IS THE BRAZILIAN REAL A COMMODITY CURRENCY? LARGE SAMPLE EMPIRICAL EVIDENCE
Filipe Monteiro de Castro Albert
University of Essex, Brazil
Email: filipe_albert@yahoo.com.br
Paolo Edoardo CotiZelati
Municipal University of São Caetano, Brazil
Email: coti_zelati@outlook.com
Davi Lucas Arruda de Araújo
Mackenzie Presbiteryan University, Brazil
Email: davi_lucas89@hotmail.com
Submission: 14/08/2013
Accept: 28/08/2013
ABSTRACT
Brazil
is one of the world’s largest base materials exporters, and this paper examines
through large time series samples whether the Brazilian Real can be
characterized as a commodity currency. The Real/US dollar real exchange rate
and a real commodity prices index are found to be nonstationary and not cointegrated,
while a risk premium appeared to have a large and statistically significant
long term relationship with exchange rate movements. Combined first difference
models showed that real exchange rate elasticity to risk premium is twice as
large as to commodity prices, although both variables have considerable
influence. Some specifications outperformed a random walk model with respect to
root mean square forecast errors for many horizons, but the latter still better
determined the exchange rate in longer terms.
Keywords: Exchange rates; Commodity Prices; Cointegration.
1.
INTRODUCTION
An affirmation like the one above
might sound extremely alarmist today, when most developed and emerging
economies follow similar and stable macroeconomic policies. Back in the 1970s,
however, and for many years after that, it made perfect sense for a country
with a currency crisis every three or four years like Brazil. It was kind of a
mantra for those defending fixed exchange rate regimes, and not until the
second half of the nineties, when big economic reforms came into place, it
became outdated.
A floating exchange rate regime is
today a powerful tool for current account imbalances adjustments and one of the
most indispensable policies for Brazilian economic development. In that sense,
understanding what factors relate to exchange rate movements and how
forecasting could be improved is a very important issue in Brazil. Most local
economist have turned to interest rate
differentials or current account balances to try and explain how Brazilian Real’s
value is determined and this paper will look into international literature to
find evidence, pros and cons of these traditional methods. More attention,
however, will be drawn to Meese and Rogoff (1983) successful exhibit of how a
simple random walk can outperform structural exchange rate determination
models, and also to a fresh attempt of introducing commodity prices to explain
currency movements done by Chen and Rogoff (2002). This last paper, in fact, is
going to be of highest importance for the empirical part of this study.
As most developing economies and a
few well developed ones, Brazil exports a great deal of base materials. These
commodities are traded internationally and have their price settled in US
dollars without any direct interference of a specific producer. Therefore, a
surge in commodity prices should lead to an increase of Brazilian exports value
in dollars, more foreign currency within the country and a possible
appreciation of the country’s exchange rate. If this actually happens, the Real
could be characterized as a “commodity currency”, as have been the Australian
and Kiwi dollars in more than one occasion. Indeed, evidence for developed
countries is pretty easy to find, but dealing with real exchange rates in
emerging economies is a tougher job and empirical works are scarce. This is
mostly due to lack of reliable data, since, as Brazil, most developing
countries have a very unstable past and short series of data. Special care is
then given to the quality of data used.
The key objective of this paper is
not to examine all variables that interfere with the Brazilian real exchange
rate, but only to show if real commodity prices have a significant influence
over it. In order to do that, both monthly and weekly data from March 1999 to
June 2010 were gathered so that econometric tests could have maximum validity.
As in many other studies, the real exchange rate and real commodity prices were
found to be nonstationary. After that, variables appeared to have a long run
relationship only when Johansen’s cointegration tests used very unusual
specifications, casting doubts over their results.
Therefore, actual estimation of the
real exchange rate continued with models in first differences that considered
variables not to be cointegrated. They pointed to statistically significant
coefficients of real commodity prices with theoretically expected signs, yet
with far less influence than a risk premium measure. Outofsample forecasting
performances of some specifications were then compared with a simple random
walk, and results diverged from classic findings of Meese and Rogoff (1983). By
the measure of mean root square error, both specifications outperformed random
walk depending on the time forecasting horizon.
This paper is constructed as
follows. Section 2 is a comprehensive review of theoretical approaches to
exchange rate determination, added by a deep analysis of some insightful
empirical works both classic and more recent. Section 3 is dedicated to data
description and some graphical evidence of the relationship we are trying to
check. This includes how series that were not readily available were
constructed. Section 4 shows how unit root and cointegration tests were used
to establish some properties for the data, evolving to the econometric
specifications used to determine the relationship between the Brazilian Real/US
dollar real exchange rate and real commodity prices. Section 5 compares
outofsample forecasts from our models with results from a simple random walk.
Section 6 concludes.
2.
LITERATURE
REVIEW
2.1 Early exchange rate models
There are many ways in which
economists today can try to model exchange rates medium and long term
behaviours. All of those are based, at least in some level, on a modern
approach to purchasing power parity (PPP) defined in the early 1920’s mainly by
Swedish economist Gustav Cassel. The idea that in the long term equilibrium
currencies (E) must reflect the ratio of domestic prices (P) to foreign prices
(P*), or E=P/P*, is still broadly discussed and sometimes useful to compare
currencies valuations, as in the famous Big Mac index calculated every year by
The Economist magazine. Comparing prices of a homogeneous product that exists
in many countries is a clever way to approximate how exchange rates deviate
from long term equilibrium. Yet, also in this case basic criticism to PPP
cannot be avoided, since nontradable inputs, taxes and other interferences may
apply. Defining an appropriate index to calculate PPP is the biggest problem,
given that besides all interferences cited above, there are also significant
differences in preferences between countries that make price indexes hard to
compare.
In Frenkel (1979), evidence of a
working PPP regime in the 1920’s was found, but the same could not be said
about the floating exchange rates period of the 1970’s. Real shocks (oil price
shocks, productivity growth, fiscal policies swings, etc…) were said to be the
difference, giving extreme volatility to exchange rates and permanent
deviations from PPP in the latter period. Also, there are many studies that
have tried and failed to show any convergence of exchange rates to PPP on the
long term. They all use different techniques and datasets, and are summarized
in Rogoff (1996), where the author made popular the concept of a purchasing
power parity puzzle. At that point, the BalassaSamuleson effect of higher
productivity in the tradable sector of a richer country was one of the possible
factors leading to long term PPP deviations.
Understandings on how exchange rates
behave evolved on the postwar era to a balance of payments flows approach.
Current account balances were linked to currencies fluctuations, and how to
minimize volatility using monetary and fiscal policies was a subject much
