We can observe an enormous growth in the literature on exchange rate determinations during the past 30 years. A reasonable explanation for this phenomenon is that the foreign exchange rates of the major industrial countries' currencies have experienced substantial volatility since the 1970's, when the floating exchange rate regime is officially adopted on the year of 1976.
Furthermore, partly due to the significant changes in the exchange rate of the U.S dollar against other major industrial countries' currencies, changes in exchange rates kept receiving evidently attention in the 1980's. During the period December 1980 to February 1985, the dollar appreciated by about 25% against the Japanese Yen, 125% against the Great Britain Pound, and 75% against the Deutsche Mark. After February 1985, the depreciation of the U.S dollar was even more obvious and in December 1986, the dollar was even 25 percent lower against the Deutsche Mark than it was in 1980, the same exchange rate against the Japanese Yen at the end of 1980 and it was about halfway from its peak against the Great Britain Pound.
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What causes variability in the exchange rate between two countries' currencies? What are the factors that have an influence on the exchange rate between two currencies? These questions have been the major focus of attention amongst policy makers and economists ever since.
1.2 Objectives and outline
The aim of this dissertation is to identify the empirical validity of the monetary model of exchange rate determination for the currencies, Switzerland CHF, Norway NOK, Australia AUD, Canada CAD, Great Britain Pound, Turkey TL, New Zealand NZD and Mexico MXN against the U.S dollar using the data spanning 23 years from 1988 to 2011.
The study is organized as follows. In Chapter Two, we explain the theoretical framework of the monetary model, the reduced form of the flexible price monetary model equation will be derived, and we end up with a review of previous literatures.
In Chapter Three, we describe the theoretical framework and methodology used in the empirically analysis.
In Chapter Four, we present a description of the data which we are going to use in this study. We will then use the DF and ADF tests to examine the stationarity of the data to provide the empirical results for both the monetary model and the VECM, as well as theoretical explanations for the poor results.
In the last chapter, the study ends up with summarizing the findings of empirical evidence together with some suggestions.
THEORETICAL FRAMEWORK AND LITERATURE REVIEW
2.1 The monetary approach
Some scholars proposed the theory of exchange rate determination in the 1950s. Numerous models have been developed along with their modified versions ever since. For example, the monetary models, balance of payments approach, the portfolio balance model and the purchasing power parity (also known as PPP) approach, etc, and for the purpose of explaining the variability of the exchange rate, most of the economists have switched from the flow supply and demand balance analysis to the monetary approach. Their assumption is that the exchange rate between the 2 countries' currencies should be viewed as an asset price. They defined the exchange rate as the price of one country's money in terms of another. The preliminary assumption of the monetary approach to the exchange rate is that fundamentally the same theory of the determination of prices of common shares is vital to the determination of the exchange rate.
The monetary approach to the exchange rate concentrates on a series of important assumptions, which lead us to regard the exchange rate as the relative price of national monies. Firstly, expectations are an important factor in the determination of the current exchange rate since monies can exist for a quite long time, thus expectations about future exchange rates will affect the current exchange rate. Secondly, another important assumption regarding the exchange rate as an asset price is the role of money supply and demand balance. Regarding assets as stocks, we define the equilibrium as a situation where the stock supply for money is equal to the stock demand of money. The last important assumption of using the monetary approach is that the prices are usually regarded as being determined in efficient markets, also known as the efficient market hypothesis.
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The monetary approach to the exchange rate suggests that a decrease in the domestic money supply will increase the exchange rate as the initial lack of money supply drives domestic prices down and hence, through PPP, the exchange rate up. A decrease in domestic real income causes a lack of money that, with a fixed nominal money supply, results in an increase in domestic prices and through PPP, pulls the exchange rate down. On the other hand, changes in foreign macroeconomic variables also have an effect on the exchange rate value between two trading partners. The domestic exchange rate is decreased by a reduction in the foreign money supply, by an increase in foreign real income and by a decrease in the foreign interest rate.
2.2 The simple monetary model
The simple monetary model of the exchange rate is also known as the flexible price model. All prices are assumed to be perfectly flexible. This model is also derived from other several important assumptions. Firstly, purchasing power parity, also known as PPP holds continuously, so that the exchange rate always equals price level ratio in the 2 countries. Secondly, foreign bonds and domestic bonds are perfect substitutes. Any difference in interest rates between the 2 countries equals the expected change rate in the exchange rate. These two assumptions suggest that interest rate differentials are just equal to the expected inflation rates differentials. Thirdly, the demand for money in each country is a stable function of the real income as a scale variable also the domestic interest rate as an opportunity cost variable. Fourthly, if the money market loses its equilibrium, it adjusts quickly, with domestic prices moving rapidly to eliminate any excess supply of as well as demand for money.
