CLASS 10: THE INTERACTION BETWEEN FISCAL AND MONETARY POLICY: THE INTERTEMPORAL BUDGET CONSTRAINT OF THE GOVERNMENT

• So far the only result we obtained regarding fiscal policy is that does not matter for equilibrium.
• This is true only if, for given path of the money supply, the intertemporal budget constraint of the government is satisfied.
• The intertemporal budget constraint of the government establishes a relationship between the present discounted value of taxes, and the present discounted value of seignorage revenues.
• This implies that, if the Central Bank decides to keep the money supply constant, the government needs to raise taxes, sooner or later.
• In the case we studied in the previous classes, where the Central Bank decided to stop the growth in the money supply, the seignorage revenues, which previously were positive, become zero.
  This means that the government will have to change its fiscal policy.
• Two cases: active and passive monetary/fiscal policy.
• The case we studied, in which the monetary policy change and the fiscal policy follows, is a case of active monetary policy.
• In particular, we will first study the implications for fiscal policy of the stabilization program.
• Then we will study a case of active fiscal policy and passive monetary policy: the stabilization program is implemented for one period but the government does not change its fiscal policy.
  eventually, it is monetary policy to duck in.
  We will see that the implications of this is that inflation actually rises in the period in which the money supply is kept constant.

Implications of the intertemporal budget constraint of the government for monetary and fiscal policy

• We start by studying the implications of the intertemporal budget constraint of the government for monetary and fiscal policy.
• The bottom line will be that a decline in the present discounted value of seignorage earned by the government will have to correspond to a decline (rise) in the present discounted value of transfers (taxes).
• This implies, for instance, that if the stabilization. program of the government is really going to be forever, then the present discounted value of the revenues from seignorage will decline, and the government will have to decrease transfers (raise taxes) soon or later.
• It also implies that if the government refuses to change fiscal policy following the change in regime, then the change in regime cannot be credible: the government will have to increase seignorage at some point, and so the Central Bank will have to go back printing money.

• Let us recall the government budget constraint:
  
  M_t+1-M_t+B_t+1=(1+R_t)B_t+T_t
  
  

• if we divide by the price level p_t we obtain:
  
  $$\frac{M_{t+1}-M_t}{p_t}+\frac{B_{t+1}}{p_{t+1}}\frac{p_{t+1}}{p_t}= (1+R_t)\frac{B_t}{p_t}+\frac{T_t}{p_t}$$
  
  

• If we call real government debt, seignorage, and transfers b_t, $\sigma_t$ and $\tau_t$ respectively:
  
  $$b_t \equiv\frac{B_t}{p_t},\sigma_t \equiv\frac{M_{t+1}-M_t}{p_t},\tau_t \equiv\frac{T_t}{p_t}$$
  
  
  , then we obtain:
  
  $$\sigma_t+b_{t+1}\frac{p_{t+1}}{p_t}=(1+R_t)b_t+\tau_t$$
  
  
  or
  
  $$b_{t+1}=(1+r_t)b_t+(\tau_t-\sigma_t)\frac{p_t}{p_{t+1}}$$
  
  
  (recall in fact that the real interest rate r_t is defined as $r_t=(1+R_t)\frac{p_t}{p_{t+1}}$)
• For the sake of simplicity, we will discuss the implications of the intertemporal budget constraint of the government only in the stationary equilibrium where money grows at a constant rate $\mu$.
  This is only to make algebra easy: the conclusions are the same even in a more general setting.
• If money grows at a constant rate $\mu$: r_t is constant, inflation is constant:
  
  $$\frac{p_t}{p_{t+1}}=\frac1{1+\mu}$$
  
  
  and the previous expression becomes:
  
  $$b_{t+1}=(1+r)b_t+\frac{\tau_t-\sigma_t}{1+\mu}$$
  
  

• Say that the amount of outstanding government debt at time t=0 (say 1999) is equal to b₀, then the amount of outstanding government debt at time t=1 (say 2000) is:
  
  $$b_{1}=(1+r)b_0+\frac{\tau_0-\sigma_0}{1+\mu}$$
  
  
  The amount of outstanding government debt at time t=2 is:
  
  $$b_{2}=(1+r)^2 b_0+\frac{\tau_1-\sigma_1}{1+\mu} +(1+r)\frac{\tau_0-\sigma_0}{1+\mu}$$
  
  

• Substituting again and again, the amount of outstanding government debt at time t=T is:
  
  $$b_T=(1+r)^T b_0 +\sum_{s=0}^{T-1} (1+r)^{T-s-1} \frac{\tau_s-\sigma_s}{1+\mu}$$
  
  

• Aside: What is a Ponzi Scheme?
  • Suppose you borrow from your friend Carlos 1$ and promise to pay (1+r) $ in a year.
  • You spend the money in `chupa-chupas', and in order to pay Carlos, you borrow from Maria and amount (1+r) $ and you promise her to pay (1+r)² $ in a year.
  • Notice that the debt is growing at the rate (1+r): after T periods you owe (1+r)^T $ (pyramid scheme).
  • Notice also that the scheme can continue forever, as long as you find somebody willing to lend you money.
  • We assume that the government is not allowed to run a Ponzi scheme: its debt cannot grow indefinitely at a rate (larger or equal to) (1+r). Formally, this implies that $\frac{b_T}{(1+r)^T} \rightarrow 0$ for $T\rightarrow \infty$.
  • Why would it be so? because it violates the transversality condition of the agent (we do not show it formally): it is sub-optimal for the agent to hold an ever increasing amount of government debt and not spend it.
• Let us divide the last expression by (1+r)^T:
  
  $$\frac{b_T}{(1+r)^T}=b_0 +\sum_{s=0}^{T-1} (1+r)^{-s-1} \frac{\tau_s-\sigma_s}{1+\mu}$$
  
