Interest Rate Parity in Exchange Rates - Essay Example

Interest Rate Parity in Exchange Rates The Invisible Catalyst. Xxxxxxxx x Xxxxxxxxx Department of xxxxxxxxx Xxxxxxxxx May, 2006. Abstract: The paper argues that the covered and uncovered interest rate parity conditions do figure in determining exchange rates among countries allowing free capital mobility and flexible exchange rates. However, the nature of foresights and expectations of investors along with the speed of response to economic shocks influence the equilibrium through interest parity conditions. Interest Rate Parity in Exchange Rates : The Invisible Catalyst. Introduction The exchange rates are determined in the Foreign Exchange Market (FEM). This is the market where people, banks, firms and other financial institutions buy and sell foreign exchange. FEM for any currency, say the Euro is made up of the places where Euros are bought and sold for other currencies. The principal function of FEM is the transfer of funds or purchasing power from one country or currency to another. When we consider exchange rate determination, the factors that significantly concern time dependence, become extremely important. It is somewhat reflected in the interest rates which themselves are prices of present-future substitution (abstinence); this influences savings, consumption, demand for goods, and so, money (both domestic and foreign) and hence the related prices. Thus exchange rate being a price of foreign currency in terms of the domestic currency, becomes influenced by interest rate and inflation over time. The sections below are titled along sub-themes with a critical note at the concluding section. 2 Exchange Risk and Covered Interest Parity As stated above, the exchange rate is in turn governed by a currency's interest rate and hence the question of parity and differentials become extremely important. Interest rate parity is said to occur when deposits of all currencies offer the same expected return. Two types of such parity have been envisaged in the literature Covered and uncovered that we discuss below. 2.1 Covered Interest Parity In the floating exchange rates regime exchange rates are market determined. Since Early Mundell-Flemming days (i.e. early nineteen sixties), it has been established that the degree of capital mobility is crucial in determining the open economy macroeconomics of participating countries. In this context when perfect international capital mobility occurs, bonds that are free of default risk domestically become free of default risk internationally also. With capital mobility of this degree, domestic bonds become perfect substitutes of foreign bonds on which forward cover has been taken and arbitrage brings about equality between domestic interest rate i and foreign interest rate i* plus the forward premium on foreign exchange 'f '.This is covered interest rate parity (cip) given by : i = i* + f (1) 2.2 Uncovered Interest Parity A stronger definition of capital mobility incorporates additional criterion that attitude towards exchange risk be taken as risk neutrality because that is nearly common among investors and exchange risk is perfectly diversifiable. In that case speculation turns the forward premium into equality with the expected rate of appreciation of the foreign currency: f = [(Et+1 - Et) / Et]e (2) where E is the exchange rate that the price of the foreign currency in terms of domestic currency (superscript e refers to expected status of the associated variable).Then equation (1) changes into i = i* + [(Et+1 - Et) / Et]e (3) This is the condition known as uncovered interest parity (uip). 3. Relationship between Covered and Uncovered Interest Parity In the case of perfect foresight and perfect capital mobility the two conditions will be the same. The relationship between the two lies in the characteristic of future expectation orientation of the uip that one does not take care of in the perfect capital mobility, perfect information and perfectly rational expectations. Form empirical standpoint, cip has been somewhat endorsed. However, empirical studies on covered interest arbitrage suggest that the interest rate parity condition does not always hold during times of turbulence in the foreign exchange markets. Thet implies it is a reign of uip which also is not quite supported empirically. There appears to be overwhelming empirical evidence against uip. Given that this empirical evidence has not stopped theorists from relying on uip, recently evidence is more favorable to the condition.. 