MONETARY AND FINANCIAL MACRO BUDGET CONSTRAINTS

Transcription

1 MONETARY AND FINANCIAL MACRO BUDGET CONSTRAINTS Hernán D. Seoane UC3M

2 INTRODUCTION Last class we looked at the data, in part to see how does monetary variables interact with real variables and in part as a motivation. We now turn to modeling money and monetary behavior. We start using models. Why do we need a model? Because reality is just too complicated to analyze it without any kind of simplification. A model is a theoretical structure that intends to simplify reality to highlight only the important aspects of it for the question we want to answer. When talking about monetary questions we will need models that allow us to model monetary and macro variables and most importantly that are useful to analyze economic behavior.

3 INTRODUCTION The main model we use is the Overlapping Generations Model: it highlights reasons why people want to hold money. Before going into the model we will abstract from any behavioral assumptions and we will focus on budget constraints. Understanding budget constraints is key in monetary macroeconomics. Budget constraints is the analogous of gravity laws in economics. Any model that means something or that is useful for anything needs a well defined set of budget constraints. Today we will dissect the budget constraints of 3 agents: Government, Central Bank and Private Sector. We use it also to introduce macro and monetary aggregates and definitions.

4 BIBLIOGRAPHIC REFERENCES Walsh Monetary theory and policy Chapter 4 (I follow closely his presentation) William Buiter (1982): The Proper Measurement of Government Budget Deficits: comprehensive wealth accounting or permanent income accounting for the public sector: its implications for policy evaluation and design. NBER Working Paper series. Paper Giannitsarou and Scott (2006) Inflation Implications of Rising Government Debt NBER Working paper series. Paper 12654

5 KEY CONCEPTS Inflation as a tax. Seigniorage. Intertemporal budget constraint. Intertemporal discount. Public Deficit/surplus.

6 FISCAL BRANCH OF THE GOVERNMENT ( ) G t + i t 1 B T t 1 = T t + B T t B T t 1 + RCB t This equation relates resources and uses of the government (fiscal branch): Treasury s budget constraint. Represents the budget constraint of the fiscal authority. Nominal terms in period t.

7 CENTRAL BANK ( B M t B M t 1 ) + RCB t = i t 1 B M t 1 + (M t M t 1 ) Represents the budget constraint of the monetary authority. B M t are the central bank purchases of sovereign debt. Also measured in nominal terms

8 CONSOLIDATED GOVERNMENT-CENTRAL BANK G t + i t 1 B t 1 = T t + (B t B t 1 ) + (M t M t 1 ) Here, B t = B T t BM t, the level of sovereign debt held by the private sector. Uses versus resources of the consolidated government-central bank. Political economy issues on the relationship of these two agents: central bank independence.

9 BUDGET CONSTRAINT IN REAL TERMS G t P t + i t 1 B t 1 P t = T ( t Bt + B ) ( t 1 Mt + M ) t 1 P t P t P t P t P t Divide by P t everywhere to write the budget constraint in terms of goods (real terms). We can operate a little bit more to find a nicer expression, multiply and divide the terms with t 1 using P t 1. The use lowercase letters to denote variables in real terms.

10 BUDGET CONSTRAINT IN REAL TERMS [ ] ( 1 + it 1 g t + 1 b 1 + t 1 = t t + (b t b t 1 ) + m t m ) t 1 π t 1 + π t Use r t 1 1+i t 1 1+π t 1: ex-post real return from t 1 to t The last term in this expression is called seigniorage

11 BUDGET CONSTRAINT IN REAL TERMS THE ROLE OF UNANTICIPATED INFLATION ( πt πt e g t + r t 1 b t 1 =t t + (b t b t 1 ) π t [ ( ) ] 1 m t m 1 + t 1 π t ) (1 + r t 1 )b t 1 + Use r t for the ex ante real rate of return Use πt e for the expected inflation rate We can write: 1 + i t 1 = (1 + r t 1 )(1 + πt e)

12 SEIGNIORAGE s t = M t M t 1 P t ( ) 1 = m t m 1 + t 1 π t The real change in the monetary base. s t = M ( ) t M t 1 πt = (m t m t 1 ) + m P t 1 + t 1 π t It can be decomposed: pure seigniorage and inflationary tax

13 SEIGNIORAGE 2 sources: the change in the real high powered money (the government obtains resources from the private sector) To mantain a constant level of real balances, the private sector needs to increase the nominal amount of money to compensate for the real value loss of inflation. By supplying this money, the government also acquires resources. What happens if inflation is 0? Does the government receive revenues? The government can still save interest rate payments if gets financing using money rather than debt. To see this, rewrite the seigniorage in an alernative way. Use total real liabilities fo the government, d = b + m, and rewrite the budget constraint

14 SEIGNIORAGE ( πt πt e g t + r t 1 d t 1 =t t + (d t d t 1 ) π t ( ) it 1 m t π t ) (1 + r t 1 )d t 1 + Here, we find an alternative definition of seigniorage s = ( ) i 1+π m Notice that the return on high powered money depends on the nominal interest rate

15 THE INTERTEMPORAL BUDGET CONSTRAINT The single period budget constraint, ignoring the effects of surprise inflation g t + r t 1 b t 1 = t t + (b t b t 1 ) + s t Notice that here there is a relationship between variables dated at t and t 1 periods. Moreover, we can move forward one period this equation and write g t+1 + r t b t = t t+1 + (b t+1 b t ) + s t+1 The instantaneous budget constraint holds for every period. We can use b t to merge them into one equation.