At this point we are in a position to demonstrate how to produce the reduced form equation of the simple monetary model. Starting with 2 semi-log demands for domestic and foreign money functions respectively:
m - p = a1y - a2r (1)
m* - p* = a1y* - a2r* (2)
We use equation (3) to represent the PPP relationship that links the bilateral nominal exchange rate with the price level:
s = p - p* (3)
Where m is the money supply, p represents the price level, y denotes the real income, r represents the interest rate and s denotes the nominal exchange rate which is defined as domestic currency per one unit of foreign currency, and foreign variables are denoted by asterisk. The datas are all in the natural logarithm form. Given the assumption of PPP holds in the long run and that the domestic price level is determined by the domestic money supply, therefore exogenous money supply determines the exchange rate. Substituting equations 1 and 2 into 3, rearrange the reduced form for the simple monetary model yields the following equation:
s = (m - m *) - a1 (y - y*) + a2 (r - r*) (4)
The above equation is the flexible-price monetary model of exchange rate determination in its simple form. Furthermore, equation 4 indicates that the monetary model implied another restriction on (m - m*) is that the coefficient is unity; it also suggests that there is a proportional relationship between the nominal exchange rate and the relative money supply. If we make another assumption which is that the domestic and foreign money demand equations' coefficients are equal (a=a*, b=b*), the equation 4 can be further reduced to:
s = (m - m *) - (y - y*) + (r - r*) (5)
To test the validity of long run monetary model means to test if a stable long run relationship among s, m-m*, y-y* and r-r* exists. Econometrically, we can test whether deviations of s from a linear combination of m-m*, y-y* and r-r* are stationary or not. The first step is to test the integration properties of s, m - m*, y - y* and r - r* using the unit root tests to see if they are in the same order. The three variables must be in the same order, for example I(0) ,I (1) or I(2). Then we can get the co-integration relationship to be estimate will be:
s = b0 + b1 (m - m *) +b2 (y - y*) + b3(r - r*) (6)
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We will estimate the equation (6) using the Ordinary Least Square methodology, also known as the OLS technique. As mentioned above, the simple form of the monetary model that suggests b1=1 , b2 =-1 and b3=1.We will then use the unit root tests to test the stationarity of s, m-m*,r-r*,y-y*and s-[(m-m* )-( y-y*)+(r-r*)].
2.3Empirical evidence on the monetary model
The introduction of floating regime exchange rates in the early 1970s has triggered an increasing interest in the testing and modification of models of exchange rate determination. Original equations can be found in the papers written by Frankel(1976) and Bilson(1978); Later afterwards, variations were developed by Dornbusch(1976) and Frankel(1979) in their papers. The empirical evidence on the numerous formulations of the monetary model can be divided into 2 periods. In the first period, which is the time from the inter-war years and the recent float years prior to the year of 1978, evidence is supportive of the monetary model. These studies indicate that the behavior of exchange rate is in line with the monetary model and that this model is of vital in explaining a significant fraction of exchange rate fluctuation.
Although the monetary approach appears to be reasonably valid in the first period, the situation changes dramatically in the second period. In the second period which dates from the current float period, evidence is not in favor of the monetary model as before. After that numerous studies attempted to support the results of the monetary approach, but such studies produced different results.
2.3.1A selective review of early finding
An early shot to test the monetary model was made by Bilson in the year of 1978. He used the exchange rate between the Great Britain Pound Sterling and the Deutsche Mark as the dependent variable. Bilson has noted that "the relative interest rate differential represents the relative holding cost of the two currencies compared to other real financial assets" and that "the Fisher condition may by used to express the nominal interest rate differential as the difference between the expected rates of inflation of the two price indices"(Bilson 1978 p.52) and found that it effectively supported the monetary model. He also tested the flexible price monetary model for the Great Britain Pound Sterling and the Deutsche Mark exchange rate over the period from April 1970 to May 1977, after allowing for a trend and employing the partial adjustment mechanism, according to Bilson's study , this time these results did not support the monetary model of exchange rate determination. The fact was that none of the coefficients of the money supply or real income variables were statistically significant. Bilson's unrestricted estimates revealed coefficients that were mostly insignificantly different from zero; however, by imposing a set of prior restrictions on the model, he was able to obtain estimates that were consistent with the monetary approach. Furthermore, Bilson incorporated dynamics into the equation and used a Bayesian estimation technique. He tried to solve the problems including in his model prior information; his results were in broad accordance with the monetary approach.
The results lead Bilson to the conclusion that the monetary approach may also be useful in the analysis of short- run behavior in the examined period which is from April 1970 to May 1977.
The real interest rate differential model was introduced by J.Frankel in 1979. He successfully extended the sticky price monetary model. Frankel combined sticky price monetary model with flexible price monetary model to derive a reduced form of the equation which allows discrimination between the 2 models. The hypothesis is tested using the Deutsch Mark against the U.S dollar and 2 alternative hypotheses. First is the Chicago theory, introduced by Frankel and Bilson which suggested positive sign of the coefficient of the interest rate. Second is the Keynesian theory which claimed a 0 coefficient as the expected coefficient of the expected inflation rate.