debated in that time. Fixed exchange rates regimes became fashionable. During
the 1960’s, however, the famous MundellFleming model of exchange rate
determination was developed and enlightened common knowledge of monetary
policy’s role in economic stabilization. Today’s comprehension that a central
bank should be independent and therefore exchange rates should float is due to
Mundell (1963) and Fleming (1962) findings. The incompatibility of free capital
mobility, fixed exchange rates and independent monetary policy was proven, even
though criticism to the whole theory not working with stock variables existed.
This theoretical background, that
brought attention to government policies, led to a new field of research in the
1970’s, where Frenkel (1976), Bilson (1978) and Dornbusch (1976) took
prominence. This was the monetary approach to exchange rate determination, and
can be divided into the flexible price models, where the first two economists
were responsible, and the sticky price models derived by the latter. Although
only able to partially explain (and sometimes not even that) exchange rates
movements, these were an important counterweight to the equally incomplete
balance of payments flows method. They can be differentiated by the assumption
in flexible price models that PPP holds for every period, allowing prices to
change instantaneously. Frenkel (1976) and Bilson (1978) arrive to exchange
rates influenced by money supply, real income and expectations. A more
controversial finding is that rising interest rates differentials cause currency
depreciation, contrary to the popular (but not completely verified) belief that
high interest rates should attract capital inflows and cause exchange rates to
appreciate. This is explained by differences in inflation expectations. A rise
in the domestic interest rate is viewed as higher expected future inflation and
adjustment in prices will lead to a less valued exchange rate.
Dornbusch (1976) also found
interesting results after relaxing the assumption that PPP holds in the short
term. Price adjustments occur in a slower pace in the goods markets than in the
assets market, leading to an initial overshoot of exchange rates when monetary
policy changes. In that sense, the sticky price model can relate to
MundellFleming’s when it comes to a domestic currency appreciating after an
increase in domestic interest rates.
All different monetary models of
exchange rate determination, however, have been tested throughout the years
with rather disappointing results. Some particular studies have found that exchange
rates are cointegrated with monetary fundamentals, meaning there’s a long term
relationship between them. It can be said, though, that most use insufficiently
long time series datasets for statistical inference and sometimes even consider
data from periods with a fixed exchange rate regime or other misspecifications.
Robust empirical evidence of this theory is scarce.
2.2 Real interest rates differentials models
From the monetary approach of
exchange rate determination derived the very popular method of modelling real
exchange rates with real interest rate differentials. This method uses the
concept of uncovered interest rate parity (UIP), where in a riskneutral
environment real interest rates should converge to equilibrium where no
arbitrage gains can be made. Persistent changes in real interest rates
differentials are seen as of great influence in real exchange rate
determination, although robust empirical evidence is again a big challenge.
Using Rosenberg (1996) notations, we
can algebraically demonstrate UIP’s intuition in a very simple way. Domestic
assets returns (i) must equal foreign assets returns (i*) adjusted by expected
changes in nominal exchange rates (_{}), or i = i* + _{}. Assuming that
the parity is valid for n periods or maturities (short and long run) and
rearranging, we will arrive at _{}. This can be
expressed in real terms:
Where _{} is the expected change in the real exchange
rate for _{} periods, and _{} is the real interest rate differential.
Working with a risk premium Ø, we can evolve to the covered interest rate
parity equation (CIP):
Note that rational expectations and
perfect capital mobility are basic assumptions in this line of thought, perhaps
partially explaining why it is so hard for it to be empirically proven.
Given this theoretical framework,
many studies in the past two decades have tried to model and forecast real
exchange rate behaviours. Mixed results have been obtained at best, with a
considerable improvement for long term horizons, due to many different data and
specification problems. A common problem and perhaps the most serious one are
well described by McCallum (1994b). His main explanation for the UIP failure in
the short run is that it does not consider a system of equations. In other
words, modelling real exchange rates through uncovered interest rate parity
ignores a simultaneity bias that is clear from all agents and central banks
actions. A policy reaction function is
developed, and other economists like Christensen (2000) made use of that more
recently, although with equally unsatisfactory results even for the long term.
Since it considers a central bank reaction to deviations of inflation target, a
newer dataset that would include emerging countries (who adopted inflation
targeting just more recently) and a larger sample for developed economies could
probably help.
Meredith and Chinn (1998) follow a
similar line of work and extend McCallum’s macroeconomic model, using data from
G7 countries. They recognize its “intrinsic dynamics” and attribute to the
failure of UIP, especially in the short run, timevarying risk premia and expectation
errors. Only in longer horizons, when shocks to premia tend to fade,
fundamentals appear to relate to interest and exchange rates. This relationship
between risk premia and exchange rates will be explored in the empirical part
of this paper.
Another paper with a good insight
for the empirical part of this study is Edison and Pauls (1991). As they try to
relate real exchange rates to real interest rate differentials, dynamic models
(something that will be seen in other papers) slightly improve results after a
series of test failures. Both nominal and real variables are found to be
nonstationary and not cointegrated, something that is quite common in the
literature and as we will see occurs with our dataset. The problem is that not
even 100 observations are used by the authors, putting results under doubt.
With more observations and using
data for a larger array of countries, MacDonald and Nagayasu (2000) also found
nonstationary for both exchange rates and interest rates, along with very weak
cointegration results for individual countries. When panel cointegration
tests were made, however, strong evidence of a longrun relationship between
fundamentals is seen. This is used as an argument for how deficiency of
structural models may come from estimation methods rather than the data itself.
Also of interest for the empirical
part of this paper is a short study about evidences of UIP working in the case
of Brazil. Ferreira (2008) uses exchange rate expectations data and an
Instrumental Variables (IV) model to try and reduce the negative simultaneity
bias occurring in uncovered interest rate parity. Several misspecification and
robustness problems can be drawn from the apparently acceptable results. First,
using the Brazilian target interest rate with a US 3month treasury bill is not
ideal. Short term market rates could have been used for Brazil, or maybe longer
maturity US bonds could have been used. Other problem arises from not including
control variables in the model. It is known that the Real (BRL) fluctuation in
the last decade was affected by some exogenous shocks that could have been
controlled by including dummy variables or risk premium, for example. In the
end, the biggest issue is that results look ok but no robustness checks are
made. There are no tests for stationary or cointegration and these issues are
not even mentioned, maybe because of the small sample used.
2.3 Seminal papers: Meese and Rogoff 1983/1988
