Seoul National University Mini-Course: Monetary & Fiscal Policy Interactions III

Transcription

1 Seoul National University Mini-Course: Monetary & Fiscal Policy Interactions III Eric M. Leeper Indiana University July/August 213

2 Generalizing the Model Up to now, have focused on endowment economies exogenous real interest rate convenient for analytics but can be misleading Now introduce nominal rigidities track MP & FP impacts on real rates and output

3 Nominal Rigidities Follows Woodford (1998) Sticky prices: fraction 1 α of goods suppliers get to set a new price each period Continuum of identical households indexed by j [, 1], each specializes in production of single differentiated good Continuum of differentiated goods each period indexed by z [, 1] Household j maximizes { ( E β [u(c t t) j + v j= M j t P t ) w (y t (j)) where y t (j): HH j s supply of its product and [ 1 ] θ Ct j c j t(z) θ 1 θ 1 θ dz, θ > 1 ]}

4 Nominal Rigidities Household j s budget constraint 1 p t (z)c j t(z)dz + M j t + Q t,t+1 B j t W j t + p t (j)y t (j) P t τ t with P t [ ] 1 1 p t(z) 1 θ 1 θ dz Government s budget constraint and W j t M t 1 + B j t 1 Q t,t+1 B t = B t 1 + P t t (M t M t 1 ) with t τ t, primary deficit Aggregate resource constraint: C t = Y t

5 Nominal Rigidities Equilibrium conditions Q t,t = β T t u (Y T ) u (Y t ) v (M t /P t ) = R t 1 u (Y t ) R t 1 = βe t R t P t P T [ u (Y t+1 ) u (Y t ) lim E t[q t,t W T ] = T P t P t+1 Integrating over all households, intertemporal HH bc { [ E t Q t,t P T C T + R ]} T 1 T=t = R T M T E t {Q t,t [P T Y T P T τ T ]} + M t 1 + B t 1 T=t ]

6 Nominal Rigidities Price-setting behavior HH chooses new price, P t, to satisfy { ( ) } P α k θ E t Q t,t+k Y t t+k [P t µs t+k,t ] P t+k k= = where µ θ/(θ 1) > 1: markup ST,t : marginal cost at T of good whose price was set at t ( ) ) w (Y P θ t T P T S T,t = u P T (Y T ) and price index is P t = [ αp 1 θ t 1 ] 1 1 θ + (1 α)p (1 θ) t Flexible prices: P t = µs t,t, so P t = P, Y t = Y where Y solves u (Y ) = µw (Y )

7 Fiscal Policy as Source of Instability Suppose there are no constraints on FP, so { t } is exogenous Then fiscal disturbances must affect inflation, output, and interest rates, regardless of MP behavior Proof by Contradiction: Suppose there is a MP that delivers stable prices despite fluctuations in t then Yt = Y all t Rt and M t constant and Q t,t = β T t, R = β 1, C t = Y β j R 1 R m = m j= HH s intertemporal budget constraint is W t P = m δ t where δ t j= βj E t t+j

8 Fiscal Policy as Source of Instability W t P = m δ t δ t β j E t t+j j= (IBC) But W t predetermined at t Equilibrium condition (IBC) fiscal shock cannot change δ t Conclusion: Random variation in FP necessarily inconsistent with price stability Conclusion is independent of MP behavior so nothing MP can do to offset instability

9 Analytics for Cashless Limit Version Four-equation system y t = E t y t+1 σ(i t E t π t+1 ) π t = βe t π t+1 + κy t b t = i t + β 1 (b t 1 π t ) + (β 1 1) t i t = απ t + ϕ t Can show that (1 αβ) β j E tπ t+j = b t 1 + β β j E tϕ t+j + (1 β) β j E t t+j ( ) j= j= j= 1. present value of inflation determined by policy shocks 2. more hawkish MP higher α amplifies positive impacts of deficits & interest rates

10 Analytics for Cashless Limit Version Flexible-price case: κ = y t Constant real rate: i t = E t π t+1 Note that E t π t+j = α j π t + α j 1 ϕ t + α j 2 E t ϕ t αe t ϕ t+j 2 + E t ϕ t+j 1 Solve for π t from ( ) π t = b t 1 + β(1 αβ) β j E t ϕ t+j + (1 β) β j E t t+j ( ) j= 1. higher inflation from higher PV deficits or interest rates 2. effect of deficits on π t not affected by MP 3. more hawkish MP increases effect of deficits on expected π Note: E t π t+1 from ( ) consistent j=

