Since the breakdown of the Bretton Woods system and subsequent short-lived experiment with freely floating exchange rates, international monetary arrangements have been characterized by a wide variety of intermediate exchange rate systems. Although there exists a large analytical literature concerned with the vulnerability of managed exchange rate systems to speculative attacks, empirical studies of exchange rate crisis are rare. The most obvious reason for surprising scarcity of empirical work is the absence of a generally-accepted summary statistic that can be used to characterize the conditions prevailing in international currency markets.

A currency crisis occurs when there is an abnormally large international excess demand for a currency which forces monetary authorities to take strong counter measures, often at the expense of other policy objectives. This suggests that a natural way to obtain a summary statistic that can be used to characterize exchange market conditions is to develop an analytically sound measure of the total international excess demand for a currency.

The best-known measure of the international excess demand for a currency is Girton and Roper’s exchange market pressure formula. (Girton et al. 1977) Girton and Roper used the term ‘exchange market pressure’ to refer to the magnitude of money market disequilibrium that must be removed either through reserve or exchange rate changes. Their model specification and their assumption that policy authorities do not employ domestic credit changes to influence the exchange rate levels ensures that exchange market pressure is the simple sum of the percentage change in the exchange rate and in foreign reserves. In the context of the model they employ, Girton and Roper’s exchange market pressure formula measures the magnitude of external imbalance.

While Roper and Turnovsky used a different model specification and allowed intervention to take the form of changes in domestic credit as well as changes in reserves. (Roper D. and Turnovsky S.J. 1980) Roper and Turnovsky found that the excess demand for money is equal to a linear combination of changes in the exchange rate and in monetary base. In general these two components are not equally weighted. Given their assumptions about the nature of exchange market intervention and the model specification, the linear combination identified by Roper and Turnovsky measures the magnitude of the international excess demand for domestic currency.

Neither Girton and Roper nor Roper and Turnovsky were primarily concerned with developing a general measure of exchange market pressure for economies with intermediate systems of exchange rate management. Girton and Roper were interested in investigating empirically the extent to which monetary policy can be formulated independently in open economies. Exchange market pressure was used as the dependent variable in their estimations in order to allow for changes in intervention policy over the sample period. The study of Roper and Turnovsky focused on optimal stabilization policy in a small open economy. They formulated their problem in terms of the policy authority’s optimal response to changes in exchange market pressure.

Diana N. Weymark apply the formulae derived by Girton and Roper and Turnovsky as a point of departure for developing a general approach to measuring exchange market pressure. (Diana N. Weymark, 1998) Specifically, Weymark construct model-dependent exchange market pressure indices based on general, model-dependent definition of the concept of exchange market pressure. In any model in which the demand for domestic currency responds contemporaneously to exchange rate changes, the definition generates a model-specific functional relationship between exchange market pressure and observed changes in both the exchange rate and the components of the monetary base used to implement intervention policy. A small open economy model with rational expectations is used to illustrate this method of model-consistent measures of exchange market pressure.

2.2 THE GIRTON-ROPER MODEL

The small open economy version of the model that Girton and Roper (Girton, 1977) employed can be expressed in logarithm as:

Eq. (2.1)

Eq. (2.2)

Eq. (2.3)

Eq. (2.4)

Where is the logarithm of the nominal domestic money supply, is the percentage change in domestic credit, is the percentage change in foreign exchange reserves, is the logarithm of the demand for nominal domestic money balances, is logarithm price of traded goods, is logarithm of output, is the logarithm domestic nominal interest rate, is the logarithm foreign interest rate level, is the logarithm of nominal exchange rate that domestic currency cost of one unit of foreign currency. is the change in the uncovered interest rate different, is the deviation from purchasing power parity.