Considering all questions discussed
above, and without doubt being the best critique to fundamental exchange rate
models made so far, there is a classic paper by Meese and Rogoff (1983) that
shall be looked into more carefully. Many insights can be drawn from this very
controversial study that shows random walk as a better exchange rates
forecasting tool than many structural models.
The authors’ idea is to compare out
of sample root mean square forecast errors of different modelling
strategies. Side by side there is a
FrenkelBilson flexible price monetary model, a DornbuschFrankel sticky price
variation and a current account augmented HooperMorton model. These structural
models are compared to a random walk model, forward exchange rates and univariate
and vector auto regressions (VAR). Statistics are calculated for the
dollar/pound, dollar/mark, dollar/yen and trade weighted dollar relations,
during the floating exchange rate period of the 1970’s. Ordinary least squares
(OLS), general least squares and Fair’s (1970) instrumental variables
techniques are used. A general specification for the structural models can be
defined as:
Where _{} is the real exchange rate logarithm, _{} is money supply ratio logarithm, _{} is the log of real income differential, _{} is shortterm interest rates differential and _{} the expected longrun inflation differential.
TB stands for trade balance and u is the disturbance term. Depending on the
theoretical background constraints are added up, but all cases look up for _{}.
As already mentioned in this
literature review, the monetary approach for exchange rates determination
(including interest rate differential models) might suffer from endogeneity of
explanatory variables. This is also indicated by Meese and Rogoff, and not just
briefly. The VAR specification, where variables are not treated as exogenous a priori, yield results that support
endogeneity possibilities. Even so, explanatory variables are said to be
legitimate regressors in OLS and GLS, with endogeneity not precluding
consistent estimation of structural parameters. In any case, instrumental
variables (IV) technique can be used (and in fact it was) if the error term
follows an autoregressive process. In the end, however, results from GLS where
not worse than IV estimations.
Finally, root mean square errors
(RMSE) were taken from one month, six months and twelve months horizon
forecasts. Results from the random walk model were not inferior to all other
six specifications, being significantly better than them in longer horizons. It
is particularly intriguing that models with fundamentals were not able to
improve random walk out of sample forecasts even so they were based on realized
values of all explanatory variables. Between the three structural models, none
could be defined as superior. Estimations in first difference did not help.
Regarding the inability of forward exchange rates to beat random walk, the
existence of a risk premium is once again brought up. Again, this will be
treated in the empirical part of this paper, given Brazil’s unstable past.
Still, strong assumptions like market efficiency and rational expectations are
also to blame.
In sum, Meese and Rogoff establish
many reasons for unsatisfactory results with structural models, mainly
simultaneity bias, sampling error and misspecifications, although none could
fully explain poor results. It is obvious, however, that the period considered
for this study was not ideal, given all structural shocks. Also, expectations
variables, still today notably difficult to model, were even less trustworthy
back then. Nevertheless, the excellent structure and questions generated by the
paper make it very important for exchange rate modelling studies still today,
being a benchmark for almost all interesting works in the past two decades.
Meese and Rogoff (1988) is an
extension of their previous work, with a larger dataset that allows for unit root
and cointegration tests. As seen in most papers, real exchange rates and real
interest rates are defined as nonstationary and there is no strong evidence of
a stationary linear combination of the two (no cointegration). Authors realize
that reasons for nonstationary are different between variables and suggest
that there is an omitted variable in the relationship. Note, however, that
although sample size is sufficient for these tests, the ones employed
(DickeyFuller and EngleGranger) can be considered outdated, with stronger
versions available nowadays. Even so, more recent papers with modern tests
(including this one) fail to find different results.
Rerunning regressions, now with an
extra technique, the generalized method of moments (GMM), the random walk model
continued to be unbeatable when considering root mean square errors. An
improvement from other studies is that the theoretically anticipated sign of
the coefficients can be seen. Failure to produce better results falls again on
real structural shocks, with some consideration of speculative bubbles getting
in the way.
A more recent extension of Meese and
Rogoff’s classic paper of the early 1980’s is Cheung, Chinn and Pascual (2003),
where exchange rate models of the nineties are put into proof by similar
criteria. Main differences are the inclusion of a productivity differentials
model and a composite specification,
along with estimations in firstdifference and error correction specification.
Forecasting horizons are also distinct, with one, four and 20 quarters ahead.
Even with these changes and a very long dataset, results are not much different
from past ones. No structural model outperformed random walk using mean square
error as criteria, and direction of change depended on the model/specification/currency
bundle. This is actually a useful result, since it shows that what might work
in one period, or for one currency, might not work for a different structure.
From this author point of view, it is an argument against the improved results
of panel data specifications. The idea of a unique real exchange rate
determination model for every country/period combination sounds
misleading.
2.4 Commodity currencies: introducing a new fundamental
Another fundamental that can be
included in exchange rate determination models, but only in specific cases, are
commodity prices. Differently from terms of trade, that can be defined to any
country and have been extensively studied as a part of exchange rate models,
commodity prices can only influence countries reasonably dependent on commodity
exports and is a factor that is not often included in exchange rate studies. In
fact, most empirical studies are only about developed commodity exporters such
as Australia, Canada and New Zealand, leaving the relationship between
commodity prices and exchange rate in developing countries to be explored. The
interesting idea behind choosing commodity prices instead of terms of trade is
that these prices are most of the times completely defined internationally, not
reflecting any domestic fundamental. In that sense, their changes might
represent real shocks, something that has been showed as not captured by
traditional models.
A wellstructured paper on this
topic is Chen and Rogoff (2002), where they analyse if the three countries
cited above have socalled commodity currencies. They all fit in the
welldeveloped, small open economy criteria for a good empirical work, with
globally integrated financial markets and floating exchange rate regimes.
Australia and New Zealand are highly dependent on commodity exports, while
Canada has a more diversified trade pattern but still holding large amounts of
metals, wood and oil exports. Given that background, authors use variations of
this simple linear trend regression of real exchange rates to real commodity
prices indexes weighted by the export pattern of each country:
They use the nonparametric GMM
NeweyWest approach to correct for the biased standard errors estimates, and
manipulate the equation above with a HodrickPrescott filter and an AR(1)
process for the residuals. This last inclusion brings DurbinWatson statistics
