Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic

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1 Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic Behzad Diba University of Bern May 2011 (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

2 A Coordination Problem Sargent and Wallace (1981) highlight a coordination problem between fiscal and monetary policies (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

3 A Coordination Problem Sargent and Wallace (1981) highlight a coordination problem between fiscal and monetary policies The basic questions are about which policy is ultimately responsible for satisfying the public sector s consolidated PVBC (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

4 A Coordination Problem Sargent and Wallace (1981) highlight a coordination problem between fiscal and monetary policies The basic questions are about which policy is ultimately responsible for satisfying the public sector s consolidated PVBC Will the treasury deliver the requisite surpluses, given the path of inflation set by the central bank? (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

5 A Coordination Problem Sargent and Wallace (1981) highlight a coordination problem between fiscal and monetary policies The basic questions are about which policy is ultimately responsible for satisfying the public sector s consolidated PVBC Will the treasury deliver the requisite surpluses, given the path of inflation set by the central bank? Or, will the central bank eventually deliver the seigniorage revenues needed to make up for a shortfall of fiscal surpluses? (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

6 A Coordination Problem Sargent and Wallace (1981) highlight a coordination problem between fiscal and monetary policies The basic questions are about which policy is ultimately responsible for satisfying the public sector s consolidated PVBC Will the treasury deliver the requisite surpluses, given the path of inflation set by the central bank? Or, will the central bank eventually deliver the seigniorage revenues needed to make up for a shortfall of fiscal surpluses? We can see the main point using our simple cash-in-advance model with a constant endowment and government purchases (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

7 A Coordination Problem Sargent and Wallace (1981) highlight a coordination problem between fiscal and monetary policies The basic questions are about which policy is ultimately responsible for satisfying the public sector s consolidated PVBC Will the treasury deliver the requisite surpluses, given the path of inflation set by the central bank? Or, will the central bank eventually deliver the seigniorage revenues needed to make up for a shortfall of fiscal surpluses? We can see the main point using our simple cash-in-advance model with a constant endowment and government purchases Following Sargent and Wallace, we assume that the government issues real bonds to finance its deficit; we will see later how the results change in a model with nominal bonds (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

8 A Simple Setup In our CIA model with real bonds, a constant endowment, and constant government purchases, we got the PVBC b t = E t β {τ j t+j + j=0 ( Pt+j P t+j 1 P t+j ) } y G (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

9 A Simple Setup In our CIA model with real bonds, a constant endowment, and constant government purchases, we got the PVBC b t = E t β {τ j t+j + j=0 ( Pt+j P t+j 1 P t+j Define the inflation rate (just for present purposes) as and write the PVBC as b t = E t π t = P t P t 1 P t β j s t+j + ye t β j π t+j j=0 j=0 ) } y G where s t τ t G is the primary surplus exclusive of seigniorage (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

10 A "Leading" Central Bank Suppose an independent central bank is the "leader" in the ensuing game and sets the present value of seigniorage revenues K m,t ye t β j π t+j j=0 (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

11 A "Leading" Central Bank Suppose an independent central bank is the "leader" in the ensuing game and sets the present value of seigniorage revenues K m,t ye t β j π t+j j=0 Then, the fiscal authority has to set the present value of its surpluses, K f,t E t β j s t+j, j=0 to satisfy K f,t = b t K m,t (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

12 A "Leading" Treasury Alternatively, suppose an intransigent fiscal authority is the leader and sets the present value of its surpluses K f,t E t β j s t+j j=0 (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

13 A "Leading" Treasury Alternatively, suppose an intransigent fiscal authority is the leader and sets the present value of its surpluses K f,t E t β j s t+j j=0 Then, the central bank has no choice and must deliver the present value of seigniorage revenues that satisfy the PVBC: K m,t ye t β j π t+j j=0 K m,t = b t K f,t (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

14 A Game of Chicken There is nothing in this setup to pin down which policy leads and which one follows (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

