Walsh Chapter 4 Part 1: Fiscal Policy, Prices, and Inflation

Transcription

1 Walsh Chapter 4 Part 1: Fiscal Policy, Prices, and Inflation

2 1 Government Budget Constraint 1.1 Flow Budget Constraint Fiscal Authority G t + i t 1 B T t 1 = T t + B T t BT t 1 + RCB t where superscript T denotes total bonds and RCB denotes receipts from the central bank Sources of revenue are taxes, increases in total bonds, and receipts from the central bank Uses of revenue are for spending and interest payments

3 Monetary Authority B m t B m t 1 + RCB t = i t 1 B m t 1 + H t H t 1 where H is high-powered money Sources of revenue are interest on bonds and increases in high-powered money Uses of revenue are for purchases of bonds and payments to treasury

4 Consolidated budget constraint : add, letting B denote bonds held by the public B = B T B m G t + i t 1 B t 1 = T t + B t B t 1 + H t H t 1 Sources of revenue are taxes, increases in bonds held by the public, and increases in high-powered money Uses of revenue are for spending and interest payments

5 Consolidated budget contstaint in real terms where t is real taxes and b t + h t = g t t t i t 1 b t 1 + h t π t π t = P t 1 P t

6 How does inflation affect the budget constraint, allowing uncertainty on inflation: must solve for 1 + i t 1 Let consumer s value function by Subject to V t ω = max {u c t, m t + βe t V ω t+1 } ω t = c t + b t + h t + k t = f k t δ k t 1 t t + [ 1 + it 1 b t 1 + m t π t ]

7 FO conditions u c c t, m t = 1 + it βe t V ω ω t π t+1 = βe t V ω ω t+1 f k k t + 1 δ βe t V ω ω t r t Assume the utility function yields superneutrality making E t V ω ω t+1 independent of money and solve for the nominal interest rate 1 + i t = 1 + r t E 1 t 1+π t+1

8 Substitute into the government budget constraint b t + h t = g t t t r t 1 b t 1 E 1 t 1 1+π 1 + πt + h t π t t inflation reduces the outstanding value of money, generating real revenue seigniorage only unexpected inflation affects the real value of bonds expected inflation causes a corresponding increase in the nominal interest rate

9 1.2 Intertemporal Budget Constraint flow budget constraint b t + h t = g t t t i t π t b t 1 + h t π t define expost real interest rate as 1 + r t = 1 + i t 1 + π t+1 solve for present-value budget constraint

10 add present value debt terms b r 1 b r r b r 0 b r 1 b r 1 b 1 = 1 + r 1 b 1 + lim b T Π T 1 T j= r j

11 add present value high-powered money terms, defining method 1 R 0,t = Π t 1 j= r j h t h t π t R 0,t, where first discount factor R 0,0 is understood to be unity. = H t H t 1 h t h t 1 = H t H t 1 P t π t P t P t 1 P t Ht H = t 1 Ht 1 P t 1 P t 1 P t H t 1 P t = θh t π t

12 by definition h t = 1 + θ H t π t P t 1 = 1 + θ 1 + π t h t 1 solving for h t 1 h t 1 = 1 + π t 1 + θ h t therefore θh t 1 = θ 1 + π t 1 + θ h t PV seigniorage = θ 1 + θ h t R 0,t

13 IBC becomes 1+r 1 b 1 = t t g t + θ 1 + θ h t R 0,t + lim T b T R 0,T 1

14 method 2 collect terms on money for each particular period h 0 P 1 h 1 P r r h 1 P 0 h 0 P r 1 = P 1 h 1 + h 0 P r 0 h 1 = P 1 P 0 h it h 2 P 1 P 2 h r r i i P0 P 1 P1 P 2 h t R 0,t lim h T Π T 1 T j=0 lim h T Π T 1 T j= r j r j

15 setting limit to zero implies PV seigniorage = θ 1 + θ h t R 0,t = it 1 + i t h t R 0,t H 1 P 0 Present value seigniorage is the present value of interest expenditures on money less initial real money valued at P 0 treating seigniorage as interest expenditures on money overstates its value, since it does not subtract P 1 P 0 h 1 cannot get seigniorage without money growth.

16 setting limit terms to zero, IBC becomes 1 + i 1 B 1 + H 1 P 0 = t t g t + it h t R 0,t 1 + i t Fiscal Theory of the Price Level Let g 0 increase with no offseting increase in present value taxes Requires P 0 to increase to reduce the government s outstanding debt

17 2 Price and Inflation under perfect foresight 2.1 Monetary Policy Monetary policy determines expected inflation P t P t+1 = 1 + r t 1 + i t 1 + r t determined by real part of economy, independent of money or monetary growth monetary authority can choose i t, thereby controlling π t+1

18 beginning with t = 0 P 0 P 1 = 1 + r i 0 choice of i 0 determines P 1 relative to P 0, but what determines P 0?