towards 2 and therefore end the significant positive serial correlation
observed before. Coefficients have consistent estimates, but they are
significant only for Australia and New Zealand.
A problem with these results is the
assumption of stationary for all variables, since tests for unit roots cannot
be taken with such small samples (fewer than 100 observations). As we have
seen, there is vast empirical evidence of exchange rates being nonstationary,
and although authors don’t recognize this, a dynamic OLS model to estimate cointegrating
relations is designed, also with positive yet likely misleading results. Again,
a small sample is the obstacle for cointegration tests, and a model in
firstdifference is developed to account for nonstationary and noncointegration.
Coefficients are then significant and with the correct expected sign (as seen
in other specifications), suggesting with greater robustness that changes in
real commodity prices have great impact on real exchange rates. Commodity
prices are considered a good alternative for the missing shocks seen on other
structural models.
Main criticism can be made on the
assumptions of stationary and cointegration, since there is major evidence
otherwise. Most results can be invalid, and interpretations would not be that
strong. It is not explained why samples used were so small, given the
availability of extended monthly datasets. Also, periods with structural breaks
were considered and the Hansen test used to account for that, which relies on
asymptotic properties, is not valid.
Still, the paper is very comprehensive, since it considers endogeneity
problems (and uses a GMM IV specification to account for that), measures the
persistence of shocks, and tries productivity differentials as one influence
over real exchange rates (yet with less explanatory power than commodity
prices). The simple approach to the relationship between real exchange rates
and real commodity prices will be followed for the case of Brazil in the
empirical part of this paper, with greater attention to stationary and cointegration
features.
First, however, it is also
interesting to look at evidences for developing countries. Cashin, Céspedes and
Sahay (2003) used data from 58 different commodity dependent countries to
establish a long run relationship from their base materials exports prices and
real exchange rates. Authors had a large data set (from 1980 to 2002) and use
GregoryHansen cointegration test to allow for structural shifts, since
working with unstable developing economies. One third of all countries analysed
seem to have cointegrated real exchange rates and real commodity prices, with
statistically significant estimates for the real commodity prices elasticity of
real exchange rates. Good improvements from previous works are the indication
from weak exogeneity tests of real exchange rate adjustment to longrun
equilibrium, and extremely fast halflives of adjustment (only ten months).
Criticism can be made to the dataset used, which included very underdeveloped
countries, with illiquid, fixed or pegged exchange rates. Also, no control
variables or dummies to account for macroeconomic instabilities were included,
what could have improved results.
3. DATA
DESCRIPTION AND GRAPHICAL EVIDENCE
A major concern in this paper was to
work with data from reliable sources and for a period without greater
disturbances, knowing the unstable past of Brazil’s macroeconomic environment.
Therefore, only observations from March 1999 to June 2010 were collected, as in
order to minimize excessive volatility or structural breaks in the series.
Using older information would cause disruptions, since Brazil only adopted a
free floating exchange rate regime and an informally independent, inflation
targeting monetary policy, in the beginning of 1999. Before that, and
especially before the Real was adopted in 1994, the country would suffer from
chronic hyperinflation, frequent currency crisis, capital flights and other
severe economic imbalances, turning the development of appropriate econometric
specifications a true nightmare.
Also, it was seen as crucial for the
success of following econometric procedures to have large enough samples, so
tests that have asymptotic properties could have valid results. In that sense,
both monthly and weekly datasets were constructed, the latter having an
excellent size of 584 observations. Both datasets used the exact same time
series, except for Brazil’s inflation (P), where the main index was only
available on a monthly basis. The seasonally adjusted IPCA (national consumer
price index), calculated since 1979 by IBGE (Brazilian Official Geography and
Statistics Institute) with surveys on the 11 greater metropolitan areas in the
country, was used for monthly
regressions. For weekly models, the chosen index was the IPC calculated by an
economics research private institute, FIPE, since 1973. It uses surveys taken
in São Paulo, Brazil’s largest metropolitan area, and compare moving average
prices seen in the last four weeks with a period before that, always weekly
updated. They both have high correlation and come from equally renowned
institutes.
Note
that a private weekly inflation measure is even older than the official survey,
a heritage of many years of rampant inflation and lack of statistical scrutiny
in government offices. Although prices are well controlled in Brazil for almost
two decades now, many other indexes are still calculated by different
institutes. The two indexes are used in this paper to deflate exchange rate and
international commodity prices series.
For the same purpose, the seasonally
adjusted urban all items consumer price index (CPIU) calculated by the United
States Department of Labour’s Bureau of Labour Statistics was used. This
measure of inflation is produced only monthly, inducing us to use a cubic
spline interpolation^{[1]} method to
arrive at weekly data. It was taken as foreign inflation (P*) since only the
relationship between the Brazilian Real and the US dollar is considered.
That takes us to the nominal
exchange rate (E) used in this study, accounted by the Brazilian Central Bank;
the commercial mid spot rate of Brazilian Real per US dollar (R$/US$). Data was
gathered through Bloomberg. To turn it into the real exchange rate (RER) used
in regressions, basic purchasing power parity (PPP) theory led to the formula _{}. Also through
Bloomberg, JP Morgan’s Emerging Market Bond Index (EMBI) for Brazil was
collected to participate as a control variable. It considers the spreads
between Brazilian foreign debt bonds and a theoretically riskless US Treasury
bond, working as a measure of risk premium. As in every series used in this
paper, index base date was March 1999 = 100. It can be seen in figure 1 how the
EMBI captures some abrupt moves from real exchange rate, especially during the
unstable electoral period of 2002/03, when left wing presidential candidate,
Luis Inácio Lula da Silva, was about to win his first mandate. Risk premium rose
to unprecedented levels in a few months, just to fall back after fears of an
extreme change in the country’s orthodox economic policies didn’t materialize.
Figure 1. Real/US
dollar exchange rate. March 1999 to June 2010
Finally,
a commodity prices index suitable for Brazil’s pattern of trade had to be
created. It required prices from different trade boards in the world, always
aiming for the most liquid spot or future commodity contracts traded. Also,
weights used reflected the average participation of each commodity on all
Brazilian base materials exports during the period between March 1999 and June
2010. In the end, almost 95% of all commodity exports were counted, and the
index composition can be summarized as in Table 1. Exports of Petroleum and its
products were not considered (as in other significant studies), given their
outstanding price volatility. Anyhow, oil has only been significant for
Brazilian exports more recently, when large deep water reserves were
discovered. In fact, Brazil used to be a petroleum and fuels small net importer
for many years.
Table 1.
Composition of Nonfuels Commodity Price Index
March 1999 – June
2010 