The money market equilibrium condition, yields the following relationship between reserve and exchange rate changes

Eq. (2.5)

In Eq. (2.5), is the observed exchange change and the term in brackets is the exogenously-generated excess demand for domestic currency, . In the absence of intervention, =0 and . The measure of external imbalance generated by the Girton- Roper model is therefore

Eq. (2.6)

With . Taking the partial derivative of Eq. (2.5) with respect to confirms that .

2.3 THE ROPER-TURNOVSKY MODEL

Roper-Turnovsky employed a stochastic small open economy IS-LM model. (Roper, 1980) The Roper-Turnovsky model, expressed in terms of changes over time, is describe by Eq. (2.7)-Eq. (2.10)

Eq. (2.7)

Eq. (2.8)

Eq. (2.9)

Eq. (2.10)

Where , and are stochastic disturbances that have zero means, known variances, and are independently distributed over time.

Eq. (2.10) indicates that Roper-Turnovsky regard all domestic credit changes as a form of exchange market intervention. In their views, is not a component of so that it is the relationship between and rather than the relationship between and that is relevant to the calculation of exchange market pressure. Substituting Eq. (2.7), Eq. (2.9) and Eq. (2.10) into Eq. (2.8) yields

Eq. (2.11)

Where , is the observed exchange rate, and the term in brackets is the exogenously-generated excess demand for domestic money, .

When is set equal to zero in Eq. (2.11) the Roper-Turnovsky model yields the following exchange market pressure formula

Eq. (2.12)

Where . Substituting into Eq. (2.11) and differentiating with respect to confirms that . Note that Roper and Turnovsky implicitly define exchange market pressure in terms of monetary units. The measure employed by Roper and Turnovsky is therefore equal to .

2.3 THE WEYMARK MODEL

This model employed is one of a small open economy in which the domestic price level is influenced by both the level of foreign prices and the exchange rate, but purchasing parity does not necessarily hold. Domestic output and foreign price level are exogenous. It is assumed that the small open economy has well-developed financial markets and that domestic and foreign assets are perfect substitutes. Domestic residents hold domestic currency for transactions purposes as well as speculative balances of foreign claims. Foreign and domestic interest rates are linked through an uncovered interest parity condition. (Diana et al. 1995)

Eq. (2.13)

Eq. (2.14)

Eq. (2.15)

Eq. (2.16)

Eq. (2.17)

Where:

= the logarithm of the money stock in period t with the superscript s and d denoting supply and demand, respectively.

= the logarithm of domestic price level in period t.

= the logarithm of real domestic output in period t.

= the logarithm of the domestic interest rate level in period t.

= the stochastic money demand disturbance in period t.

= the logarithm of the period t exchange rate expressed as the domestic currency cost of one unit of foreign currency.

where is the money multiplier in period t, is the stock of domestic credit, and is the inherited money stock in period t.

where is the stock of foreign exchange reserves in period t, with and defined as above.

= the policy authority’s time-variant response coefficient.

Asterisks are used to denote the foreign counterparts of the relevant domestic variables and the notation represents the value that rational agents expect the variable e to take on in period t+1, conditional on the information available in period t. For concreteness, it is assumed that private agents and the policy authority have access to the same information and that the exchange rate,, and the domestic interest rate,, are the only variables that domestic agents can observe contemporaneously.

Eq. (2.13) and Eq. (2.15) are standard to small open economy models in which output is assumed to be exogenous and domestic and foreign assets are free-traded perfect substitutes. Eq. (2.14) characterizes domestic prices as responsive to the level of foreign prices and to exchange rate but does not impose purchasing power parity a priori. Eq. (2.16) describes the supply of money as depending on the inherited money stock,, the change in domestic credit,, and the change in foreign exchange reserves,. Eq. (2.17) described changes in foreign exchange reserves occur as a result of the policy authority’s response to contemporaneous changes in the exchanges rate,. When, the policy authority allows the exchange rate to float freely and no change in domestic money supply. Under a system of perfectly fixed exchange rates, the policy authority uses direct exchange market intervention to hold the exchange rate constant and . Value of that fall between 0 and ∞ are characteristic of intermediate intervention policies. Negative values of are associated with intervention activities that generate changes in the exchange rate that are either of the opposite sign or, if of the same sign, larger than the changes that would have occurred under a pure float.

