CLASS 14: FIXED EXCHANGE RATES AS A WAY OF STOPPING INFLATION

In the 90's (and late 80's) many Latin American countries stopped the hyperinflation by tying the local currency to the US Dollar: Argentina created a currency board, Brazil started the 'Real Plan', Mexico adopted crawling peg (until 1995). Why did they do that? Why did most of these arrangements initially succeed in stopping inflation? And why did some (or most) of these arrangements ultimately fail?
In this class we are going to analyze the following issues:

• Exchange rate policy and price stabilization.
• The choice of the parity in a fixed exchange rate regime.
• Exchange rate policy and fiscal policy: the origin of currency crises.

The Change in Regime: from Flexible to Fixed Exchange Rate Regime

• Let us suppose that the economy is initially under a flexible exchange rate regime (which is seen as permanent by the public):
  money supply grows at the rate $\mu$
  
  $$M^s_t=M^s_0 (1+\mu)^t$$
  
  
  and the exchange rate is free to fluctuate.
• We know that this implies the following -stationary- equilibrium (we assume that foreign assets held by households and government are constant over time: A^g_t=A^g₀ and A^p_t=A^p₀ all t):
  • The exchange rate depreciates at the rate $\mu$ (assuming $(1+r^w)=\frac1\beta$):
    
    $$\frac{e_t}{e_{t-1}}=\frac{\frac{1+\mu}{\beta}}{1+r^w}=1+\mu$$
    
    

  • $\mu$ is also the rate of inflation:
    
    $$p_t=\frac{M^s_t}{m^*(\mu)}$$
    
    

  • Real money balances are equal to $m^*(\mu)$
  • consumption is equal to:
    
    $$c_t=y+\frac1{p^w} (A^p_0+A^g_0) r^w$$
    
    

  • and real transfers are equal to:
    
    $$\tau_t=\mu m^*(\mu)+\frac1{p^w} A^g_0 r^w$$
    
    

• At the beginning of period T/ end of period T-1 the fixed exchange rate regime is announced: the value of domestic currency in terms of foreign currency, e^*, is fixed forever after.
• The case of fixed exchange rate is a special case of 'crawling peg' with $\gamma=0$. Therefore the new equilibrium is the same one studied in the last class with $\gamma=0$. In particular:
  • Consumption is constant at the level:
    
    $$c_t=y+\frac1{p^w} (A^p_T+A^g_T) r^w=c^*$$
    
    
    where A^p_T+A^g_T is the sum of foreign reserves held by the public and the Central Bank respectively at the beginning of period T (right after the announcement).
  • Money supply is constant at the level M^s_t+1=M^s_t=M^s_T, where M^s_T is money supply at the beginning of period T (right after the announcement).
  • Real money balances are constant at the level m^*(0)
  • The price level is constant, and the level is determined -for given exchange rate parity- by the no-arbitrage in the goods markets condition:
    
    p_t=p^*=e^* p^w
    
    

  • Note that the choice of the exchange rate parity e^* has implications for the level of money supply at the beginning of period T (after the announcement). In fact:
    
    M^s_T=p^* m^*(0)
    
    

  • Real transfers are constant at the level:
    
    $$\tau^*=\frac1{p^w} A^g_T r^w$$
    
    

• What we have not determined yet is the amount of foreign reserves held by the public (A^p_T) and by the Central Bank (A^g_T) respectively at the beginning of period T. We will see that these variables depend on the choice of the exchange rate parity.

The Choice of the Parity in a Fixed Exchange Rate Regime

This issue is very much of relevance for current economic policy in Mexico: if Mexico chose to fix the exchange rate again (or to establish a Currency Board, or to adopt the Dollar as legal tender), which parity should it choose? And what are the implications of the choice of the parity for fiscal policy?

• The choice of the parity e^* affects the amount of reserves that the Central Bank has at the beginning of period T and, since real transfers are constant at the level $\tau^*=\frac1{p^w} A^g_T r^w$ forever after, affects fiscal policy.
• Remember that at the beginning of period T, before the announcement of the change in regime, money supply is equal to $M^s_0 (1+\mu)^T$, and that after the announcement, money supply is equal to
  
  M^s_T=e^* p^w m^*(0).
  
  

• Remember that the government budget constraint is:
  
  M_t+1-M_t-e_t(A^g_t+1-A^g_t)+e_tA^g_tr^w_t=T_t.
  