11 Analytics for Cashless Limit Version Return to sticky-price model: < κ < output and real interest rate endogenous Real rate: r t+j i t+j 1 π t+j Rewrite ( ) as π t β j E t r t+j = b t 1 + (1 β) j=1 β j E t t+j j= News about higher deficits shows up as a mix of 1. higher current inflation 2. lower path of real interest rates 3. transmits to higher output 4. MP behavior determines split between inflation & real activity

12 Analytics for Cashless Limit Version Combine Euler equation, Phillips curve, MP rule E t π t+2 β 1 (1+β+σκ)E t π t+1 +β 1 (1+ασκ)π t = β 1 σκϕ t Can show two real roots: λ 1 < 1, λ 2 > 1 Solution for expected inflation E t π t+1 = λ 1 π t + (βλ 2 ) 1 σκ j= λ j 2 E tϕ t+j Solve recursively given exogenous { t, ϕ t }, predetermined b t 1 1. solve for π t from ( ) 2. π t & E t π t+1 yield y t 3. i t from MP rule 4. b t from government budget constraint 5. repeat

13 Return to Cash Version with Exogenous FP Assume MP rule that doesn t react to fiscal variables R t = Φ(π t, Y t ) Government issues only 1-period nominal debt B t = R t [B t 1 + P t t (M t M t 1 )] Steady state is t = <, Φ(1, Y ) = β 1 1, R = β 1 Log-linearize system around steady state

14 Equilibrium Consistent with Exogenous FP System is (ˆx t ln(x t ) ln(x )) [ ( ) ] β ˆm t = χ σ 1 Ŷ t ˆR t 1 β Ŷ t = E t Ŷ t+1 σ(ˆr t E tˆπ t+1 ) ˆR t = φ πˆπ t + φ Y Ŷ t ˆb t = ˆR t + β 1 (ˆb t 1 + ˆπ t ) + (β 1 1) ˆ t + γ(ˆm t 1 ˆm t ˆπ t ) ˆπ t = βe tˆπ t+1 + κŷ t where ˆ t t, σ u (Y ), χ v (m ), γ m u (Y )Y v (m )m βb κ (1 α)(1 αβ) ω+σ, ω w (Y ) α σ(ω+θ) w (Y )Y Solve for {Ŷ t, ˆπ t, ˆR t, ˆb t, ˆm t } given ˆ t = ρ ˆ t 1 + ε t

15 Impacts of Deficit With { ˆ t } exogenous, unique eqm requires relatively weak reactions to inflation and output β κ φ 2(1 + β) Y κσ < φ π < 1 1 β κ φ Y Benchmark calibration β =.95, κ =.3, χ = σ = 1, γ =.1, ρ =.6, Y = 1, b /Y =.5 Vary MP choices of φ π and φ Y Pegged interest rate: φ π = φ Y = Weak lean against wind: φ π = φ Y =.3 Aggressive stance: φ π =.9, φ Y =.5

16 Impacts of Deficit: Pegged Rate φ π =φ Y = Output φ π =φ Y = Inflation Nominal Rate φ π =φ Y = Real Rate φ π =φ Y =

17 Impacts of Deficit: Pegged Rate Inflation Debt Output φ π =φ Y =.5 1 φ π =φ Y = Money Growth 2 Deficit φ π =φ Y =

18 Impacts of Deficit: More Hawkish Output Inflation φ π =φ Y = φ π =φ Y = φ π =φ Y = φ π =φ Y = Nominal Rate.1 Real Rate φ π =φ Y = φ π =φ Y = φ π =φ Y = φ π =φ Y =

19 Impacts of Deficit: More Hawkish Inflation Debt Output φ π =φ Y =.5 φ π =φ Y =.3 φ π =φ Y = φ π =φ Y = Money Growth 2 Deficit φ π =φ Y =.3 φ π =φ Y =