The Frankel model makes it clear that a disequilibrium set of real interest rates will lead to a real exchange rate deviation from its long-run equilibrium value. In his study Frankel proxies the expected rate of inflation by a long term interest rate and estimated the model from monthly data set between July 1974 and February 1978 for the Deutsch Mark against the U.S dollar. The results were not seriously affected by the choice of monetary aggregate; those using M1 are reported in table 1:
Table 1:Test of Real Interest Differential Hypothesis
(Sample: July 1974 - February 1978)
Note: Standard errors are shown in parentheses.
As we can see in the table, the signs of all the coefficients are as hypothesized under the real interest differential model in all of the 4 regressions. The results are even more noticeable when the null hypothesis of a positive or 0 coefficient is a reasonable and even greatly maintained hypothesis. Frankel's estimates were quite supportive of the monetary model theory. The depreciating of the Deutsch Mark during this period seemed to have a reasonable theory base. Especially, estimates of the monetary exchange rate equation for the Deutsch Mark against the U.S dollar at times report coefficients that indicate that a relative decrease in the domestic money supply lead to a reduction in the foreign currency value of the domestic currency which will be represented as an exchange rate appreciation.
He claimed that since the coefficients on the expected inflation terms and interest rate were both significant, both the sticky and flexible price models were rejected in favor of the real interest differential model. The empirical evidence does prove the validity of the theoretical predictions and the model against the 2 alternatives. The Chicago and Keynesian hypothesis are rejected in that data sample.
The monetary theory claims that a decrease in domestic interest rates induces an appreciation and a fall in domestic relative income induces a depreciation. Dornbusch conducts another test of equation s=(m-m*)- a(y-y*)+b(r-r*) based on quarterly data for the time spanning 1970s. He estimated the monetary model for the Deutsch Mark against the U.S dollar exchange rates. His finding indicated that even with the coefficient on relative money stocks constrained to unity, the estimates did not have a supportive power for the model. The results are reported in table 2:
Table 2:Equation explaining the monetary approach to exchange rate determination. Using the the Deutsch Mark against the U.S dollar exchange rates,
(Sample: Fenruary 1973 - April 1979)
SD error of estimates
Note: The numbers in parenthesis are t-statistics.
As we can see from the table ,the real interest difference model estimates reported by Dornbusch trigger doubt on its ability to model the exchange rate in the sample. The reason is that although interest rates are significantly different from 0 and have the expected sign, the relative monies' coefficient is negative and also residual autocorrelation is a problem. Dornbusch also proved that PPP to be completely unreasonable for explaining exchange rate fluctuation in the short run. The evidence on PPP suggests that the monetary approach is not a satisfactory theory of exchange rate determination. The simple monetary approach only represents a poor description of this period.
Also he concluded that the portfolio shifts arising from limited substitutability among securities and current account developments were also important additional determinants of exchange rates.
Meese and Rogoff (1983)
The aim of the Meese and Rogoff's studies were to compare the time series models with the flexible price monetary model, sticky price monetary model and sticky asset model. They compared the out of sample "static" simulation forecast of a random walk model against several structural models and concluded that even a random walk model would successfully out perform all the other monetary models as a predictor of major industrial countries' exchange rates during the period 1970's in logarithm form. They analyze the reasons for the poor performance of a variety of exchange rate models and showed that none of the outstanding exchange rate models that were successful in1970's were at all successful in predicting exchange rates out of sample into the near future. As a matter of fact, none of the monetary models had a better out of sample predictive power than a random walk model in 10 years' exchange rate prediction.
Firstly, Meese and Rogoff estimated the models for the time spanning from March 1973 to July 1981. They adjusted all the data seasonally using dummy variables for the U.S dollar exchange rates against the Great Britain Pound , the Japanese Yen and the Deutsche Mark . Secondly, they used 3 main criteria to assess the validity of the structural models. Mean error(ME),Mean absolute error (MAE) and Root mean square error (RMSE). Meese and Rogoff valued more about the result of the first criterion.
The result are reported in table 3:
Table 3:Root mean square forecast errors
Univariate Autoregress Sign
Vector Autoregress Sign
$ against Mark
$ against Yen
$ against Pound
Table 4:Mean forecast errors
Univariate Autoregress Sign
Vector Autoregress Sign
$ against Mark
$ against Yen
$ against Pound
As we can see from the results, they have successfully proved that the forecasting performance of the monetary approach to exchange rate is out-performance by even a simple random walk. Furthermore , they have tested and claimed that the random walk is at the lowest as good as predictor as the structural monetary models. More specifically, they compared the out-of-sample fit of various structural and time series exchange rate models and they found that the random walk model performs as well as any estimated models at 1-12 months horizons for the U.S dollar exchange rates against the Great Britain Pound, the Japanese Yen and the Deutsche Mark. As for the trade weighted dollar exchange rates, it was also the same situation. Their conclusion is that it is not likely that more efficient estimations restrictions would yield parameters estimates which would perform better.