Product 
Weight 
Source 
Iron Ore 
19,3% 
SFCJ 
Soybeans 
14,8% 
CBOT 
Sugar 
10,8% 
NYMEX 
Soybean Meal 
8,7% 
CBOT 
Poultry 
8,0% 
IMF 
Coffee 
7,2% 
NYMEX 
Cattle Feeder 
7,0% 
CME 
Hardwood Pulp 
6,7% 
IMF 
Orange Juice 
4,4% 
NYMEX 
Aluminium 
3,5% 
LME 
Soybean Oil 
3,3% 
CBOT 
Lean Hog 
2,1% 
CME 
Ethanol 
1,7% 
CEPEA 
Corn 
1,6% 
CBOT 
Cotton 
0,8% 
NYMEX 
Note: SFCJ (Sinterfeed Carajás), CBOT (Chicago Board of Trade), NYMEX (New
York Mercantile Exchange), IMF (International Monetary Fund), CME (Chicago
Mercantile Exchange), LME (London Metals Exchange), CEPEA (Centro de Estudos
Avançados em Economia Aplicada). World Market Prices (USD)
It is
also interesting to see that base materials excluding fuels responded for
roughly 40% of Brazilian exports between 1999 and 2008 on average, according to
data from the World Trade Organization (WTO). It is not nearly as much as in
other Latin American countries, but it is twice as much as in Canada and around
what Australia exports, as exemplified on figure 2. That shows how Brazil’s
trade pattern is diversified, yet dependent on commodity prices in some level.
We should expect then results for Brazil comparable to Chen and Rogoff’s
findings for Australia.
Figure 2. Base
Materials Exports excluding Fuels (% of total, 2008). Selected Countries
It is
graphically evident in figure 3, however, that Brazil has its own special
features that add volatility to the real exchange rate, so that we needed more
information than only commodity prices (as Chen and Rogoff used for Australian
regressions) to explain currency movements. As said before, the country has a
quite unstable past, and control variables are needed. A dummy variable, for
example, was used to try and capture 2002/03 pre electoral swings, but with
much less success than risk premium as it will be described later in this
paper.
Figure 3.
Real/US dollar exchange rate, Real Commodity Price Index, March 1999 to June
2010
4. Empirical Analysis
As described before, the idea behind
this paper and its econometric procedures is not to validate (or not validate)
any kind of theoretical approach to exchange rates determination, nor it is to
present the most efficient model in forecasting Brazil’s Real movements. It is
simply to determine whether or not commodity prices influence the Brazilian
currency, and perhaps measure the size of its impact. A starting point was the
simplest model defined by Chen and Rogoff:
Before evolving from that, however,
important steps had to be taken for results not to be misinterpreted. First of
all, with a large enough sample of 584 observations, Augmented DickeyFuller
(ADP) and PhillipsPerron (PP) unit root tests were ran, producing similar
results that pointed to nonstationary of both the log of Real/US dollar real
exchange rate and the log of the real commodity price index calculated for
Brazil. Insignificant differences between tests were already expected, since
the dataset was constructed in order not to have structural breaks, something
that could have been captured by the more complex PP test.
Large sample testing confirmed
results obtained using monthly data that reduced the number of observations to
136. Table 2 summarizes these results; there are in line
with previous findings for different exchange rates. Note that with the smaller
sample, tstatistics tended to be more negative and closer to critical values.
Even so, results were far from leading us to wrongly reject the null hypothesis
of a unit root.
Table 2.
Augmented DickeyFuller and PhillipsPerron unit root tests, in levels with
intercept and trend
Levels 
In (Real Exchange Rate) 
In (Real Commodity Prices) 
In (EMBI) 