  
  If transfers in period T-1 are not changed, this implies that the reserves of the Central bank have to change by an amount equal to:
  
  $$A^g_T-A^g_0=\frac{M^s_T-M^s_0 (1+\mu)^T}{e^*}$$
  
  

• Remember that M^s_T=e^* p^w m^*(0): if the parity e^* is chosen high enough that $M^s_T-M^s_0 (1+\mu)^T>0$, then the Central Bank can print more money and use it to buy foreign reserves.
  In turn, this means that it will be able to have higher transfers in the future.
• The private sector is on the other side of the deals: it demands an amount M^s_T of nominal money balances, and, if that amount is larger than the amount of money balances it already has, namely $M^s_0 (1+\mu)^T$, is willing to purchase it by selling foreign assets:
  
  $$A^p_T-A^p_0=-\frac{M^s_T-M^s_0 (1+\mu)^T}{e^*}.$$
  
  

• Therefore note that the total amount of foreign asset (and therefore consumption) is unchanged:
  
  A^p_T+A^g_T=A^p₀+A^g₀
  
  
  and that the choice of the parity determines the fraction of foreign assets held by the Central Bank and by the private sector.
• If the Central Bank wanted to stop inflation already in period T, that is p_T-1=p_T, then the parity wold be determined at the level:
  
  $$e^*=\frac{p_{T-1}}{p^w}$$
  
  
  and money supply would have to be equal to:
  
  $$M^s_T=p_{T-1} m^*(0)=\frac{M^s_{T-1}}{m^*(\mu)}m^*(0)=$$
  
  
  
  
  $$=\frac{M^s_0 (1+\mu)^{T-1}}{m^*(\mu)}m^*(0)$$
  
  

• This implies that the intervention of the Central Bank on the market for foreign currency has to be equal to:
  
  $$A^g_T-A^g_0=\frac{M^s_T-M^s_0 (1+\mu)^T}{e^*}=$$
  
  
  
  
  $$=\frac{\frac{M^s_0 (1+\mu)^{T-1}}{m^*(\mu)}m^*(0)-M^s_0 (1+\mu)^T}{e^*}=$$
  
  
  
  
  $$=m^*(\mu)p^w(\frac{m^*(0)}{m^*(\mu)}-(1+\mu))$$
  
  

• If $\frac{m^*(0)}{m^*(\mu)}>(1+\mu)$ then price stabilization requires issuing money and buying foreign assets.
• Real transfers, which before were at the level
  
  $$\tau=\mu m^*(\mu)+\frac1{p^w} A^g_0 r^w$$
  
  
  now have to be set at the level:
  
  $$\tau^*=\frac1{p^w} A^g_T r^w=\frac1{p^w} A^g_0 r^w+[m^*(0)-m^*(\mu)(1+\mu)]r^w$$
  
  
  If seignorage is higher than the increased interest on foreign reserves, transfers will have to decrease.
• In a situation of hyperinflation, where real money balances are very low and therefore seignorage is also low in spite of the high rate of money creation, stabilization via a fixed exchange rate regime may even loose fiscal policy, given that the government can bank on the fact that -due to the fixed exchange rate regime and the consequent end of inflation- people demand more domestic currency than before.
• What if people do not believe the fixed exchange rate regime? we will see that, unlike the closed economy case, inflation does not continue and the government is able to stabilize the price level, albeit only temporarily, that is, until the reserve will last.

When Fiscal Policy Is Inconsistent With The Fixed Exchange Rate Regime: A Source of Currency Crises

We will see that a fiscal policy which is not consistent with the exchange rate regime forces the country to abandon the regime, and let the exchange rate float.
This happens because the amount foreign reserves held by the Central Bank will be depleted, making the fixed exchange rate unsustainable.

• What happens if the government does not adjust its fiscal policy, that is, if its budget deficit $\tau'$ is above $\tau^*$?
• From the government budget constraint it is clear that reserves are going to be depleted:
  
  $$A^g_{t+1}-A^g_t=p^w(A^g_T r^w-\tau').$$
  
  

• When foreign reserves are over the government can no longer fulfill its promise to convert domestic currency into foreign currency at the rate e^*, simply because it has no more foreign currency (and none is going to lend foreign currency to the government either, given that the equilibrium would violate the no-Ponzi game condition).
• Therefore it must be that at some future date $\bar{T}$ the exchange rate regime is going to collapse.
  1) We will first see what happens after the collapse.
  2) Then we will see what happened before the collapse
  3) Finally we will study what happens at the time the crises occurs.
• (1)After the collapse of the fixed exchange rate regime the government, as we know, does not have reserves any longer. This means it has to finance the whole budget deficit by printing money at some rate $\mu'$ (seignorage):
  
  $$\tau'=\mu' m^*(\mu')$$
  
  