4. Exchange rate Dynamics and the Interest Parity Conditions -A Simple Cagan-Dornbusch Model When we consider exchange rate dynamics, i.e., the moment time essentially enters, the role of present future trade-off and arbitrage gathers weight in determining all prices, spot or future. This trade-off on the other hand is somewhat reflected in the interest rates which is itself a price of present-future substitution (abstinence) influences savings, consumption, demand for goods and so for money domestic and foreign and hence related prices. Thus according to the analysis made earlier, covered interest rate parity enters determination of exchange rates over time. As a result, depending on the stability property of the system, the process may lead to a dragged upward movement of the exchange rate known as the 'overshooting' a la Dornbusch (1976)1 Starting from an unanticipated increase in an economy's money supply an immediate decline in her domestic interest rate may ensure which will lead to a big and fast jump in favor of demand for foreign currency as investors increase their demand for foreign assets. Generally the related trade flows reacting to immediate resultant rise in exchange rate are quite slow, while forex transaction effect remains dominant. Hence the exchange rate overshoots compared to its long run equilibrium level. The effect depends crucially on one major building block of exchange rate dynamics- the uncovered/covered interest rate parity- caused by the international differential on interest rates. This we discussed relating dollar-euro transactions above. The analytics may be borrowed from Dornbusch's model that built up keeping some of the Cagan type models: Starting with a PPP condition ( acrucial building block in the entire open economy macroeconomics, we have Pt = Et P*t (4) Implying , pt = et + p*t , when in logs; (5) Now our uip is approximated in this log terminology and expected rates,2 it+t= i*+ et+1- et (6) i.e. with open capital markets and perfect foresight, uncovered interest parity holds. As only domestic residents hold the domestic currency and domestic monetary equilibrium is charactreised by Caegan type aggregates, the money demand equation is, mt-pt= -it+1+ yt (7) where m is the log of nominal money supply, p is the log of the domestic currency price level, y is the log of domestic output. Making consistent substitutions of uip in logs into the respective money demand equation, we get the difference equation, mt- yt + it+1-p*t - et = [et+1e - et ] (8) Skipping the well known steps, the solution for the exchange rate is : et = [1/ 1 + ] [ / 1 + ] s - t[ms- ys]e (9) s = t This is the monetary model of exchange rate determination. In this scenario, if the home money supply increases the domestic price level and pushes e upward through 5the PPP process. Note that the assumption of uip is crucial in this model. A highly significant insight of this simple model basing on uip is that the nominal exchange rate is an asset price and so, depends on the expectations on future variables. Dornbusch's extension incorporates demand for home country output (aggregating all domestic output as a single commodity) as an increasing function of real exchange rate 'q' where PPP does not necessarily hold.[ as q = et + p*t - pt becomes zero with PPP]. Thus, in the line of Dornbusch., ydt = y + (et + p*t - pt - q ) , > 0 (10) with y and q as the long run equilibrium levels of the respective variables. Holding p*t constant at p*, i.e. retaining the small country assumption), constant, as the real exchange rate is given by q et + p*t - pt (11) there will be a q , the equilibrium real exchange rate consistent with y , that is consequently the full employment output. What now is important to note is that the excess demand for goods when appears, works out slowly rendering pt to respond sluggishly to date t shocks. Then as Dornbusch points out, price level adjusts slowly along the inflation-expectations-augmented Phillips curve line: pt+1 - pt = (ydt - y ) + (pt+1 - pt) (12) where pt = et + p*t - q (D) This is a definitional equation (D) defining price level if the output market clears. Differentiating (D) we get, pt+1 - pt = (et +1 + p*t +1 - q t+1) - (et + p*t - q t), and substituting this in (12), pt+1 - pt = (ydt - y ) + et +1 - et (13) This is the basic dynamical equation in Dornbusch model. Through consistent manipulating transformation and introducing deviations in real exchange rate from its long run equilibrium value we get, qs - q = (1 - )s-t (qt - q ), as the solution. Substituting (6), (10) and (11) in (7), with some simplifying normalization we alsio get the equation on nominal exchange rate: et+1 - et = et/ - (1- ) qt / - ( - mt) / Applying appropriate methods it is found that the implied e - q space has consistent laws of motion around q = 0 and e = 0 generating a saddle path. It is easy to see the conditional possibility of overshooting to result from a deviation through money supply shock. Rewriting the system introducing a money-supply-growth equation: mt.= m + t, being the growth rate and the nominal interest rate being i + . Through appropriate substitutions and postshock values represented by primes, the solution becomes: it+1 - (i + ) = ( - ') - (1- )t[e0 - (e0flex)'], The two systems are the same and subsumes the interest rate parity conditions. Conclusion:The model works with rather restrictive assumptions withwell known lack of empirical validity of the two interst rate parity conditions, though very recent empirical works are supporting them. When time dependence of international arbitrage becomes central, the conditions does not say much beyond flexibility of prices with respect to excess demand. Reference M.Obstfeld & K.Rogoff Foundations of International Macroeconomics, MIT Press, 1997. Read More