Empirical Analysis of the Monetary Approach

The monetary model for the exchange rate assumes perfect capital mobility, perfect substitution among different financial assets, perfect integration of the goods and financial markets, and the validity of purchasing power parity (PPP). In monetary models with flexible prices, it moreover assumes uncovered interest rate parity, with which the exchange rate responds to the fundamentals, where the most important variable is the relative quantity of money (^{Mussa, 1982}). On the other hand, in monetary models with rigid prices, the exchange rate dynamics do not match with the PPP in the short term; the financial and goods markets have different adjustment speeds, which gives rise to overshooting the exchange rate vis-à-vis the long-term equilibrium value (^{Dornbusch, 1976}).

Among the empirical analyses, ^{Gardeazabal et al. (1997)} found important evidence of cointegration between the exchange rate of the British pound sterling, the German Deutsche mark, the Italian lira, and the Spanish peseta with respect to the United States dollar and its fundamentals; MacDonald and Taylor (1992) analyzed the long-term behavior of the exchange rate of the sterling pound and the United States dollar using multivariate cointegration techniques in an unrestricted monetary model and were able to validate the monetary approach. In summary, these authors asserted that the monetary model does indeed explain exchange rate dynamics in the long term, particularly when the model is complemented with the Balassa-Samuelson effect.

The Microstructure Approach: Speculators’ Net Positions

The microstructure approach highlights other variables not considered in the monetary model. Among the most relevant, the order flow that measures the net purchasing pressure (^{Lyons, 2001: 7}), the conduct of the heterogeneous stabilizing and destabilizing agents that take part in the foreign exchange market with different expectations not necessarily consistent with the fundamental macroeconomic variables, asymmetrical sharing of information, and the net positions of speculators that balance the markets and transmit information (^{Torre Cepeda and Provorova Panteleyeva, 2007: 15-18}).

In their pioneering study on the microstructure of the exchange rate market, ^{Evans and Lyons (2002)}, based on data from Reuters D 2000-1 on the net positions held by speculators, analyzed the daily variation between the dollar, the mark, and the yen during a four-month period (May-August 1996) and found substantial correlation between the negotiations of the net positions held by speculators and the published exchange rates. This conclusion was proven again by ^{Danielsson, Luo, and Payne (2012)}, although the latter concluded that, lacking a perfect forecast of the future explanatory variables, the net positions of speculators have little or practically no explanatory power at all when it comes to the exchange rate.

Various studies have underscored the explanatory significance of the net positions of speculators. ^{Bjønnes, Rime et al. (2005)} concluded that these positions could explain one third of the daily volatility in the Swedish krona and the euro. This conclusion is consistent with others. ^{Osler (2002}, ²⁰⁰³⁾ and ^{Bates, Dempster et al. (2003}) examined the ledger of daily orders made at HSBC Bank. ^{Torre Cepeda and Provorova Panteleyeva (2007)} conducted an excellent and pioneering analysis of the microstructure of the influence of the net positions of speculators in the Mexican peso futures market to determine the exchange rate with respect to the United States dollar in the time period 1999-2005; they found that due to the accelerated growth of this market, the relationship between the two currencies has not been constant.

Based on the foregoing, we can say the following: the monetary model explains the exchange rate in the long term; the net positions of speculators determine the behavior of the exchange rate in the short term; finally, a combination of the two approaches could better capture the dynamics of an exchange rate, given that the net positions of speculators requires prior information that could be provided by the monetary model.

Stylized Facts

In the presence of non-stationary variables, we must look for robust empirical evidence as to the role played by the net positions of speculators in the exchange rate in a flexible regime. First, we discuss some of the main stylized facts pertaining to the exchange rate (Brazilian real/dollar) and its cardinal determinants, including the net positions of speculators and a few fundamental variables.

The data consisted of monthly, non-adjusted observations taken during the time period 2002.4-2012.8. The variables considered were as follows: the nominal exchange rate (Brazilian real/dollar); net positions of speculators; the difference between the log of the interest rate and M1 of Brazil and the United States. We did not consider the product, given that we could not find monthly data on this factor for Brazil. The following graphs display the behavior of each of the series:

Source: Created by the authors using data from the Applied Economics Research Institute (IPEA).