2.3.2 A selective review of recent finding
Since the 1980s numerous tests have been performed to test the long run validity of the monetary models using co-integration specification, more precisely the 2 step procedure suggested by Engle and Granger (1987).
The monetary model of the exchange rate has also been examined using the specification of co-integration in papers by Meese(1987), Kearney and Mac Donald(1990). These studies failed to find a co-integration relationship between the explanatory variables' vector and the exchange rate in the monetary models.
Furthermore, it was generally found that the relative money supplies and relative prices are integrated of order I(1); relative levels of real income are integrated of order zero I(0) with a time trend relevant; the interest rate differentials are I(0); exchange rates are I(1); exchange rates are not co-integrated with price level or relative money supplies; These findings weakened the validity for the monetary model. These findings even rejected the earlier assumption that the failure of the monetary model was due to its nature as a long term model.
The invalidity of the exchange rate determination monetary models has been widely debated. Although the simple form of the monetary model seemed to have a quite precisely prediction for the data for the first 4 years of the adoption of the flexible exchange rates, there were still some exclusions ( Bilson 1978 ).
According to Dornbusch(1980), Frankel(1983), models incorporating sticky prices out-performed the simple form of monetary model. And according to Frankel (1979), Meese and Rogoff (1983), none of the structural models had a better performance than a random walk model in terms of the out-of sample predictive power. There are several reasonable interpretations for the failure of the monetary model of exchange rate determination.
Based on all the negative evidence Lane lists some prominent reasons for the explanation of the monetary model invalidity.Firstly, recently, the demand for money estimates is quite unreliable.Secondly, the assumption of PPP and the related assumption of stationarity of the real exchange rate. Thirdly,the assumption that the parameters in the demand for money functions are equal in both countries.Fourthly, the assumption of UIRP, implying either risk neutrality or that exchange rate is entirely diversifiable.Fifthly, the assumption of exogeniety of the money supply, which if present, would contribute to the empirical failure of the monetary model.
Lane concluded that "it is perhaps less surprising that the monetary model has failed empirically than that it ever appeared to succeed at all"(p.p. 214). In contrast, Lane interprets empirical evidence on the monetary model in the light of a theoretical model. It is, in essence, a two country variant of the Mundell-Fleming IS-LM model which predicts that exchange rates are not cointegrated with either the relative money supply or relative price level.
The main features of the model were:
Estimation and testing of the model has specific implications for the dynamic behavior of the exchange rate, price levels , money supplies, income and interest rates. The monetary models of exchange rate, emerge as special cases, subject to restrictions that should be tested. The model takes on board some of the criticisms that have been leveled at the monetary model. It implies specific prescriptions for the degree of differencing of each variable that is appropriate for testing.
Lane defends his arguments and concluded that "the model is not the only one that might provide a satisfactory interpretation of the time series evidence presented. The task that remains is to test the restrictions implied by this model, in order to permit a comparison with alternative interpretations".
The model was designed specifically on the basis of the empirical evidence on integration and cointegration. The model although is slightly more general than the monetary model, is still quite simplified, it does illustrate a possible interpretation of the empirical results.
In his study, I.Moosa tested the validity of another form of monetary model of exchange rates again, which he imposed a distinction between traded and non-traded goods. On the assumption that PPP is only valid for traded goods and invalid for the non-traded goods, he applied a Johansen multivariate technique of co-integration to an unrestricted form of the basic monetary model.
Using the U.S dollar against the other 3 targeting exchange rates and monthly data spanning from the year1975 to 1986,I.Moosa found evidence in favor of the existence of a co-integration relationship between a vector of explanatory variables and nominal exchange rates. He used the Dickey-Fuller (DF) and Augmented Dicky-Fuller (ADF) techniques to test for stationarity. He found that except in case of the Deutsch Mark against the U.S dollar , all the other statistical testing of coefficients' restrictions in the monetary model led to a rejection of the restrictions. The DF and ADF statistics are measured for the level of variables and their first differences with and without a time trend accordingly. Using the DF and ADF tests he found that most of the relevant variables were integrated of order 1 series. The relative lower power of Engle and Granger method led him to test for co-integration using the Johansen technique.
The results are presented in table 4:
Table 4:Stationarity test
In the US case the max eigen values and the trace statistics rejected the null hypothesis r=0 and râ‰¤1. In the German case the results were the same but the null hypothesis râ‰¤2 was also rejected in the trace test. In the Japan case the results were more supportive since the trace test rejected the hypothesis râ‰¤3. These results were also in accordance to MacDonald's and Taylor's findings in theirs papers.