Substituting Eq. (2.14) and Eq. (2.15) into Eq. (2.13) reveals that the demand for money in this economy is determined by:

Eq. (2.18)

Under the assumption that the money market clears continuously, for all t. Using this assumption together with Eq. (2.16), Eq. (2.17) and Eq. (2.18) allows money market equilibrium to be expressed in deviation form as:

Eq. (2.19)

Eq. (2.19) show that the magnitude of exchange rate change needed to restore money market equilibrium subsequent to an exogenous disturbance depends on the policy authority’s choice of. In this model, the possible sources of exogenous disturbances to the economy are: changes in the foreign price level , changes in the level of domestic output , changes in the foreign interest rate level , changes in domestic credit and the random money demand shock .

Eq. (2.19) indicates that the change in the value of exchange rate in small open economy is given by:

Eq. (2.20)

where

The term inside the parentheses is the excess demand of money that is generated by the combination of exogenous disturbances that occur in period t and also by the agent’s expectations about exchange rate changes. Eq. (2.20) indicates that the policy authority’s choice of and the structural parameters and jointly determine the magnitude of equilibrating exchange rate changes that are observed. When , and indicating policy authority has chosen to hold the exchange rate fixed using some combination of direct and indirect intervention. The policy authority refrains from all exchange market intervention when and . In this case any existing excess demand for domestic money is eliminated by private market forces and . When , is the same sign but greater than the exchange rate change that would have been observed in the absence of intervention by the policy authority. For , the observed exchange rate change, , and the change in exchange rate that would have been observed in the absence of intervention are of the opposite sign.

Weymark define exchange market pressure as the measurement of total excess demand for a currency in international markets as the exchange rate change that would have been required to remove this excess demand in the absence of exchange market intervention, given the expectations generated by the exchange rate policy actually implemented.

The exchange market pressure formula that is consistent with the model employed can be obtained from Eq. (2.20) can be expressed as:

Eq. (2.21)

The elasticity converts observed reserve changes into equivalent exchange rate units. In order for this conversion to be accomplished without altering the underlying size of the excess demand associated with the components of and the actual exchange rate policy implemented by the policy authority in period t, the expectation change,, must be held constant when exchange market pressure is imputed. With the independent of and held constant, the model-consistent elasticity obtained on the bases of Eq. (2.22) is . The measure of exchange market pressure implied by the model presented as below:

Eq. (2.22)

where . Because varies with the model specification, calculated values of exchange market pressure will not, in general, be model independent.

The index of exchange market intervention that measures the intervention activity of the policy authority in terms of the proportion of exchange market pressure relieved by exchange market intervention. When the policy authority engages only in direct exchange market intervention, the intervention index,, is defined as:

Eq. (2.23)

When a policy authority is known to use direct as well as indirect intervention, Eq. (2.23) must be modified in order to capture the impact of the change in domestic credit on the exchange rate.

2.4 INFLATION TARGETING AND OPTIMAL CONTROL THEORY

Inflation targeting is now a new gold standard for central banks. The regime is believed to perform better than, for instance, the alternative of controlling money for clamping down on inflation by giving monetary policy more transparency and thus credibility. Instead of trying to meet monetary targets, central banks use their own money to determine short-term interest rates and thus control inflation directly. Tethering inflationary expectations is vital under this regime. If agents believe that the inflation target will be hit, then inflationary shocks will be absorbed. (Veloso, Thiago, Meurer, Roberto & Da Silva, 2007)

The optimal control model is built on the Taylor rule model of Eichengreen. (Eichengreen, 2002) Eichengreen’s model tracks the major features of open emerging markets, and can be described by equation Eq. (2.24) – Eq. (2.26).