Figure 1. Logarithm of the Nominal Exchange Rate (Brazilian Real/Dollar), Quarterly Data 

Source: Created by the authors using data from the IPEA.

Figure 2. Logarithm of the Nominal Exchange Rate and Logarithm of Speculators’ Net Positions 

Source: Created by the authors using data from the IPEA.

Figure 3. Brazil (m) and the United States (m*): Logarithm of M1. 

Source: Created by the authors using data from the IPEA.

Figure 4. Logarithm of the Interest Rates of Brazil (i) and the United States (i*). 

In Figure 1, we see that from 2002.4 to 2002.12, the exchange rate rose, as competitiveness was sought via depreciation of the nominal exchange rate. However, starting in 2003-1 and up until 2007-12, the Brazilian real appreciated, due to the inflow of foreign capital, as well as an improved balance of payments, in this way prompting an increase in the international reserves. The devaluation observed in 2008 was due to the global financial crisis that year. Following the crisis, foreign capital began to flow in again and, once more, the balance of payments improved. As a result, the nominal exchange rate continued to appreciate, exceeding pre-crisis levels (both in real and nominal terms); the Brazilian currency – together with that of Colombia and Uruguay – is the currency that has appreciated the most since the end of 2009.

Below, we examine the presence of unit roots in the nominal exchange rate, the net positions held by speculators, the interest rate, and the M1, in both Brazil and the rest of the world. Table 1a, in the Appendix, suggests that all of the variables are integration order I(1), which means that the estimation of the series in levels could lead to spurious conclusions, unless the series cointegrate.

Figure 2 exhibits the positive relationship between the nominal exchange and speculators’ net positions beginning in 2006; this is because when there are buying pressures (exerted by the net positions), the exchange rate price rises. On the other hand, Figures 3 and 4 show that the trends between the various national rates and the rest of the world (m - m*, i - i*) have the same behavior, which indicates the existence of more than one cointegration vector.

Table 1b, in the Appendix, shows that the differences between the variables for Brazil and the United States are stationary. As such, it is possible to find cointegration between the variables. In this way, the cointegrated VAR model could be our point of departure for the structural analysis, in other words, for the SVAR. This not only would permit us to determine if the explanatory power of the macroeconomic model is enhanced when the net positions of speculators are included, but also the structure of how the net positions of speculators transmit information to the price in a multivariate set.

Method

In this section, we describe the empirical method that shows the relevance of the net positions of speculators in determining the exchange rate and its role in the transmission of information to price, using a cointegrated SVAR model. First, we show how the SVAR model is used to detail how the net positions of speculators transmit non-public information to prices in the monetary model context.

The analysis shows not only the estimation of the long-term cointegration equation associated with the theoretical exchange rate equation (3), but also the impulse-responses associated with the variance and covariance matrix of the cointegrated VAR model of the structural form to calculate the contemporaneous correlations between the variations in the net positions of speculators and the variations in the exchange rate. At the same time, we derive the short- and long-term transmission mechanisms.

In the presence of unit roots, the structure of the VAR model can be shaped in three stages: the first, specify a VAR representation that is adequate for the set of variables, including a selection of the order of lags, the cointegration range, the type of deterministic polynomial analyzed, and a specification sensitive to the cointegration space. If one of the cointegration relationships identified is consistent with the coefficient suggested by (3), we can conclude that the net positions of speculators plays an important role in explaining the long-term behavior of price. More specifically, we analyze the existence of a statistically solid cointegration relationship, which includes the net positions held by speculators, which are related to the cointegration equation in the following manner:

(8)

If speculators’ net positions have a permanent influence on determining the exchange rate, in this long-term specification, β₃ should be positive. On the other hand, the determination in the Bilson model in the monetary approach to determining the exchange rate is given when the expected coefficients are β₁ > 0 and β₂ > 0.