19 2.2 Determination of P 0 Fiscal Policy and the Fiscal Theory of the Price Level Agent intertemporal budget constraint with endowment economy y t c t t t it 1 + i i h t R 0,t i t 1 B 1 + H 1 P 0 = 0 Solving for consumption c t R 0,t = 1 + i t 1 B 1 + H 1 + P 0 y t t t it 1 + i i h t R 0,t

20 Goods market equilibrium y t = c t + g t Substituting into agent s IBC yields government IBC FTPL g t t t it 1 + i i h t R 0,t i t 1 B 1 + H 1 P 0 = 0 s t R 0,t = 1 + i t 1 B 1 + H 1 P 0 Consider a tax cut which raises disposable income The tax cut is not offset by future tax increases or by government spending reduction

21 PV agent wealth is up, implying agent wants more consumption As agent tries to raise consumption P 0 increases The increase in price reduces wealth until they want the same consumption Using FTPL, tax cut reduces PV surpluses, requiring reduction in liabilities, ie real debt

22 Ricardian world Tax cut must be offset by future tax increases or by government spending reduction to that government IBC holds at any price level P 0 is indeterminate

23 2.3 Controlling Inflation Sargent and Wallace "Unpleasant Monetarist Arithmetic" Put time subscripts on monetary growth rates 1+r 1 b 1 = t t g t + θt 1 + θ t h t R 0,t + lim T b T R 0,T 1 limit term must be zero from household s transversality condition bonds are real, and real interest rate is offerred on real bonds, so inflation does not affect debt increase in g t with no corresponding change in t t must raise θ eventually, and the longer the increase is postponed, the larger the eventual increase must be

24 calls for independent monetary authority which cannot be forced to comply with fiscal policy

25 implications for current price level θt 1 + θ t h t R 0,t = it 1 + i i h t R 0,t H 1 P 0 increase in θ t will increase i t and agents will want less real money cannot have future anticipated jump in P therefore, expectation that P will rise in the future so real money right when i increases implies that it rises today fiscal expansion causes inflation today even if the monetary authority does not accomodate with money growth until the future

26 Compare effects of fiscal policy under UMA and FTPL UMA 1 + r 1 b 1 = t t g t + θ 1 + θ h t R 0,t FTPL 1 + i t 1 B 1 + H 1 P 0 = t t g t + it 1 + i i h t R 0,t With nominal bonds, price level increase has substantial affect on government debt, even if money growth does not rise. Non-monetary economy lim H 0, can still determine price level

27 3 Price and Inflation under Uncertainty 3.1 Present value surplus shocks create shocks to P 0 Define the present value of future real surpluses at time 0 ŝ 0 = 1 P 0 1 P t s t Π t j=1 1 + it j Let nominal initial government debt be D 1 = 1 + i t 1 B 1 + M 1

28 Government intertemporal budget constraint P 0 ŝ 0 = D 1 Let D 1 = 0 ŝ 0 cannot be stochastic and must equal 0 to satisfy IBC FTPL cannot apply with zero outstanding debt initially a goverment must plan on no PV surpluses or deficits if a deficit in first period, must be planning PV surpluses after that

29 PV surplus shocks create price shocks ŝ 1 can be stochastic if D 0 > 0 P 0 ŝ 0 = P 0 s 0 + P 1ŝ i 0 P 1 ŝ 1 = D 0 positive jumps in ŝ 1 must be offset by negative jumps in P 1 ŝ 1 = D 0 P 1 going forward, government cannot plan future surplus adjustments that violate this budget contraint

30 future surplus shocks, which cause actual PV surpluses to deviate from ŝ 1, must be unexpected

31 Surplus shocks cannot generate systematic revenue no free lunch ŝ 1 is stochastic, but it is subject to restrictions monetary authority sets E 0 π 1 with its choice of i 0 E 0 ŝ 1 = E 0 D 0 P 1 = d π cannot generate revenue with "surprise" surplus reductions each period because will not be a surprise A government with no shocks to ŝ 1 has fiscal policy which is Ricardian and passive no effect on prices A government with shocks to ŝ 1 has fiscal policy which is dominant, non- Ricardian, and active determines price level

32 3.2 Observational Equivalence Government budget constraint has to hold whether debt responds to the surplus or the surplus responds to debt How does real debt respond to a fall in the surplus? Canzonerie et al showed that real debt rises when the surplus falls due to flow budget constraint, not accounting for change in price If surpluses are autocorrelated, then s down implies ŝ down, and FTPL says real debt should fall Cochrane shows that the only way to raise real debt with a fall in the surplus is for agents to believe ŝ has gone up so the government can pay the new debt

33 Use policy regressions, with the surplus regressed on lagged debt