CLASS 11: ACTIVE/PASSIVE MONETARY AND FISCAL POLICIES

• First we will study a case of active monetary policy and passive fiscal policy (the Ricardian case), and analyze the implications for fiscal policy of the stabilization program we already studied.
• 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, so that in the next period the Central Bank will have to resume printing money.
  We will see that the implications of this is that inflation may actually rise in the period in which the money supply is kept constant.

Implications for fiscal policy of the stabilization program

• Let us remember how the stabilization program worked: in periods t=0,1,...,T-1 money grew at a rate $\mu$, and people expect it to grow at that rate forever:
  this implies that nominal money supply is equal to $M_t^s=M_0(1+\mu)^t$, real money balances are equal to the equilibrium level $m_t=m^*(\mu)$
• Let us recall the government budget constraint, which can be written as:
  
  M_t+1-M_t+B_t+1-B_t=R_t B_t+T_t.
  
  

• Let us assume, without loss of generality, that the level of public debt is zero before the stabilization program:
  B_t^s=0, all $t \leq T-1$
• Before the stabilization, real transfers from the government to individuals (which are equal to seignorage in real terms) are equal to:
  
  $$\frac{T_t}{p_t}=\frac{M^s_{t+1}-M^s_t}{p_t}=\mu m^*(\mu).$$
  
  

• In period T it is announced that the money supply will be kept constant at the level reached in period T, which is $M_T^s=M_0(1+\mu)^T$
• the total amount of liabilities of the government in period T is
  
  $$W_T=M^s+B^s=M_0(1+\mu)^T$$
  
  

• What are the implications of the stabilization program for fiscal policy?
  In other words, what are the options open to the fiscal authorities, given that money supply is to be kept constant from period T onward?
• One possible option is to simply reduce transfers (raise taxes) from $\mu m^*(\mu)$ to zero, and keep government debt constant at zero, that is:
  
  $$B_t^s=0 \mbox{, all }t \mbox{,} \frac{T_t}{p_t}=0\mbox{, all}t \geq T.$$
  
  

• However, this is not the only option: the government may change the composition of the total liabilities at time T, by issuing some debt and using the proceedings to buy back some money, or alternatively by printing more money (liquefaction) and using it to buy credit (buy back some debt, if the original debt was greater than zero) from the private sector.
  All these policies are consistent with the stabilization program, as long as money supply stays constant from period T onward.
• We know that in the post-stabilization equilibrium prices are going to be constant at the level
  
  $$p^*=\frac{M^s_T}{m^*(0)}$$
  
  
  and the nominal interest rate is going to be constant at the level
  
  $$R_t=R=\frac1\beta -1$$
  
  

• We are going to consider only stationary policies, that is, policies that involve a constant amount of debt from period T onward:
  
  $$B_t^s=B^s \mbox{ all }t \geq T$$
  
  
  From the budget constraint we see that this implies that transfers are also going to be constant:
  
  $$\frac{T_t}{p_t}=-R \frac{B^s}{p_t}=-R m^*(0) \frac{B^s}{M^s_T}$$
  
  
  all $t \geq T$
• It follows that the choice of the composition of total government liabilities, $M^s_T+B^s=W_T=M_0(1+\mu)^T$, affects the amount of transfers the agents are going to receive from period T onward.
  If the government chooses to issue debt in order to buy back money, the agents will have to pay taxes in order to cover the interest on the debt.
  Viceversa, if the government chooses to print more money to buy credit (reduce outstanding debt), the agents will receive a positive transfer from the government, equal to the interest on the debt.
• These issues are of crucial importance if Mexico is choose to adopt the dollar, or to adopt a fixed exchange rate regime: the rate at which the parity is fixed determines whether the amount of taxes mexican are paying will rise or decrease.
• The choice of the composition of total government liabilities also affects the price level.
  We can see that using the equality
  
  $$M^s_T+B^s=W_T=M_0(1+\mu)^T$$
  
  
  
  
  $$\frac{T_t}{p_t}=-R m^*(0) \frac{W_T-M^s_T}{M^s_T}=$$
  
  
  
  
  $$=-R m^*(0) (\frac{M_0(1+\mu)^T}{M^s_T}-1)$$
  
  
  
  
  $$=-R(\frac{M_0(1+\mu)^T}{p^*}-m^*(0))$$
  
  
  so there is a trade-off between price level and taxes: the lower the money supply, the lower the price level, the higher taxes have to be.
  Viceversa, if the government chooses to liquefy the economy, the price level will be higher, but the government will be able to buy credit from the private sector (reduce outstanding debt) and pay transfers to agents.
• This is the policy followed by Germany in 1923: adjust fiscal policy so that the commitment to stop printing money could be credible, and, at the same time, liquefy the economy (increase money supply at time T) and use the money supply to buy back private debt.