I.Moosa concludes that: "The monetary model should be reappraised at least as a long run representation of the behavior of exchange rates"(p.p 008)
Rapach and Wohar (2001)
In the paper "Testing the Monetary Model of Exchange Rate Determination: New Evidence from a Century of Data" ,Rapach and Wohar (2001) tested validity of the long run monetary model. The authors used the annual data for 14 industrialized countries time spanning from the 1800s to the late 20th century, and they used bilateral exchange rates against the U.S. dollar. The results of the estimates are strongly supportive for the basic long run monetary model for France, Italy, Holland, and Spain; moderate for Belgium, Finland, and Portugal; and is quite weak for Switzerland. There is no supportive evidence of the model for Australia, Canada, Denmark, Norway, Sweden, and the Great Britain.
2.4 The empirical failure of the monetary model
Due to all the results that are not supportive to the theoretical model, it should be reasonable not only to test the validity of the assumptions of the monetary model but also trying to find out an interpretation for the failure of the model.
It would be not possible to have an explanation for the monthly exchange rate variability with any empirical version of the monetary model, even if it were true that the actual and estimated behavior of relative money supplies are the only factors that affecting the exchange rates. The first one reasonable explanation is that no formal statistical analysis can be formed when the information about the future behavior of market money supply are received through numerous different channels
The second reasonable interpretation for the failure of the monetary model is that one of the assumptions of the monetary model is that the money demand equation's coefficients are all the same in the sample countries. For instance, Haynes and Stone (1981) have tested this assumption in Frankel's (1979a) sticky price model. Their evidences proved 2 facts. Firstly, that not only the hypothesis of income and interest rate coefficients' equality of money demand functions was rejected by the data, but also the fact that Frankel's rejection of the simple flexible price exchange rate model in favor of his own was also due to this assumption.
The third reasonable interpretation for the failure of the monetary approach equations may be due to the money demand functions' instability. The monetary model is built on the assumption of the stability of the demand for money function in each country. However, as numerous empirical studies have shown ,the money demand function is unreliable. As a result, it is reasonable that the reduced form equation is also unreliable.
Fourthly, the monetary model assumes that the PPP holds on a continuous basis. This assumption is supported by some evidence for specific periods, but was later rejected by other evidences, particular from the recent floating period .It was then widely recognized that short term or continuous PPP was rejected explicitly by the sample data. Furthermore, there is evidence that deviations from PPP follow a process that is non-stationary. Such results weaken the validity of PPP even as a long-run assumption.
Fifthly, some basic factors that matters to the result are omitted is a more fundamentally deficiency in the simple form version of monetary model. For instance, traded and non-traded goods are not clearly distinguished.
The final one reasonable interpretation for the failure of the monetary approach equations is that the uncovered interest parity (UIRP) is rejected. The evidence on UIRP still remains debatable. The assumption must be based either on the exchange rate risk is neutral or on the assumption that the risk is completely diversifiable ( Frankel , 1979b). However, according to the historical data and examination, both of the assumptions have been rejected. After this evidence it has been concluded that UIRP does not hold, but in the forward market, there exists a risk premium that varies with the time. If this assumption is validity, it could be one reasonable interpretation for the not ideal performance of the monetary model.
Due to the invalidity of the assumptions used to derive the monetary model, the monetary model of exchange rate determination has been seriously challenged.
Numerous historical studies on the monetary model have proved that PPP theory is invalidity and have argued that the conditions of money market equilibrium are more closely related to the exchange rate determination in the short term. In reality, the monetary model predictions are not closely related to the nominal exchange rates' actual movements. Theoretically, there is no explicitly reason why exchange rates volatility should be a random process.
Overall, the empirical test results of the monetary model and the monetary model's variants have been quite disappointing. Evidences show that the estimates of the simple form of monetary model are not supportive to the theory around the year of 1978 (Dornbusch 1980):Sticky-prices that incorporated monetary models out-performed the simple form of monetary model. Bilson (1978) also examined the empirical validity of the simple form monetary exchange rate determination model, and the results suggested that the monetary approach of the exchange rate may be useful in both of the long term analysis and the short term intervention policies guidance. Bilson adapted the basic model by assuming that both of the domestic prices and the money supply are unable to be observed in the current period. Furthermore, he tested the assumption using a vector autoregression (VAR) technique. Bilson's empirical results showed controversial evidence on the assumption. Economists like Dornbusch(1980) and Frankel(1981) have suggested to make an assumption that eliminates all ex-ante profit opportunities so that the foreign exchange rate market is efficient is a correct way to model exchange rate volatilities. Furthermore, highly supportive results were found in their new approach studies,.
