to ignore it and focus on MP alone Normal times are over for the foreseeable future FP s effect on inflation are far more subtle than the unpleasant arithmetic story of running the printing press FP can undermine MP s control of inflation even if MP aggressively targets inflation

69 Research Agenda 1. Identifying policy behavior creative approaches to restricting policy rules 2. Quantifying fiscal limits political economy in detailed stochastic general equilibrium models 3. Integrating heterogeneity & policy uncertainty re-slicing the pie has large welfare consequences 4. Understanding sovereign debt default optimal default models too stylized other models too ad hoc 5. Anchoring fiscal expectations MP s control of inflation hinges on correct anchoring what FP frameworks can ensure this? 6. Learning from the past unprecedented things don t happen much how can we extrapolate from past data?