CLASS 9: THE EFFECTS OF ANTICIPATED CHANGES IN MONETARY POLICY

• in this class the forward looking nature of prices will play a major role
• we will show that anticipated future changes in monetary policy affect the current rate of inflation

• Let us consider the following situation: in periods t=0,1,...,T-j money grows 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 $m_t=m^*(\mu)$, and therefore that the price level is equal to:
  
  $$p_t=\frac{M_0}{m^*(\mu)}(1+\mu)^t$$
  
  
  (if we further assume that the level of public debt is zero (B_t^s=0, all t), we obtain that transfers from the government to individuals (which are equal to seignorage) are equal to: $T_t=M^s_{t+1}-M^s_t=\mu M_0(1+\mu)^t$)
• In period T-j it is announced that there will be a regime change in economic policy in period T: it is announced (and the people believe it) that from period T onward (for all $t \geq T$) the money supply will be kept constant at the level reached in period T, which is $M_T^s=M_0(1+\mu)^T$
  (if the level of public debt is still kept at zero, B_t^s=0 all t, this means that transfers from the government to individuals will be zero as well in all periods: T_t=0)
• Given that people expect money supply to be constant forever after, the equilibrium real money balances from period T onward will adjust accordingly to the new stationary equilibrium. In particular, real money balances will be equal to m^*(0) (if $\mu>0$, then $m^*(0)>m^*(\mu)$)
  The price level will also be constant forever after:
  $p_t=\frac{M_T}{m^*(0)}=\frac{M_0}{m^*(0)}(1+\mu)^T$, all $t \geq T$
• The question is: what is going to happen between period T-j and period T?
• This question is relevant to understand a number of issues, like:
  
  • What happened to inflation in Europe in the years between the announcement of the Monetary Union and its actual implementation?
  • What would happen to inflation in Mexico if the adoption of the US Dollar was announced?
• Let us use the first order condition for money holdings (after imposing the equilibrium conditions: c_t=y and M_t=M^s_t, and assuming that income is constant):
  
  $$\frac1{p_t}u_c(y,\frac{M^s_t}{p_t})=\frac1{p_{t+1}}\beta [u_c(y,\frac{M^s_{t+1}}{p_{t+1}})+u_m(y,\frac{M^s_{t+1}}{p_{t+1}})]$$
  
  

• when t=T-1 this equation becomes:
  
  $$\frac1{p_{T-1}}u_c(y,\frac{M^s_{T-1}}{p_{T-1}})=\frac1{p_T}\beta [u_c(y,\frac{M^s_T}{p_T})+u_m(y,\frac{M^s_T}{p_T})]$$
  
  
  since we know that $\frac{M^s_T}{p_T}=m^*(0)$, we know the time path of the money supply between T-j and T (that is, we know M^s_T and M^s_T-1), and we know p_T ( $p_T=\frac{M^s_T}{m^*(0)}$), this equation will deliver a value for p_T-1.
  But once we have p_T-1, we can use the same equation to find p_T-2, and so on and so forth until we get to p_T-j
• For simplicity we choose to use the same approach to find the path for real money balances, instead of prices (we know that it is equivalent).
  Multiplying both sides for M^s_t, and multiplying and dividing the right hand side for M^s_t+1, the above equation becomes:
  $\begin{array}{l} \frac{M^s_t}{p_t}u_c(y,\frac{M^s_t}{p_t})=\\ \frac{M^s_t}{M... ... [u_c(y,\frac{M^s_{t+1}}{p_{t+1}})+u_m(y,\frac{M^s_{t+1}}{p_{t+1}})]\end{array}$
  that is:
  
  $$m_t u_c(y,m_t)=\frac{\beta}{1+\mu}m_{t+1} [u_c(y,m_{t+1})+u_m(y,m_{t+1})]$$
  
  

• It is clear that the above equation is satisfied by
  
  $$m_t=m_{t+1}=m^*(\mu)$$
  
  
  so that is the only point (if $m^*(\mu)$ is unique) where the function m_t+1=f(m_t) crosses the 45 degree line.
• In order to understand whether the solution is stable, we have to see what is the derivative where it crosses the 45 degree line:
  $\begin{array}{lll} \frac{dm_{t+1}}{dm_t}&=& \frac{1+\mu}{\beta}\frac{u_c+u_{c... ... &=& \frac{u_c+u_m}{u_c}\frac{u_c+u_{cm}m}{u_c+u_m+(u_{cm}+u_{mm})m}\end{array}$
  where all derivatives are evaluated at $m_t=m_{t+1}=m^*(\mu)$.
• If m(u_c+u_m) is an increasing function of m the denominator is positive, and hence the whole expression is positive. Furthermore, one can show that under the same condition that guarantees that $m^*(\mu)$ is unique, namely u_m u_cm+u_c u_mm>0 the numerator is larger than the denominator.
• In practice, this means that starting from m_T=m^*(0) we can solve the equation backward and obtain m₍T-j).
• Notice that, unless $j=\infty$ (the announcement is given many many periods in advance), real money balances will jump at the time of the announcement: $m_(T-j)>m^*(\mu)$
• Notice also that real money balances are growing from the time of the announcement to the time of the actual implementation:
  The announcement is enough to have inflation growing at a rate less than the rate of money growth
  
• "Money, unlike regular goods like bread, derives its value from convention, institution and, more than any other good, from expectations
  (Guillermo A. Calvo)
• In Germany (1923) money supply stops growing only in November, but real money balances stop decreasing three months in advance
  the announcement was given only the 15th of October, but the public was expecting a change in regime since August (new government, fiscal reform, refusal of the Central Bank to buy more government debt with maturity greater than one month)
• The experiences of Greece and Hungary also suggest that a model with adaptive expectations (inflation expectations depend on past levels of inflation) cannot explain the increase in real money balances before the change in the rate of growth of money supply