Richard Meese and Kenneth Rogoff have well documented about the poor explanatory power of the theoretical models of the 1970s. According to the Meese and Rogoff findings, the 3 structural models out-perform the random walk specification in terms of the long term forecasts. So the conceptual framework underlying the asset market approach to determinate the exchange rate is not rejected by the result. Nasser Saidi makes a note on their results saying that "since the residual errors for various exchange rate are likely to be correlated, a joint estimation of the various exchange rate equation could improve the forecasts accuracy of the structural models."
However, after the adoption of floating exchange rate schemes, recent empirical studies have indicated that to model a reasonable empirical model of exchange rate determination is quite impossible. Lane (1991) made a reasonable interpretation for the invalidity of the monetary model. He also introduced an alternative of modeling a theoretical model that is in line with the existing empirical evidences.
Major industrial countries adopted the floating exchange rate system in the year of 1976. Ever since then, numerous studies on the process of exchange rate determination have been carried out. The monetary approach has become one of the reasonable interpretations for the exchange rate determination. A number of empirical studies were carried out to explain the major currencies' volatility. In this chapter an empirical analysis is conducted for the monetary approach to exchange rate determination for 8 exchange rates, they are: the dollar against the Switzerland CHF, Norway NOK, Australia AUD, Canada CAD, Great Britain Pound, Turkey TL, New Zealand NZD and Mexico MXN.
3.2 The data
The data for the analysis of monetary approach of the exchange rate for the 8 countries are all from the IMF's International Financial Statistics. The data is quarterly organized and time spanning from the year of 1988 to the year of 2011. Each of the 8 samples is consisted of 96 observations. The exchange rate variable is represented by the nominal exchange rates of the currency of the 8 target countries against the US dollar. Except for the interest rates, all the other series were put into their logarithmic form.
All the data from the 8 target countries used are seasonally unadjusted. As Meese and Rogoff (1983) explained that, without the variables being adjusted by the same period, seasonally adjusted data is highly possible to distort the structural parameter estimates. To avoid the use of certain information unavailable at a given forecast time is another reason why to use the seasonally unadjusted data.
In order to test the validity of the monetary model, we require the data of the money supplies (m), the real income levels (y), and the differential of interest rate (r). The equilibrium of income levels is represented by an industrial production. The nominal interest rates are chosen to be the long term government bond yield.
For the purpose of judging the performance of the economic model the following steps should be implemented from the perspective of econometric field. Firstly is the estimation step. At this stage we will have a test on the specification of the model and we will choose an appropriate technique to test the model. Secondly is the diagnostic check. At this stage we will try to solve the econometric problems that come from the estimation process.
In this empirical work the following equation has been fitted:
s = b0 + b1 (m - m *) +b2 (y - y*)+b3(r - r*) (7)
The model represented by equation 7 was tested over the period 1988 to 2011 quarterly observations. 3 techniques were used, namely the Ordinary Least Square (OLS), the Engle and Granger technique and the Johansen method.
Firstly, we need to use the OLS technique to obtain the coefficient of the parameters. Secondly, we will test for the stationarity properties of the estimated variables, for which we will use the Engle-Granger method of the DF and ADF tests. However, due to the relatively low indicative power and as a matter of fact that the Engle-Granger method makes implicit the assumption that the co-integration vector is unique, we need to implement an alternative method of testing for co-integration, namely the multivariate Johansen technique developed by Johansen (1988, 1989) and was later extended by Johansen and Juselius (1990).
3.4 Unit root test results
Firstly, we need to have an investigation on the integration properties of s, m-m*, y-y* and r-r* using the DF unit root tests. The results for the tests for our data are reported in table 5.Columns (1) of Table 5 show the country, time period, and variable tested in the unit root tests. We define a variable as I(0) if both of the tests reject the null hypothesis of non-stationarity at certain levels of significance or if at least 1of the tests rejects it at the 5 percent level of significance. If none of the test rejects the null hypothesis of non-stationarity at a conventional level of significance, we then define the variable as I(1). Finally, if only 1 test rejects at the 10 percent level, we designate the series as I(0) or I(1).
Unit root test results
Test Statistic after first differentiating
y - y*
r - r*
y - y*
r - r*
y - y*
r - r*
y - y*
r - r*
Great Britain (1988-2011)
y - y*
r - r*
y - y*
r - r*
New Zealand (1988-2011)
y - y*
r - r*
y - y*
r - r*
a :Dickey-Fuller tests of H : Non-stationarity; 1, 5, and 10 percent critical values equal -3.517,-2.894 and -2.582 respectively; when a first differentiating is conducted, 1, 5, and 10 percent critical values equal -3.518,-2.895 and -2.582, respectively.
Based on the unit root test results in Table 5, we can get the conclusion that the variables, s , m-m* , y-y*,and r-r* for both of the 8 countries are of the first order I(1). Next, we continue to our co-integration test process.
3.5 Co-integration test results
Now we will have an investigation on the stationarity properties of s-[(m-m* )-( y-y*)+(r-r*)] namely the residual, to see if a co-integration relationship between s and the residual exist or not. We will use the 5 steps method.