The second stage is the “structural” step; the VAR model is used in its vector error correction model (VECM) version to identify the association between the exchange rate and speculators’ net positions in the short term, which is hidden in the covariance matrix of the residuals of each multivariate model. This is the point of departure for structuring the VAR representation of the exchange rate equation:

(9)

Where

To recover the coefficients of the short-term model, we use the variance and covariance matrix of the VAR in their error correction form (9); to verify the statistical validity of the various transmission channels between the net positions of speculators and the exchange rate, we work based off of equation (7). For example, to validate the short-term version of equation (3), we use the decomposition of the following variance and covariance matrix (which will be analyzed in the next section).

Restrictions on the Short-Term SVAR

(10)

This set of restrictions corresponds to the following short-term transmission mechanism:

Source: Created by the authors.

Chart 1. Instantaneous Links in the Exchange Rate Model 

The structure of the matrix can be rewritten as the following equations related with the monetary model that includes the net positions of speculators:

(11)

(12)

(13)

(14)

If the monetary model plays a relevant role in uncovering the expected price in the short term, it means that the coefficients have to be: ∂ℇ _e / ∂ℇ _(m-m*) = a ₄₁ > 0 and ∂ℇ _e / ∂ℇ _(i-i*) = a ₄₂ > 0, according to Chin et al. (2007). Moreover, a short-term impact exerted by the net positions of speculators on the price, for example, ∂ℇ _e / ∂ℇ _(m-m*) = a ₃₁ * a ₄₃ > 0, implies that the temporary monetary shock transmits information to the price by way of the net positions of speculators. It is important to emphasize that the monetary model must be identified or over-identified and the short- and long-term restrictions must be validated by way of the likelihood ratio test.

Finally, the third phase is the short- and medium-term validation of the monetary model by way of plausible modeling of the instantaneous correlations via the impulse-response functions.

Empirical Results and Discussion

In the econometric analysis, we estimated a correctly specified VAR model with non-stationary variables for the time period 2002.4 to 2012.8. The data have monthly periodicity; all of the variables are in their logarithmic form. The series used were: the nominal exchange rate Brazilian real/dollar (e), the net positions of speculators (x), and the national and external interest rate differentials (i, i*) and M1 (m, m*). The VAR model includes a restricted constant, two lags, and dummy variables to capture the financial shocks of 2002, 2008, 2009, and 2011. The unit root tests, with correct individual and joint specification, are shown in Tables 1a, 1b, 1c, and 1d in the Statistical Appendix. The number of lags was chosen based on the adequate model with correct specification. Other tests were also used, such as the Schwartz information criteria test, the Godfrey Portmanteau test, and the LR test (the latter is suggested by ^{Sims (1980)}). All of the correct specification tests are reported in the Appendix.

We began by analyzing the range of cointegration, using Johansen’s reduced range method. The trace statistic, in Table 1, suggests the existence of at least three cointegration vectors.

To test further evidence, a sequential test was conducted for the joint determination of the cointegration range and the polynomial trend ⁴ (^{Johansen, 1995}; see Table 2). First, we report the deterministic (constant and trend) tests, and then the joint test (the statistic).

The results suggest the existence of at least three cointegration vectors at a confidence level of 99% and indicate that a sensible model implies the existence of a linear trend in the cointegration vector and a constant in the series of the model. To ensure a robust model for the cointegration range over time, we used the ^{Hansen and Johansen (1992)} iterative process. Figure 5 shows the results of the test. The test reinforced the hypothesis of the existence of three cointegration vectors over time at a 99% confidence level. However, the test indicated that only two of them are stable over time (R Model).

Source: Created by the authors based on data from IPEA.

Figure 5. Hansen and Johansen Test. Stability of the Cointegration Range: R Model (Size=5%) 

The Johansen maximum likelihood procedure estimates a base for the cointegration space; the problem of identification remains open. One treatment used for identification is to impose a set of sensible a priori restrictions in the space of the parameters. In this case, the first cointegration vector is normalized as a long-term exchange rate equation and we consider the hypothesis where the differences between the national variables and the rest of the world are stationary; those restrictions permit a sensible identification of the space for the cointegration vector. Below, we report the equation of the cointegration vector:

Source: Created by the authors.