tStat (ADF) 
 1.8225 
 2.0659 
 2.3782 
 2.5173 
 2.0923 
 2.0738 
Adj. tStat (PP) 
 1.8605 
 2.2093 
 2.3758 
 2.6223 
 2.0328 
 2.2238 
Coefficient 
 0.0091 
 0.0493 
 0.0184 
 0.0869 
 0.0152 
 0.0648 
Std. Error 
[0.0050] 
[0.0238] 
[0.0077] 
[0.0345] 
[0.0073] 
[0.0312] 
Observations 
584 
136 
584 
136 
584 
136 
Note: Critical values for the weekly data are 3.9738,
3.4175 and 3.1311 for 1, 5 and 10 percent (%) levels of significance. For
monthly data, critical values are 4.0279, 3.4437 and 3.1466 for 1, 5 and 10
percent (%) levels of significance.
Many
possible I(0)/deterministic trends specifications become automatically invalid
after results like the ones above, including ones with detrending methods or
autoregressive process for the residuals that were used in other papers to
correct for clear serial autocorrelation. Just as an exercise, however, a model
with linear trend and AR(1) process for the residuals was taken into account,
with apparently reasonable, yet clearly deceiving, results. At this point,
including the log of the risk premium variable, which is also nonstationary
(look at Table B for results), did bring some improvements for coefficients and
parameters, yet not changing the validity of results. Results for these
specifications are then not reported.
Given all that, the next step is to
run cointegration tests that can say whether or not stationary linear
combinations between variables, and therefore long term relationships between
them, exist. This is made easier since all three variables are integrated of
the same order (order one or I(1)), as seen after unit root tests in first
differences (Table 3).
Table 3.
Augmented DickeyFuller and PhillipsPerron unit root tests, in first
differences with intercept
Levels 
In (Real Exchange Rate) 
In (Real Commodity Prices) 
In (EMBI) 