Step 1: We will start with the most general ADF specification which represents as
yt = Î¼ + Î³yt-1 + Î´t + Î£ Î²yt-i + Îµt. We then use the Information criterion approach to choose the length of lags. And table 6 shows the AIC and BIC value of each of the 8 countries. As we can see from the table 6 that we choose 1 period lag for both of the 8 countries. We will also then check the residuals are following a white noise process.
Choice of lag length results
Great Britain (1988-2011)
New Zealand (1988-2011)
Step 2: The next thing to do is to have a test on the joint hypothesis:H0: Î³ = Î´= 0.
We can find that time trend is not relevant for all of the 8 countries.
Step 3: Run the ADF test without deterministic trend: yt = Î¼ + Î³yt-1 + Î£ Î²yt-i + Îµt.
We can see from the results that the time trend is not relevant for all of the 8 countries.
Step 4: The next thing to have a test would be the joint hypothesis: H0: Î³ = Î¼ = 0.
We can find that the drift term is irrelevant for all of the 8 countries.
Step 5: Run ADF with no deterministic trend and no drift term:
yt = Î³yt-1 + Î£ Î²yt-i + Îµt and test: H0: Î³ = 0.
Table 7 shows the result of the test:
Unit root test results,residual
1% Critical Value
5% Critical Value
10% Critical Value
s-[(m-m* )-( y-y*)+(r-r)]
s-[(m-m* )-( y-y*)+(r-r)]
s-[(m-m* )-( y-y*)+(r-r)]
s-[(m-m* )-( y-y*)+(r-r)]
s-[(m-m* )-( y-y*)+(r-r)]
s-[(m-m* )-( y-y*)+(r-r)]
New Zealand (1988-2011)
s-[(m-m* )-( y-y*)+(r-r)]
s-[(m-m* )-( y-y*)+(r-r)]
And from table 7, we can see that the test statistic for all of the 8 countries is greater than the critical values, which means we do not reject the null hypothesis- we have a unit root. Then the conclusion is the series is no stationary, with no drift, there is no co-integration between s and (m - m *) - (y - y*) + (r - r*).
3.6 Error-correction models
In order to understand the adjustment process between the monetary fundamentals and nominal exchange rates, and how to restore the long term exchange equilibrium, the following vector error-correction model (VECM) is estimated, where
We estimate the VECM for Australia in Table 8, with the exception of Switzerland and Norway, due to the nominal exchange rate and monetary fundamentals relationship does not hold in the Countries. Table 8 reports OLS estimates of the error-correction coefficients, short-run adjustment parameters as well as the long-run adjustment parameters coming from the long-run co-integrating relationship. The OLS estimates of the error-correction coefficients, and which determine the adjustment process back to the long-run equilibrium, are 0.197448 (0.002),with standard error in parenthesis. Estimate is significant at conventional levels.
For Australia, the results support the underlying assumption that the long-run monetary model is reasonable. The co-integrating relationship between nominal exchange rates and monetary fundamentals exists. It is further found that it is in fact, only the relative output (y-y*) that adjust to restore the long-run equilibrium exchange rate. This implies that neither the nominal exchange rate nor the other monetary fundamentals (m-m*, r-r*) in Australia are weakly exogenous relative to the long-run equilibrium exchange rate, In other words, when deviations from the long-run equilibrium occur in Australia, it is primarily the relative output that adjusts to restore long-run equilibrium over our sample, rather than the exchange rate or any other monetary fundamentals.
3.7 Explain the poor results of exchange rate models
Numerous researchers have also tested the monetary exchange rate models with different degrees of econometric technicality. Generally speaking, the results indicate that the failure of exchange rate models is not quite uncommon. As far as I am concerned, there are quite a lot of reasons to explain why the exchange rates will be quite not easy to model in reality.
Firstly, not only the monetary policy stance, but also the mixture of fiscal policy and monetary policy can affect the exchange rate volatility. Furthermore, exchange rate is also depending on the macroeconomic policies interactions between different countries. The principle is quite complex and as far as I have concerned that currently we do not have a thorough understanding of the manner.
Secondly, both of the present monetary fundamentals and the expected change of those monetary fundamentals can determine the exchange rate volatility. Therefore, new information which will matters to the future development of these fundamental factors will also matters to the current exchange rate. It is quite impossible to observe and model all the changes even the minor ones in new information and discount the information into the current exchange rate accordingly.
Thirdly, another reasonable interpretation is named 'Peso Problem'. This problem means that even if we have a correct model of exchange rate determination and a relevant event to the exchange rate is almost confirmed to be happening at some point in the future, for example, a new Prime Minister is to come in, a decrease in the GDP or a decline in the amount of money supply, this will affect the current exchange rate. However, if the expected affair does not happen as the way that expected before, then the exchange rate will move irrelevant to the supposed underlying determinants. The model will then become impossible to be empirical estimated. Therefore, whether a given policy shock or disturbance has been anticipated or not will result in a totally different dynamic path of the original exchange rate model. As far as I am concerned, currently, it is also quite impossible for us to accurately take such effects into consideration to model an empirically exchange rate model.