20 Impacts of Deficit: Even More Hawkish Output Inflation φ π =.9, φ Y = φ π =.9, φ Y = Nominal Rate.5 x 1 3 Real Rate φ π =.9, φ Y = φ π =.9, φ Y =

21 Impacts of Deficit: Even More Hawkish Inflation Debt Output φ π =.9, φ Y =.5 5 φ π =.9, φ Y = Money Growth 2 Deficit 5 1 φ π =.9, φ Y =

22 Sources of Fiscal Financing Write government budget constraint as ˆb t + E tˆδt+1 = ˆR t + β 1 (ˆb t 1 + ˆδ t ˆπ t ) + γ(ˆm t 1 ˆm t ˆπ t ) ˆδ t (1 β) β j E t ˆ t+j j= Solving for the present value of deficits ˆδ t = (ˆb t 1 ˆπ t ) }{{} surprise revaluation ˆµ t ˆm t ˆm t 1 + ˆπ t +γ β j+1 E t ˆµ t+j β j+1 E t [ˆR t+j ˆπ t+j+1 ] j= } {{ } PV(seigniorage) j= } {{ } PV(real discount rates)

23 Quantitative Implications ˆδ t = (ˆb t 1 ˆπ t ) + γ β j+1 E t ˆµ t+j β j+1 E t [ˆR t+j ˆπ t+j+1 ] j= j= Percentage Due to % Change in ˆπ t PV(seig) PV(r) PV(π) PV(Y) γ =.1 φ π = φ Y = φ π = φ Y = φ π =.9, φ Y = γ = φ π = φ Y = φ π =.9, φ Y = Dynamic Impacts of Exogenous Serially Correlated Deficit Increase seig: seigniorage; r: real discount rate; PV(X): present-value change in X; γ m /(βb ); φ π, φ Y : MP parameters

24 Implications: Monetary Policy Effects An open-market sale of B reduces M, raises R If higher nominal R means higher real r holding FP fixed, this lowers Et PV(s) induces people to substitute out of government debt, into goods raises aggregate demand highly irregular Conventional view implicitly requires FP to generate higher expected surpluses If surpluses rise enough to raise E t PV(s), even with higher real discount rates... tighter MP reduces demand and inflation otherwise, demand and inflation rise

25 Implications: Monetary Policy Effects In new Keynesian model Ŷ t = E t Ŷ t+1 σ(ˆr t E tˆπ t+1 ) ˆπ t = βe tˆπ t+1 + κŷ t ˆπ t = (ˆb t 1 ˆδ t ) γ }{{} = β j+1 E t ˆµ t+j + β j+1 E t [ˆR t+j ˆπ t+j+1 ] j= } {{ } PV(seigniorage) j= } {{ } PV(real discount rates) Tighter monetary policy with fixed surpluses raises ˆR t E tˆπ t+1 in short run: lowers output raises entire path of {Etˆπ t+j }: raise inflation appears as an adverse shift in the Phillips curve More hawkish MP stronger response to inflation prolongs rise in r higher real debt service enhances wealth effects raises inflation still more

26 Implications: Monetary Policy Effects Output Exogenous Rate Inflation Exogenous Rate Nominal Rate Exogenous Rate Real Rate 1.5 Debt Output 4 Money Growth.25.2 Exogenous Rate Exogenous Rate Serially correlated exogenous monetary policy contraction

27 Implications: Monetary Policy Effects Output Inflation Nominal Rate Exogenous Rate More Hawkish More Hawkish Exogenous Rate More Hawkish Exogenous Rate Real Rate 3 Debt Output 4 Money Growth Exogenous Rate More Hawkish More Hawkish Exogenous Rate Serially correlated exogenous monetary policy contraction

28 Empirical Implications MP & FP shocks have very different effects in Regimes M & F Isn t it easy to tell which regime generated observed data? No. For example, Regime F implies: negative correlation between inflation & debt-gdp positive correlation between inflation & money growth any correlation between inflation & nominal debt growth inflation can Granger-cause deficits Common misperception that Regime F creates high inflation Regime M can generate same pattern of correlations Are Regimes M & F observationally equivalent?