• The above condition actually determines the rate of inflation, and of currency depreciation, after the crises.
• Note that, since the government no longer has reserves, it has to finance the whole budget deficit by seignorage (remember that $\tau_t=\mu m^*(\mu)+\frac1{p^w} A^g_0 r^w$ before the introduction of the fixed exchange rate regime): If the budget deficit before and after the fixed exchange rate regime is the same ($\tau'$), inflation and currency depreciation must be higher after the collapse: $\mu'>\mu$.
• The new -stationary- equilibrium after the collapse of the exchange rate regime is more specifically as follows:
  • $M^s_t=M^s_{\bar{T}} (1+\mu')^{t-\bar{T}}$ all $t>\bar{T}$
  • Assuming that foreign assets held by households are constant over time: A^g_t=0 and $A^p_{t}=A^p_{\bar{T}}$ all $t>\bar{T}$.
  • The exchange rate depreciates at the rate $\mu'$ (assuming $(1+r^w)=\frac1\beta$):
    
    $$\frac{e_t}{e_{t-1}}=\frac{\frac{1+\mu'}{\beta}}{1+r^w}=1+\mu'$$
    
    

  • $\mu'$ is also the rate of inflation: $p_t=\frac{M^s_t}{m^*(\mu')}$
  • Real money balances are equal to $m^*(\mu')$
  • Consumption is equal to: $c_t=y+\frac1{p^w} (A^p_{\bar{T}}) r^w$. and real transfers are equal to $\tau_t=\mu' m^*(\mu')$
• (2)Before the collapse the equilibrium is the same one we described before for the `credible' fixed exchange rate regime, even if people know that the regime is not going to last.
• Note in fact that from the law of one price we have:
  
  p_t=e^* p^w.
  
  
  If all goods are tradable the central bank can stop inflation by simply fixing the exchange rate, even if the regime is only temporary.
• This is different from the case in which the Central Bank stops printing money: we know that it does not succeed to stop inflation -due to future inflationary expectations.
• Perhaps this is one of the reasons why many Latin American countries chose to stop hyperinflation by fixing the exchange rate: their plan is temporarily successful even if it is ultimately not sustainable because of fiscal policy.
  Note that this is true only if all goods are tradables: with non-tradables (services) it may no longer be the case.
• In particular, the equilibrium before the collapse is exactly the one we saw before:
  • Consumption is constant at the level
    
    $$c^*=y+\frac1{p^w} (A^p_T+A^g_T) r^w$$
    
    

  • Money supply is constant at the level M^s_T.
  • Real money balances are constant at the level m^*(0)
  • Note that the reserves the Central bank is losing are acquired by the private sector, so that A^p_T+A^g_T=A^p_T+A^g_T is constant over time.
• (3) What happens at the time the crises occurs?
• First of all we know that the exchange rate cannot jump between time $\bar{T}$ and $\bar{T}+1$: there cannot be any equilibrium with anticipated jumps in the exchange rate.
  If it did jump, in fact, those holding foreign currency would have an infinite return, and this would of course prompt them to borrow in domestic currency and invest in foreign currency, thereby precipitating the crises. This cannot be an equilibrium.
• This implies that prices cannot jump either, because of the Law of One Price.
• We also know that real money balances decrease from m^*(0) before the crises, to $m^*(\mu')$ after the crises.
  Since prices do not move, it must be that at the end of period $\bar{T}$ people get rid of an amount of money equal to $M_{\bar{T}}-M_{T}=m^*(0)-m^*(\mu')$, and buy foreign currency.
• The loss of foreign currency by the Central bank at time $\bar{T}$ is equal to:
  
  $$A^g_{\bar{T}+1}-A^g_{\bar{T}}=p^w(\frac{A^g_T r^w}{p^w}-\tau')-e^*(m^*(0)-m^*(\mu'))$$
  
  
  This can be called a speculative attack on the currency on the side of the public: before the Central Bank runs out of reserves completely, the public converts domestic currency into foreign bonds, thereby precipitating the crises.
• Note that the speculative attack does not occur before time $\bar{T}$, as people know that the Central Bank has enough reserves to defend the currency.
• Is this a good explanation of currency crises? It certainly has some of the features of currency crises: often times (but perhaps not so evidently in Asia and in Mexico) fiscal imbalances are at the heart of the crises (and this is why the IMF insists on fiscal discipline); also, speculative attacks on the currency do occur.
  However, this particular currency crises is a chronicle of a death foretold: every one knows when it is going to happen. This is often not the case with currency crises: notice in fact that we have no jump of the exchange rate in the model, while in reality the exchange rate does have abrupt depreciation.