tStat (ADF) 
 26.1974 
 6.5058 
 23.7237 
 10.6576 
 25.6931 
 11.166 
Adj. tStat (PP) 
 26.1261 
 11.6189 
 23.7215 
10.6576 
 25.6897 
 11.166 
Coefficient 
 1.0834 
 1.0031 
 0.9851 
 0.9295 
 1.0627 
 0.9886 
Std. Error 
[0.0413] 
[0.0869] 
[0.0415] 
[0.0872] 
[0.0413] 
[0.0867] 
Observations 
584 
136 
584 
136 
584 
136 
Note: Critical values for the weekly data are 3.4413,
2.8662 and 2.5693 for 1, 5 and 10 percent (%) levels of significance. For
monthly data, critical values are 3.4800, 2.8832 and 2.5784 for 1, 5 and 10
percent (%) levels of significance.
Johansen’s test is the most
convenient and uptodate tool, and results are found to be negative for cointegration
between real exchange rate and real commodity prices in many specifications.
Allowing for a linear deterministic trend and including an intercept, a long
term relationship between these two variables was only found with more than 72
lags for weekly data and 24 lags for monthly data, and considering a 10% confidence
level. Both trace and maximum eigenvalue tests pointed for the same result
using monthly observations and only trace test suggested cointegration for
weekly data, results that cannot be considered as anywhere near robust.
A large number of lags can be used in financial markets high frequency
variables modelling, but this is not the exact case. The inclusion of the risk
premium did not help the results for the group. In fact, it was even trickier
to find anything near cointegration when all three variables were considered.
Results for the cointegration tests with only the two basic variables and
weekly observations can be summarized as in Table 4.
Table 4.
Johansen’s Cointegration test, linear deterministic trend, Intercept and 72 lags