Fourthly, all the exchange rate determination monetary models are based on one assumption which is that the expectation for the future will impact the exchange rate volatility today. However, in the real world economy, restrained by the econometrics techniques, some major simplifications both in the theoretical models and empirical tests are required to be adopted. For instance, most theories are based on the assumption that expectations are homogeneous factors, while in the real world economy, expectations are heterogeneous factors. Furthermore, when it comes to an empirical test, further major simplifications will have to be adopted. Some models are based on the assumption that expectations are fully in line with the underlying theoretical models in terms of foreign exchange market players, while other models are based on the assumption that exchange rate expectations follow a regressive expectations scheme. But when it comes to the reality, none of these expectations theories correctly specifies expectations formation in an uncertainty world.
Fifthly, another problem that may be specially paid attention to is that it has not only been changes in the supply of money that have been important in explaining the exchange rate, but also the changes in the demand for money. Theoretically such shifts are also vital in determining the exchange rate volatility. In reality, the money supply is not always stable. Frankel (1984) in an empirical test of money demand movements found that if we can take such kind of shifts into consideration then the performance of the monetary model will be obviously improved. Finally, there are numerous changes in the real structure and the financial condition of real world economies which have had vital meanings for the economies' performance and thereby affect exchange rate volatility.
The flexible exchange rate theory has still provided inconvincible interpretation for the determination of exchange rate volatility. Numerous methodologies have been used to identify a simple form monetary model which has some theoretical foundation of the literature.
Those who support the monetary approach denote the exchange rate as the relative price of the 2 countries' currencies. While PPP concludes that the exchange rate is the relative price of goods between 2 nations, the monetary approach gives the conclusion that the exchange rate is the relative price of 2 currencies.
One of the vital assumptions for the equilibrium is that the demand for the stock of each national currency is required to equal the stock of that currency available to be held.
The monetary model provides a useful tool for the analysis of exchange rate volatility because it clearly defines the role of assumptions among the variables of the exchange rate, relates the equilibrium rate to the fundamental mechanisms of monetary policy and provides a straightforward definition for the exchange rate equilibrium.
The empirical evidences on the monetary approach lead to a mixed conclusion, some studies find supportive evidences for the monetary approach predicted relationships. On the other hand, some other studies prove those hypotheses to be invalid. Early tests of the monetary approach conducted by Bilson (1978) or Frankel (1979) inclined to be supportive of the monetary approach. They found that the estimated coefficients largely gave a confirmation to the priors and the equations had a quite reasonable performance in terms of the in-sample forecasting. Numerous other studies using static or dynamics models have tested different versions of the monetary model for the period after 1976. The models performed quite disappointing in the period after 1976, with estimated coefficients often signed wrongly or insignificant, and have a rather poor performance in terms of in-sample forecasting.
Besides its theoretical simplicity and appeal, research has put doubt on the empirical validity of the model. Due to these findings it would be reasonable to test the foundations of the monetary model again, so I tested the empirical validity of the monetary approach using data for the recent periods with flexible exchange rates.
The results did not provide any supportive evidence for the monetary model in 7 of the 8 target countries. However, they provide supportive evidence for the monetary model in the way that long-run co-integration relationship is found between the nominal exchange rate and money supply deviation, the output and interest rate differentials in Australia. However, the results rejected the theoretical restrictions that are required by the monetary model. An adjustment process, through which the long term equilibrium of exchange rate is restored, is identified through the estimation of a VECM. The conclusion is that if there is a disturbance in the long term equilibrium, it is the relative social output variables that adjust to restore the model to its balanced status.
Our results also indicate directions for a future research. Since the monetary model has several weaknesses like questionable assumptions that seldom valid and the simplification of the dynamic economies, it would be reasonable to develop a more theoretical valid model. For example, since PPP in long term seems to be held for most of the countries, therefore the invalidity of the long term monetary model for some countries using long spans of data must be due to the reason that the long term relationship between the monetary fundamentals and relative price levels is not stable for those countries. It would thus be reasonable to search for the instability factors in the long term relative price level and monetary fundamentals relationship in the countries for which the long term monetary model is invalid.
Another further analysis is that if we can use panel co-integration to test the validity of the model. Panel co-integration tests normally including to test the stationarity properties of the residuals from a levels regression. However, panel techniques may be better able to detect co-integrating relationships since a pooled levels regression exploits cross-sectional information in the data when estimating co-integrating coefficients. Furthermore, the number of observations available when testing the stationarity properties of the residual series from the levels regression is substantially enlarged in a panel framework , therefore the power of co-integration tests will be significantly increased.