Eq. (2.24)

Eq. (2.25)

Eq. (2.26)

where and are inflation rate and inflation rate target respectively. is output deviation from its natural level, is the nominal exchange rate, , , and are domestic, foreign and neutral interest rate respectively, and Ƞ are disturbance terms, and v is a financial disturbance.

Eq. (2.24) id the expectational Phillips curve, and Eq. (2.25) is aggregate demand for an open economy. The interest rate impact on output is captured by parameter . Eq. (2.26) is uncovered interest parity, where is assumed to be constant when deriving the Taylor rule.

High degree of pass through is tracked by both a big and a small because these values mean that exchange rate depreciation causes rapid increase in domestic and tradable prices, decreased competitiveness, and then low effect on output. Excess liabilities in foreign currency can also be represented by a small . If is small and positive, the central bank has less fear of floating. Yet a big depreciation means a negative , and this increases the fear of floating.

Figure 2.1: Developed countries’ optimal path for GDP and inflation

Figure 2.2: Developed countries’ optimal path for GDP and inflation

Figures 2.1 and 2.2 show the paths for output and inflation after optimization at t=1, the targets were not hit in figures 2.1 and 2.2 because neglect the stochastic part in the loss function. Targets are only hit when the number of variables in the loss function matches the number of instrumental variables. This cannot occur in this model of two variables: output and inflation, and only one instrumental variable that interest rate. Calibrating the inflation weight in the loss function (i.e. making ) shows that the countries can approach more approach more closely the inflation target at the expense of the output target.

2.5 EXCHANGE MARKET PRESSURE AND INTERVENTION ACTIVITY IN CHILE

Using the index proposed by Weymark for small open economies, Emanuel-Werner Kohlscheen computes exchange market pressure and intervention indexes for Chile in the period 1990 to 1998. This statistic can be used to access timing and scale of currency crises, as include exchange rate and variations in one single indicator. The index is suited for intermediate exchange rate policies, since it gives due consideration to the possibility of accommodating exchange market pressures through changes in domestic credit. The monetarist model developed suggests low effectiveness of controls in affecting the exchange rate level, when the interest rate-elasticity of money demand is low. Substantial appreciative pressure on the Chilean peso is found over the period, with the exception of isolated quarters following the introduction of the reserve requirement and following outset of Asian crisis. (Emanuel-Werner Kohlscheen, 2000)

Exchange market pressure is defined for a small open economy model (assumed to be the case of Chile in the period under study). Eq. (2.27) is the money demand expression in the log-linear form, with exogenous output, where clearing of the money market is assumed.

Eq. (2.27)

The price is dependent on the external price level and the nominal level of the exchange rate.

Eq. (2.28)

The financial assets are perfect substitutes. The existence of a reserve requirement for each unit of capital inflow increases the cost of external financing, so that the uncovered interest parity condition is changed to incorporate this additional cost. For the sake of simplicity, all the deposit is assumed have the same maturity as reserve requirement period. This means that the external financing cost is increased from to . Thus, the difference is the cost of the reserve requirement.

Eq. (2.29)

Eq. (2.30) states that changes in the money supply can occur due to changes in domestic credits or changes in the level of international reserves while Eq. (2.31) expresses the response function to changes in the exchange rate.

Eq. (2.30)

Eq. (2.31)

is a policy choice that determines the extent to which exchange market pressure is absorbed by monetary authority interventions. In a free floating exchange rate regime, would be zero, so that there is no smoothing of the exchange rate level at all, while in a fixed regime would be infinite.

Substituting Eq. (2.27) and Eq. (2.28) in Eq. (2.29) and taking the first differences:

Eq. (2.32)

Now, substituting Eq. (2.30) and Eq. (2.31) in Eq. (2.32), and assuming that money market clears yields:

Eq. (2.33)

The term inside the brackets represent the excess demand for currency that originates exchange market pressure. EMP is defined as exchange rate that would prevail after elimination of excess demand in the absence of exchange market intervention.