29 Real Discount Rates M t 1 + Q t B t 1 P t = E t j= 1 r t,t+j s t+j r t,t+j is j-step-ahead real discount rate Adjustments to eqm need not occur through s t+j price rigidities make future r s important source of financing Changes in E t PV(s) need not occur through s t+j variations in expected r s can have big effects on E t PV(s) with no change in s s Leads to dramatic re-interpretations

30 Flight to Quality M t 1 + Q t B t 1 P t = E t j= 1 r t,t+j s t+j Flight to quality in financial crises and recessions Investors hold debt at lower expected returns As demand for debt rises, demand for goods falls Lower demand reduces inflation Intertemporal equilibrium condition s role lower r s raises Et PV(s) if surpluses unresponsive higher Et PV(s) raises value of debt Fluctuating discount rates can be a source of business cycles in Regime F not in Regime M MP response: raise rates to increase aggregate demand

31 Implications: Discount Rates The recession: conventional story doesn t hold up (Cochrane) Sharp increase in precautionary demand for money not met by supply lower demand & real output Fed flooded economy with reserves no flight to money, out of bonds no bank runs Instead, a flight to all quality M & B out of goods Similar to convention, but focuses on all government debt, rather than just money Appropriate policy responses? announce cuts in fiscal surpluses if surpluses fixed and MP can affect real interest rates, then MP should raise rates Highly irregular

32 The Hungarian Case Hungarian facts courtesy of Magyar Nemzeti Bank Inflation targeting adopted since 21 had mixed success average inflation is lower but still consistently above target real interest rates have tended to be high

33 Hungary: Inflation Experience

34 Hungary: Inflation Experience

35 Hungary: Real Rates

36 Hungary: Real Rates

37 The Hungarian Case Unfair to declare inflation targeting a failure Fiscal policy has been highly volatile huge expansion (6 7% GDP) dramatic reversals: spending cuts & tax hikes but government debt continued to rise as share of GDP About 5% of Hungarian government debt is in HUF it s nominal Even if only a small fraction in HUF, fiscal theory can operate fiscal theory disappears only if all debt is indexed

38 Hungary: Government Debt GDP Ratio

39 Europe: Government Debt GDP Ratio

40 Inflation Targeting Like many countries, Hungary adopted IT without corresponding fiscal reforms Counterexamples include Chile, New Zealand, Norway, Sweden to varying degrees, they imposed fiscal rules in most cases, the rules have been obeyed Monetary & fiscal policies must be consistent long-run IT must be consistent with long-run surpluses most important: views about long-run surpluses must be anchored Ultimately, MP derives its power to control inflation from fiscal backing no fiscal backing MP cannot achieve long-run IT

41 Hungarian Inflation Targeting Suppose Hungarian fiscal surpluses do not credibly adjust to stabilize debt What is the best monetary policy for Hungary? One response is obvious: not aggressive inflation targeting without necessary fiscal backing, aggressive inflation fighting counterproductive makes inflation & output more volatile permanently aggressive inflation fighting generates explosive inflation Depending on maturity structure of debt, MP has power to determine the timing of inflation but not average long-run inflation

42 Hungarian Inflation Targeting Optimal MP under fiscal dominance has not been thoroughly studied see Cochrane s Econometrica 21 paper for a theory of optimal inflation smoothing in a frictionless model see Sims (213) & Leeper-Zhou (213) Existing work on optimal monetary-fiscal policy finds that Regime M dominates Regime F given the observational equivalence between the regimes, this finding is puzzling must stem from auxiliary assumptions, rather than policy behavior More basic research is needed

43 Hungarian Inflation Targeting What about practical advice? Bear in mind effects of real interest rates on E t PV(s) keeping real rates high to fight inflation keeps Et PV(s) low low Et PV(s) depresses value of debt, encourages demand higher demand leads to higher inflation High debt need not imply high inflation if the debt is backed by surpluses, there is no inflation if it s backed by future seigniorage, it might be inflationary effects of higher debt depend on Et PV(s) Need to think about what anchors fiscal expectations Transmission mechanism: E t PV(s) π t+j anything that changes Et PV(s) can affect inflation before s s change