Table 3. Normalized Cointegration Vector 

This is one of the ways to write the cointegration vector, which implies that there is a long-term relationship associated with the monetary model suggested by Bilson, but which includes the net positions of speculators in determining price in the long term. In this particular interpretation of the cointegration space, we can see a positive relationship between net positions of speculators and the exchange rate in the long term. Figure 6 also confirms that the long-term equation – which is a linear combination of the exchange rate and its determinants – has stationary behavior, just as the monetary model suggests. The long-term relationship confirms that the net positions of speculators have a permanent effect and transmit fundamental macroeconomic information to the market, as the strong flow-centric version suggests. We can conclude, therefore, that the net positions of speculators are correlated with the fundamental future variables, like in the Bilson version of the monetary model, and that the relationship between exchange rate and speculators’ net positions is not inconsistent with the macroeconomic approach in determining the exchange rate.

Source: Created by the authors based on data from IPEA.

Figure 6. Impulse-Response for the Structural Effects 

To estimate the contemporaneous relationships in which we were interested, associated with the coefficients of equation (3), we used the restrictions suggested by equation (10), included in matrices A and B, to obtain the structure suggested by equations (11), (12), (13), and (14). It is important to emphasize that to find each restriction, we begin with an exact identification structure given by the decomposition of the lower triangle of the variance and covariance matrix of errors of the estimated VAR. Then, in matrix A, we save the coefficients to identify the monetary model (MAER), as long as the variables are statistically significant, and restrict to zero the parameters that are not significant, with which we arrive to a situation of over-identification. Finally, we secure the validity of the previously imposed restrictions through the LR test. The coefficients estimated for the contemporaneous interactions that represent the short-term version of the monetary model are shown in equations 15 to 18. The final estimate supports the graphical representation of the instantaneous relationships among the variables shown in Figure 5.

Source: Created by the authors based on data from IPEA.

Table 4. Estimated Contemporaneous Effects. Estimates of the SVAR Parameters 

The statistical validity of the mechanism in Table 4 confirms the a priori assumptions of the short-term connections between the fundamental variables and the exchange rate. The impacts of the structural shocks of money and the interest rate on the nominal exchange rate are positive. Finally, monetary shocks also have a positive influence on the exchange rate via speculators’ net positions. The simulation shows that the latter have a substantial contemporaneous effect on the exchange rate because the money supply shock affects the exchange rate through the net positions of speculators. As such, speculators’ net positions are correlated with monetary policy news, the liquidity channel, which confirms that temporary monetary shocks are transmitted to prices via the net positions held by speculators.

The evidence on the mechanisms can be proven using typical simulation techniques, such as impulse-response functions (IRF), based on the estimated VAR model and restricted to satisfy the cointegration range restrictions. The IRFs and their asymptotically valid intervals are shown below:

Source: Created by the authors based on data from IPEA.

Figure 7. Impulse-Response for Structural Effects 

Figure 7 shows the responses of the exchange rate to the shocks of the money supply and the interest rate differential, respectively, in graphs (a) and (b). As can be observed, both have a positive effect in the short term. This confirms the search for contemporaneous shocks and allows us to say that the MAER is a good approach to understanding the behavior of the currency in Brazil. In summary, the empirical results reveal that exchange rate movements respond to the shocks of the variables in the monetary model proposed by Bilson. On the one hand, pursuant to graph (c), we can see that the net positions of speculators have had a positive effect on the exchange rate, as mentioned in the initial hypothesis. This reflects the effect of the net positions of speculators on the exchange rate in the short term.

Finally, Table 5 shows the explanatory power of the net positions held by speculators. Although they are not the strongest, it is important to include them in the model, as the F test indicated that they should not be excluded from the SVAR model, as they help the model on fit. ⁵ Table 6 shows that the precision of the forecast improves once the net positions of speculators are introduced into the VAR model. This means that the net positions held by speculators are necessary to explain the long-term behavior of the exchange rate in Brazil.