15 A Game of Chicken There is nothing in this setup to pin down which policy leads and which one follows The PVBC is viewed as a constraint that the two policies must jointly satisfy (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

16 A Game of Chicken There is nothing in this setup to pin down which policy leads and which one follows The PVBC is viewed as a constraint that the two policies must jointly satisfy The monetarist view of price determination and inflation control is accurate only if the fiscal authority follows the central bank s lead (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

17 A Game of Chicken There is nothing in this setup to pin down which policy leads and which one follows The PVBC is viewed as a constraint that the two policies must jointly satisfy The monetarist view of price determination and inflation control is accurate only if the fiscal authority follows the central bank s lead in this case, the central bank can set the path of the money supply, and the CIA constraint determines the path of the price level (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

18 A Game of Chicken There is nothing in this setup to pin down which policy leads and which one follows The PVBC is viewed as a constraint that the two policies must jointly satisfy The monetarist view of price determination and inflation control is accurate only if the fiscal authority follows the central bank s lead in this case, the central bank can set the path of the money supply, and the CIA constraint determines the path of the price level but this entails an assumption that fiscal policy will adjust surpluses to satisfy the PVBC (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

19 A Game of Chicken There is nothing in this setup to pin down which policy leads and which one follows The PVBC is viewed as a constraint that the two policies must jointly satisfy The monetarist view of price determination and inflation control is accurate only if the fiscal authority follows the central bank s lead in this case, the central bank can set the path of the money supply, and the CIA constraint determines the path of the price level but this entails an assumption that fiscal policy will adjust surpluses to satisfy the PVBC Avoiding a solution with fiscal leadership has motivated arguments for fiscal constraints, like the ones in the Stability and Growth Pact (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

20 The Unpleasant Arithmetic The central bank s ability to control inflation is limited in the case with fiscal leadership (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

21 The Unpleasant Arithmetic The central bank s ability to control inflation is limited in the case with fiscal leadership Inflation can be stabilized at a level that delivers the necessary present value of surpluses (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

22 The Unpleasant Arithmetic The central bank s ability to control inflation is limited in the case with fiscal leadership Inflation can be stabilized at a level that delivers the necessary present value of surpluses But reducing inflation at time t requires increasing inflation by more than the initial reduction at a future date t + T (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

23 The Unpleasant Arithmetic The central bank s ability to control inflation is limited in the case with fiscal leadership Inflation can be stabilized at a level that delivers the necessary present value of surpluses But reducing inflation at time t requires increasing inflation by more than the initial reduction at a future date t + T Given K m,t = b t K f,t and K m,t ye t the changes in inflation must satisfy β j π t+j j=0 π t + β T E t π t+t = 0 (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

24 Intuition and Extensions In our simple model implying π t + β T E t π t+t = 0 we get E t π t+t = β T π t (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

25 Intuition and Extensions In our simple model implying we get π t + β T E t π t+t = 0 E t π t+t = β T π t This is because the gross real interest rate on public debt is 1/β per period, in the simple model implying a constant path of consumption (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

26 Intuition and Extensions In our simple model implying π t + β T E t π t+t = 0 we get E t π t+t = β T π t This is because the gross real interest rate on public debt is 1/β per period, in the simple model implying a constant path of consumption More generally, reducing seigniorage revenues at t entails issuing bonds that must be redeemed with interest, by collecting more seigniorage later (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

27 Intuition and Extensions In our simple model implying π t + β T E t π t+t = 0 we get E t π t+t = β T π t This is because the gross real interest rate on public debt is 1/β per period, in the simple model implying a constant path of consumption More generally, reducing seigniorage revenues at t entails issuing bonds that must be redeemed with interest, by collecting more seigniorage later We will revisit this and other implications of the Monetarist Arithmetic later, when we study the Fiscal Theory of the Price Level (Institute) Monetary/Fiscal Interactions: Unpleasant Monetarist Arithmetic May / 8

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