When fiscal policy does not back down: the unsuccessful stabilization program

• Let us consider the same case as before: in periods t=0,1,...,T-1 money grows at a rate $\mu$, and people expect it to grow at that rate forever: nominal money supply is equal to $M_t^s=M_0(1+\mu)^t$, real money balances are equal to $m^*(\mu)$, public debt is zero (B_t^s=0, all $t \leq T-1$), and real transfers to individuals are equal to $\frac{T_t}{p_t}=\mu m^*(\mu)$.
• At the beginning of period T the monetary authorities suddenly changes its course, and decides to keep money supply constant at the level of the previous period:
  
  $$M_T^s=M^s_{T-1}=M_0(1+\mu)^{T-1}.$$
  
  

• This is accomplished by means of an open market operation: the Central Bank issues debt and buys back money.
• How much debt does it have to issue? enough to buy back the amount of money that it had initially issued in excess of M_T-1.
  
  $$B_T=M_0 (1+\mu)^T-M^s_{T-1}=\mu M_0(1+\mu)^{T-1}$$
  
  

• The fiscal authority, unlike in the previous case, does not back down: real transfers remain at the level
  
  $$\frac{T_t}{p_t}=\mu m^*(\mu).$$
  
  
  For this reason, the public understand that at some point the Central Bank will have to go back printing money.
• For the sake of simplicity, let us assume that this happens immediately: the governor of the Central Bank is replaced, and from period T to period T+1 nominal money is increased at a new rate $\bar{\mu}$, which is such that seignorage covers the whole government deficit:
  
  M_T+1-M_T=R_T B_T+T_T
  
  
  or in real terms
  
  $$\frac{M_{T+1}-M_T}{p_T}=R_T \frac{B_T}{p_T}+\frac{T_T}{p_T}$$
  
  
  or
  
  $$\bar{\mu}m^*(\bar{\mu})=R_tb_t+\mu m^*(\mu)$$
  
  

• The new governor announces that money will grow at the new rate $\bar{\mu}$ forever after, and the public is aware of this
  (notice that this is compatible with the no Ponzi scheme condition, as the debt is kept constant).
• Did prices increase between periods T-1 and T, in spite of the fact that money supply was kept constant?
  Did prices actually increase more than the rate $\mu$ at which they were increasing before?
• We know that the price level in period T-1 is equal to:
  
  $$p_{T-1}=\frac{M_{T-1}}{m^*(\mu)}$$
  
  

• What are real money balances in period T? we know that people expect money to grow at the new rate $\bar{\mu}$ forever after, so that real money balances in period T must be equal to $m^*(\bar{\mu})$, and the price level to:
  
  $$p_{T}=\frac{M_{T-1}}{m^*(\bar{\mu})}$$
  
  

• Therefore we have that:
  
  $$\frac{p_{T}}{p_{T-1}}=\frac{m^*(\mu)}{m^*(\bar{\mu})}.$$
  
  
  If $\bar{\mu}$ is higher than $\mu$, real money balances are lower and prices have to grow between periods T-1 and T.
• Is $\bar{\mu}$ higher than $\mu$?
• Let us express the government budget constraint in real terms:
  
  $$\frac{M_{T+1}-M_T}{P_T}=R_T \frac{B_T}{P_T}+\frac{T_T}{P_T}.$$
  
  
  On the right hand side, real seignorage is equal to $\bar{\mu}m^*(\bar{\mu})$
  On the left hand side, real transfers are by assumption equal to $\mu m^*(\mu)$, so we have:
  
  $$\bar{\mu}m^*(\bar{\mu})=R_T \frac{B_T}{P_T}+\mu m^*(\mu).$$
  
  

• Because the government now has to pay the interest on the debt, seignorage has to be larger than it used to be.
  Therefore (if we are at levels of inflation where seignorage is an increasing function of inflation), it must be that $\bar{\mu}$ is higher than $\mu$.
• The government has to print money at a higher rate, because seignorage has to be higher than before, given that the interest on the debt also have to be covered.
  This means that keeping the money supply constant between periods T-1 and T does not prevent prices from rises.
  In particular, if
  
  $$\frac{m^*(\bar{\mu})}{m^*(\mu)}>(1+\mu)$$
  
  
  prices grow at a faster rate than before.
• The bottom line is that a stabilization program that is not credible -i.e., that is not accompanied by the necessary changes in fiscal policy- not only is not successful, but may also be counterproductive.
  The reason being that the government deficit increase when the government stops printing money -if real transfers/taxes do not change- and this means that seignorage in the future will have to be higher.
  But as we know prices are forward looking, and future high growth rate of the money supply translates into inflation today.

The beginning of hyperinflation

• The example says something on the beginning of hyperinflation.
• When fiscal policy goes `out of control', hyperinflation begin even if money supply does not grow immediately.
• Germany, May 1922: at the conference of Genoa it becomes clear that France is going to demand war payments from Germany in their entirety (13% of GDP)
  US banks stop lending to Germany.
• Bolivia 1982: debt crises.
• Notice that debt crises may help hyperinflation to start, in the sense that the public realizes that the upper bound $\bar{B}$ for amount of debt the government can issue is lower than expected, and therefore expect the government to start monetizing the debt earlier than expected.
• Hyperinflation also make fiscal problems worse: Olivera-Tanzi effect:
  the real value for indirect (sales) taxes, which are not indexed to inflation, decreases.
• End of hyperinflations:
  • Germany: agreement of war payments with France, and fiscal reform
    
  • Bolivia: fiscal reform (Sachs plan), and new loans from the World Bank