  

• From the no Ponzi scheme condition we know that:
  
  $$\frac{b_T}{(1+r)^T} \rightarrow 0$$
  
  
  , but this implies that the right hand side also has to go to zero for $T\rightarrow \infty$, that is:
  
  $$b_0 +\sum_{s=0}^{\infty} (1+r)^{-s-1} \frac{\tau_s-\sigma_s}{1+\mu}=0$$
  
  
  or
  
  $$b_0 =\sum_{s=0}^{\infty} (1+r)^{-s-1} \frac{\sigma_s-\tau_s}{1+\mu}$$
  
  

• The expression can be rewritten as:
  
  $$b_0 =\frac1{1+r} \sum_{s=0}^{\infty} \frac1{(1+r)^s}\frac{\sigma_s-\tau_s}{1+\mu}$$
  
  

• Interpretation: in order to be solvent, i.e., not having to run a Ponzi scheme, the government must be ready to back up the existing amount of debt with either future seignorage, or with taxes (negative $\tau$).
• More formally, the current debt must be equal to the discounted present value of all future revenues from taxes and/or from seignorage.
• Implications:
  • If the government implements a stabilization scheme, such that the revenues from seignorage go to zero, and it has some outstanding debt, it must raise taxes sooner or later.
  • If the government does not change its fiscal policy, it must go back to printing money at some point.
  • This is why in the experiences of hyperinflation (Bolivia, Germany) the fiscal reform made the stabilization program more credible.
  • Inflation can begin also without growth in the money supply, if fiscal policy induces people to believe that deficits will be monetized (Mexico 1982?).

The `game of the chicken' between monetary and fiscal authorities
or
Why the Monetarist view on how to end inflation may be wrong

• The Monetarist plan to stop inflation: target a monetary aggregate (monetary base, M1, M2, M3) and have its growth rate under control (so called k-percent growth rule, where k is our $\mu$). In practice, if you want inflation to be 2%, the rule would be to have some money aggregate growing at -roughly- that rate.
• The Monetarist plan puts all emphasis on the monetary aggregates, and no emphasis at all on the fiscal side: as long as the monetary target is met, inflation can be reduced in spite of persistent budget deficits.
• Indeed, the models we studied do support the idea that if the public are convinced that money will grow forever at the rate of 2%, inflation will also be 2% - furthermore, we also studied that budget deficits are irrelevant, as long as the intertemporal budget constraint of the government is satisfied
• Are the Monetarists right? The problem with the Monetarist view lies in the inconsistency between fiscal and monetary policy in the long run. For the intertemporal budget constraint of the government to be satisfied, either fiscal or monetary policy will have to change: either the fiscal authorities will increase taxes (reduce transfers), or the monetary authorities will have to resume printing money.
• The Monetarists implicitly seem to assume that the fiscal authorities will eventually duck in and change fiscal policy.
• But this is not necessarily what the public perceives to be the case: if the public perceives that fiscal policy will not change, controlling the monetary aggregate may not be enough to stop inflation.

• The interaction (`game of the chicken') between monetary and fiscal authorities seems to have played a part in a number of historical episodes.
  • Reagan early 1980s (Sargent): `game of the chicken' between the Federal Reserve and the fiscal side of Reagan's policy: the Federal Reserve was implementing a very restrictive monetary policy, and at the same time the Congress was lowering taxes and raising military spending.
  • The public was left to guess who would eventually win the game of the chicken.
    This throws uncertainty into the system, and the uncertainty is costly.
  • The high long term interest rates that persisted until 1982 seem to suggest that the public believed that inflation was going to increase: eventually, the monetary authorities would be the chicken.
  • Sargent also claims that the early Tatcher regime in the UK was another example of game of the chicken: tight monetary policy and loose fiscal policy (in 1981 fiscal policy tightened as well).
  • Successful stabilization programs all entail avoiding the game of the chicken, and, indeed, having the fiscal reform first.
  • references: Sargent, Thomas, 1986, Rational expectations and inflation, Harper and Row, New York
    Sargent, Thomas J.; Wallace, Neil, Some Unpleasant Monetarist Arithmetic, Federal-Reserve-Bank-of-Minneapolis-Quarterly-Review; 9(1) winter 1985, pages 15-31
    Cagan, Philip, The monetary dynamics of hyperinflation, in: Studies in the quantity theory of money, Chicago University Press, 1956
    Sargent, Thomas, Interpreting the Reagan Deficits, Federal-Reserve-Bank-of-San-Francisco-Economic-Review; 0(4), Fall 1986, pages 5-12
    Webb, Steven, 1989, Hyperinflation and stabilization in Weimer germany, Oxford University Press, 1989
    Sargent,-Thomas-J, "Reaganomics" and Credibility, ...
    Sargent,-Thomas-J, The end of four big inflations,

• Lessons for policy
  • Economic policy like coordinating a football team.
  • Avoid the game of the chicken:
    Centralized power.
    Central bank independence (?): how independent central bankers really are?
• The `game of the chicken' in Mexico
  • The central bank announces only short term (1 year) targets.
    Little is known about future monetary policy.
  • On the other hand, fiscal policy seems to be so far consistent with the central bank target of reducing inflation.