44 A Provocative Proposal Many countries face substantial fiscal consolidation U.K. and U.S. in 212 U.K. net national debt about 7% GDP U.S. federal debt about 8% of GDP If debt is risk-free then bondholders must expect primary surpluses with present value consistent with current debt-gdp ratio Suppose consolidation aims to reduce ratio from 8% to 6% Two steps involved 1. put current primary deficits on path to primary surpluses 2. converge to long-run primary surpluses consistent with 6% ratio

45 A Provocative Proposal Regime M & Regime F consolidations look very different Regime M Consolidation 1. raise taxes & cut spending to convert deficit to surplus 2. continue to raise surplus to retire current debt toward 6% 3. reduce surplus to level consistent with long-run debt target Regime F Consolidation 1. raise taxes & cut spending to convert deficit to surplus 2. reduce surplus to level consistent with long-run debt target Regime F does not require higher surpluses to retire debt

46 Hypothetical Conventional Consolidation To achieve the long-run reduction in debt, must substantially cut spending or raise taxes to overshoot surplus target can overshoot for decades then can gradually reduce primary surpluses These short-run adjustments will certainly slow economic growth slower growth will automatically reduce revenues & increase expenditures these impacts are not reflected in the graph This is what many European countries have been doing, bringing new recessions What are the welfare costs of conventional consolidation?

47 Hypothetical Conventional Consolidation Primary Surplus Value of Debt Paths of Primary Surplus & Debt: Debt-GDP from 8% to 6% Surpluses Must Overshoot Long-Run Target

48 Alternative Fiscal Consolidations Conventional consolidation takes inflation off table What can inflation do? government debt is nominal & long-term current or future inflation devalues debt can avoid overshooting surplus target requires less fiscal adjustment But wait... there s more if monetary policy prevents nominal rates from rising with inflation as it has the past 4 years then real interest rates fall stimulates consumption & aggregate demand Alternative consolidation can avoid retarding growth What are the welfare costs of alternative consolidation?

49 Hypothetical Alternative Consolidation Primary Surplus Value of Debt Paths of Primary Surplus & Debt: Debt-GDP from 8% to 6%

50 Illustrative Model of Inflation Determination Endowment economy with infinitely-lived agents, at cashless limit Long-term nominal bonds, B Mt, sell at price P Mt bond issued at t pays ρ j dollars at t + j + 1 average duration of bond: (1 βρ) 1 ρ = : all bonds 1 period FP: chooses primary surplus, s t MP: chooses 1-period nominal interest rate, R t Debt Management: chooses average maturity, ρ Equilibrium: c t = y for all t

51 Government Behavior Government s choices of {R t, s t, B Mt } and ρ satisfy P Mt B Mt P t + s t = (1 + ρp Mt)B Mt 1 P t For now, government not optimizing posit ad hoc but typical rule on agenda: compute welfare consequences of alternative consolidation schemes Government s choices constrained by conditions for equilibrium market clearing household s first-order conditions household s transversality condition: optimal behavior limits growth rate of government debt

52 Asset-Pricing Relations ( ) 1 1 = βe t R t π t+1 P Mt = 1 R t E t (1 + ρp Mt+1 ) These imply P Mt = β = ( j (βρ) j E t j= i= ( j ) ρ j 1 E t R t+i i= j= ) 1 π t+i+1

53 An Equilibrium Condition Imposing equilibrium, asset-pricing relations, transversality (1 + ρp Mt )B Mt 1 P t = β j E t s t+j j= (IEC) In conventional consolidation... MP unconstrained: determines equilibrium {P t } {P Mt } FP constrained: chooses {st } to satisfy (IEC) In the alternative consolidation... FP unconstrained: determines equilibrium {Pt, P Mt } MP constrained: determines timing of inflation

54 Thought Experiment Take path of {s t } for from Congressional Budget Office Budget Projections, March 212 conventional consolidation: st for 223 & 224 increases by 1% each year alternative consolidation: st reaches long-run target early Debt-output, P Mt B Mt /P t initial: 8% target: 6% Model calibration 1. real interest rate 2% 2. initial inflation 2% 3. vary average maturity

55 Conventional Consolidation MP obeys 1 = 1 ( 1 R t R + α 1 ) π t π Combine with Euler equation ( 1 E t 1 ) = α ( 1 1 ) π t+1 π β π t π Unique bounded solution when α > β is π t = π for all t