When the government intervenes directly in the exchange rate market by buying or selling foreign exchange, the general formula for exchange market pressure in period t is given by:

Eq. (2.34)

While the first term on the right side measures actual exchange rate variation, the second term captures the share of exchange rate variation absorbed by direct monetary authority intervention.

The index of intervention activity, obtained according to the formula:

Eq. (2.35)

The intervention activity index measures the share of exchange market pressure absorbed by direct Central Bank intervention.

where

– reserve requirement on capital inflows

– where is the money multiplier, is the stock of domestic credit in billions of Chilean pesos and is the monetary base composed of domestic credits and foreign reserves

– where is the stock of foreign reserves in billions of US dollars and is the exchange rate expressed in Chilean pesos per US dollar.

– log of nominal exchange rate in Chilean pesos per US dollar (period average)

– expectation of the nominal exchange rate level at t+1 in period t with the information set available at t.

– log of nominal domestic interest rates

– log of world interest rates ( 3 month US dollar LIBOR)

– log of money stock (M2) in billion of Chilean pesos

– log of the consumer price index published by IFS

– log of the price index of relevant external inflation ( weighted average of consumer price variations in US (0.45), Germany (0.30) and Japan (0.25))

– log of money velocity shocks

– log of IMACEC index ( monthly indicator of economic activity level)

Table 21 shows the quarterly evolution of the EMP index, comparing it with Girton & Riper index. (Girton et al.) Negative values for the EMP index indicate net appreciation pressure, while the positive values mean that the currency is under depreciative pressure. The table show that, despite imposition of reserve requirements on the capital inflows, the Chilean peso was submitted to continued appreciative pressure during 90s, except for 1991:II (when the reserve requirement was introduced), 1992:I and the period following the Asian crisis.

Table 2.1: Exchange Market Pressure and Intervention Activity

2.6 EXCHANGE MARKET PRESSURE ON THE POUND-DOLLAR

This paper offers an investigation of exchange market pressure against pound sterling during the inter-war period, 1925-1931, when the pound was pegged to US dollar through their link to gold. (C. Paul Hallwood & Ian W. Marsh, 2004) This investigation is relevant today for what it tells about the viability of exchange rate pegging. Bank of England seemingly responsibly managed the money base within the confines of the latitude offered by the exchange rate band between the gold point, the pound was still subjected to speculative capital outflows – especially in the four months before it was knocked off its peg on 21 September 1931. If this interpretation of finding is correct, the viability of the open capital markets along within pegging is questionable even when the authorities behave responsibly.

An issue is whether the Bank of England played the “ruke of game,” by which is usually meant the changes in the money base were strictly determined by the balance of payments? The Bank of England cut the interest rate in order to stimulate the economy, only to have to raise them again to protect the balance of payments and the pound’s peg to gold. In fact, some latitude was afforded to the Bank of England by the pound’s fluctuation band between the gold points. Lower interest rate could be sustained so long as the exchange rate moved only within the band and did not threaten to breach them.

Figure 2.3 shows that the pound – dollar exchange rate did indeed fluctuate between estimates of the gold points. We find our econometric estimate of exchange market pressure that when the Bank of England increased the rate of domestic credit expansion, exchange market pressure on the pound- dollar exchange rate increased, i.e., the exchange rate depreciated within the fluctuation band and foreign exchange reserves fell. However, we think that the Bank of England’s monetary policy during 1925- 1931 was in fact well-behaved, because the peg to gold and the link to the dollar were maintained for more than six years in very difficult world economic circumstances and with an open capital account. Indeed, the experience of the pound during this period was far superior to that of the European Monetary System during the 1980s, when currency realignments were very frequent even though exchange rate fluctuation bands were relatively wide and capital accounts were not necessarily fully open.

Figure 2.3: Pound – dollar spot exchange rate and estimated gold points (vertical axis dollars per pound)