16 THE INTERTEMPORAL BUDGET CONSTRAINT For simplicity assume r t = r for all t. Solve forward, (1 + r)b t 1 + i=0 What s the last term? Use = g t s g t+i (1 + r) i = i=0 (1 + r)b t 1 = t t+i (1 + r) i + i=0 i=0 t+i (1 + r) i s t+i (1 + r) i + lim b t+i i (1 + r) i Important discussion: is this a constraint for the government? Or is it an equilibrium condition that has to hold for an interest rate and a price level?

17 MONETARY AND FISCAL POLICY REGIMES Monetary and fiscal policy are related through the consolidated government-central bank budget constraint. There are several theories on how fiscal and monetary policies interact and related to the way they affect dynamics Ricardian regimes Monetary Dominant Regimes Fiscal Dominant Regimes Non-Ricardian regimes: the governments budget constraint may not be satisfied for all price levels (The fiscal theory of the price level)

18 Let s focus in a Ricardian World DEFICITS AND INFLATION Use R = 1 + r and notice the IBC can be written as b t 1 = R 1 R i=0 i (g t+i t t+i s t+i ) Use s f t t t g t to denote the primary surplus Then, the constraint can be re-written as b t 1 = R 1 R i=0 i ( s f t+i ) + R 1 R i (s t+i ) i=0 The unpleasant monetarist arithmetic pops up: if the present value of surplus falls, the present value of seigniorage has to increase

19 DEFICITS AND INFLATION II What does data say? Is inflation and deficits related somehow? Estimate the effects of deficits on money growth Grier and Neiman (1987) summarize existing literature and suggest that fiscal deficit help to predict future seigniorage (so dar King and Plosser (1985)) in US Empirical literature ignore information aboutlong run behavior of taxes, debt and seigniorage implied by the IBC IBC implies that primary deficit and the stock of debt are cointegrated Bohn (1991) studied this type of model but did not consider seigniorage separately

20 RICARDIAN AND (TRADITIONAL) NON-RICARDIAN FISCAL POLICIES Let s go back to the gov budget constraint in a simplified form (1 + r t 1 )b t 1 = t t + b t + s t Specify now the budget constraint of a representative agent c t + m t + b t = y + (1 + r t 1 )b t 1 + m t π t t t Let s introduce a simple fiscal policy rule Assume the government sets taxes as T t = ψ(1 + r t 1 )b t 1 Here T t is the present discounted value of taxes

21 RICARDIAN AND (TRADITIONAL) NON-RICARDIAN FISCAL POLICIES II ( ( ) By definition T t = t t + Tt+1 E t = t t + ψ(1+rt )b E t t 1+r t = t t + ψb t And given that T t = ψ(1 + r t 1 )b t 1, 1+r t ) t t = ψ(r t 1 b t 1 b t ) Also s t = (1 ψ)(r t 1 b t 1 b t ) Our policy implies that a part of debt is backed out by taxation and the other part by seigniorage If ψ = 1, Sargent (1982) calls it Ricardian, taxes backed out all sovereign debt If ψ < 1, it is called (traditionally) Non-Ricardian. Seigniorage has to accomodate to back out a part of debt

22 RICARDIAN AND (TRADITIONAL) NON-RICARDIAN FISCAL POLICIES III Substituting t t in the households budget constraint c t + m t + (1 ψ)b t = y + (1 ψ)r t 1 b t 1 + m t π t If ψ = 1, debt and taxes disappear from the households budget constraint. Only money matters If ψ < 1, sovereign debt also matters for households options. The budget constraint ca be written as c t + w t + i t 1 m t π t = y + R t 1 w t 1 ψ will matter for the price level, through w = m + (1 ψ)b

23 RICARDIAN AND (TRADITIONAL) NON-RICARDIAN FISCAL POLICIES IV Suppose that money demand is proportional to consumption m t = δc t (1 + i t )/i t and that a consumption rule for agents is c t+1 = βr t c t Also if this economy is closed, no investment and no government spending, y = c t R t 1 w t 1 = δ β y + w t Let s focus in the steady state (a situation where all t can drop), w t = w t 1 w = δ β(r 1) y

24 RICARDIAN AND (TRADITIONAL) NON-RICARDIAN FISCAL POLICIES V Also Pw = M + (1 ψ)b P = βr [M + (1 ψ)b] δy If ψ = 1 the price level is proportional to M. Debt does not affect the price level If 0 < ψ < 1 the price level is proportional to both M and B define λ = M B+M P = βr [1 ψ(1 λ)](m + B) δy open market operations that leave total liabilities fixed, affect prices

25 RICARDIAN AND (TRADITIONAL) NON-RICARDIAN FISCAL POLICIES VI Even if ψ = 1 on average, the way government finances shocks to its deficit matters Leeper (1991): AMP - AFP