56 Conventional Consolidation After CBO projection period, s t obeys s t = s + γ(p Mt 1 b Mt 1 P Mb M) Impose the Euler equation E t 1 ( 1 + ρpmt π t ) = 1 β P Mt 1 on government s flow constraint and substitute s rule ( ) ( ) PMt+1 b Mt+1 P E Mb M t = (β 1 PMt b Mt P γ) Mb M P t+1 P t γ > β 1 1 stabilizes debt, ensuring (IEC) holds Overshooting: P Mt 1 b Mt 1 > P Mb M s t > s

57 Conventional Consolidation With MP aggressively targeting inflation... inflation cannot be used to reduce value of debt consolidation requires surplus to overshoot long-run target higher surpluses retire debt to achieve 6% target In reasonable model, where taxes distort & government spending affects demand... during overshooting, output will fall choice of γ determines speed of adjustment higher γ amplifies overshooting, exacerbating economic downturn lower γ prolongs adjustment period, keeping output persistently weak Should we take inflation off the table?

58 Alternative Consolidations FP sets {s t } exogenously independently of debt MP sets {R t } to react weakly to inflation (1 + ρp Mt )B Mt 1 P t = β j E t s t+j j= (IEC) In (IEC): right-side given, B Mt 1 predetermined (IEC) determines continuum of (P t, P Mt ) combinations Can think of this as E t PV(s) determining j= (βρ) j E t P t 1 P t+j The expected present value of inflation Longer maturity higher ρ permits inflation to be postponed

59 Alternative Consolidation #1 MP pegs R t = R π t+j = π j 1 all inflation occurs at t future inflation at π = 2% PMt = P M all t (Not a realistic scenario, as it requires flexible prices)

60 Alternative Consolidation #1 6 Inflation Bond Price Paths of Inflation & Bond Prices: Debt-GDP from 8% to 6%

61 Alternative Consolidation #2 Examine tradeoff between current & (fixed) future inflation (1 + ρp Mt )B Mt 1 = β j E t s t+j (IEC) P t With fixed future inflation, π F j= β P Mt = π F ρβ π F π t (π F ρβ) = E tpv(s) b Mt 1 Consolidation changes E t PV(s), given initial b Mt 1 at 8% Note ρ = future inflation off the table

62 Alternative Consolidations Current Inflation (π t ) Average 2% 4% 6% Maturity Future Inflation (π F ) 5-year year year year year year Feasible Current Inflation (π t ) and Future Inflation (π F ) Combinations & Average Debt Maturity (Annual %)

63 Alternative Consolidation #2 Longer average maturity, more can spread inflation over time Requires a particular monetary policy Long maturities imply small inflation cost to consolidation Some realities 1. in U.S., Fed has been shortening outstanding maturity via QE II & III efforts to reduce long rates to stimulate growth 2. irony: with fears of deflation, this is precisely the policy to pursue 3. further irony: no policy makers are seriously considering this option

64 Where To Go From Here 1. Employ new Keynesian model sticky prices: higher inflation lowers real interest rates lower real rates raise output, consumption, investment get an economic expansion from alternative consolidation 2. Introduce distorting taxes & government spending 3. Compare welfare costs of conventional & alternative consolidation 4. Brings back into the picture an old topic: optimal maturity structure of government debt

65 Take Aways In a world where FP cannot be relied on to adjust surpluses as needed to stabilize debt it is impossible for MP to stabilize the economy 2. fiscal disturbances will always affect output, inflation & interest rates 3. more aggressive MP will exacerbate the instability 4. fluctuations in confidence that affect real interest rates will transmit into fluctuations in output & inflation 5. sudden flights to quality or away from junk can have real effects 6. tighter MP raises debt service, wealth, aggregate demand, and inflation

66 Take Aways 1. Conventional perceptions of inflation miss a channel for fiscal inflation channel may be important in times of fiscal stress 2. Perception that MP can always stop an inflation that breaks out assumes the necessary fiscal backing will always be forthcoming when fiscal limit possible, the assumption breaks down 3. If inflation has fiscal roots, MP cannot offset it 4. Two policy options: i. impose enforceable rules on fiscal behavior ii. give different mandates to central banks