Trace 
MaxEigenvalue 
Statistic 
14.1597 
11.8672 
Critical Value (0.1) 
13.4287 
12.2965 
Prob 
0.0787 
0.1157 
Observations 
511 after adjustments 


In
(Real Exchange Rate) 
In
(Real Commodity Prices) 
Normalized Coint. Coefficients 
1.000 
1.1122 
Std. Error 
 
[0.1599] 
tStat 
 
6.9555 

D[In
(Real Exchange Rate)] 
D[In(Real
Commodity Prices] 
Adjustment Coefficients 
 0.0303 
 0.0015 
Std. Error 
[0.0106] 
[0.0090] 
tStat 

2.8584 

0.1666 
If these results were to be considered, interpretation would be that a
1% change in real prices of Brazilian exported commodities cause a 1,11% impact
in the Real/US dollar real exchange rate in the long term. The theoretical
relationship between variables is negative (higher commodity prices lower the
exchange rate), so the positive sign of the normalized coefficient is as
expected, since it is always the inverse of the actual coefficient (β).
Adjustment coefficients (alphas) give us the short term corrections, and the
negative and more statistically significant one shows the most endogenous
variable. In this example, real exchange rates have a greater contribution in
reducing short term deviations from long run equilibrium, as seen by the tStat
closer to the MacKinnonHaugMichelis (1999) pvalues. Again, this would be a
result theoretically anticipated.
The biggest problem is that the
specification used for these tests are completely relaxed, and results are not
robust enough to produce strong evidence of cointegration between the real
exchange rate and commodity prices. Even so, a vector error correction model
(VECM) was produced with incredibly long and confusing (probably misleading)
results. Since there is great doubt about the cointegrating relation between
variables, these modelling results are not reported.
Interesting enough, yet not
surprisingly, is the fact that the real exchange rate proved to have a long run
relationship with the risk premium variable. Cointegration tests for only
these two variables were positive (both trace and maximumeigenvalue), allowing
a linear deterministic trend, intercept and only 2 lags (with standard 5%
confidence interval).
During the whole period considered in this paper (a quite volatile one
we must say), it is clear that the Brazilian currency followed most of the
movements in the measure of risk. Perhaps disregarding the preelectoral period
of 2002/2003 would worsen these results. Anyway, results of the cointegration
tests between the real exchange rate and Brazilian EMBI are demonstrated in
Table 5.
Note
the normalized cointegrating coefficient with the correct negative sign, which
is the inverse of the actual β that shows risk premium and exchange rate’s
theoretical direct relationship. Also, the real exchange rate is again the more
endogenous variable, adjusting in the short run. The traditional specification
with few lags and robust results attest the variables long term interdependence
(yet normality of the residuals could not be verified). This would lead us to
develop a vector error correction model (VECM), but that would not be within
this paper’s scope. Our goal continues to be testing for the commodity currency
profile of the Brazilian Real. Unfavourable results seen earlier, however,
direct us to a last resource modelling specification.
Table 5.
Johansen’s Cointegration test, linear deterministic trend, intercept and 2
lags

Trace 
MaxEigenvalue 
Statistic 
18.5079 
14.9883 
Critical Value (0.05) 
15.4947 
14.2646 
Prob 
0.0170 
0.0384 
Observations 
581 after adjustments 


In
(Real Exchange Rate) 
In
(Real Commodity Prices) 
Normalized Coint. Coefficients 
1.000 
 0.6258 
Std. Error 
 
[0.1009] 
tStat 
 

6.2021 

D[In
(Real Exchange Rate)] 
D[In(Real
Commodity Prices] 
Adjustment Coefficients 
 0.0088 
 0.006 
Std. Error 
[0.0036] 
[0.0109] 
tStat 

2.4444 

0.5504 
Following common procedure when
variables are found to be nonstationary and not cointegrated, a model in
first difference that avoids spurious regressions was developed. Only variables
used so far were included, but all possible influences in exchange rates
discussed in Section 2, especially interest rate differentials, could have
taken part in the experiment. The basic first difference regression augmented
by the risk premium measure can be written as:
Both explanatory variables have
statistically significant coefficients at the 5% confidence level, with _{}being almost
twice as large as _{}. This is in
line with cointegration tests results that pointed to a closer relationship
between the real exchange rate and risk premium. Also, including lags for the
EMBI (t3, t4) slightly improved some coefficients, while no commodity prices
lag proved to be statistically significant. Similarly beneficial was to include
a dummy variable for “stress periods”, namely when real exchange rate varied
more than 10% in one week. That occurred three times. Once right before
Brazilian elections, in September 2002, and also on the first two weeks of
October 2008, in the beginning of the most recent financial markets crash and
consequent credit crunch with persistent recession in developed countries.
Results for the base first difference model and improved variations can
be seen in Table 6. Regressing the real exchange rate against solely the real
commodity prices index resulted in larger and statistically significant coefficient,
but with an extremely low explanatory power (adjusted R^{2}). All
coefficient signs are correct and as expected for every specification.
Table 6.
Dependent Variable: Log of R$/US$ Real Exchange Rate Sample. Period: March 1999 – June 2010

I(1) / NonCointegration 

Basic 1^{st}
differencing 
Augmented 1^{st }differencing 
Augmented 1^{st }differencing
with lags 
1^{st }differencing
with dummy 

In(Real Commodity Prices) 
 0.2048 [0.0510] 
 0.1279 [0.0379] 
 0.1305 [0.0379] 
 0.1107 [0.0367] 
In(EMBI) 
  
0.2195 [0.0100] 
0.2214 [0.0100] 
0.2145 [0.0097] 
In(EMBI)_{t3} 
  
  
0.0210 [0.0100] 
  
In(EMBI)_{t4} 
  
  
0.0236 [0.0101] 
  
Dummy 
  
  
  
0.0541 [0.0080] 
DurbinWatson Stat 
2.1843 
2.1290 
2.1424 
2.1176 
Adj. R^{2} 
0.0253 
0.4645 
0.4699 
0.5046 
Observations 
583 
583 
579 
583 
Note: Standard Errors in parentheses.
It is clear from results that real
commodity prices fluctuations then have a quite not negligible influence over
real exchange rates, although overshadowed by the larger impact of the EMBI
when this variable is considered. Loglinear models in first differences denote
elasticity in their coefficients and in the augmented one with lags, total real
exchange rate elasticity to the risk premium is more than double the one to
real commodity prices.
The main question that arises from
these regressions is the validity of including a cointegrating variable (EMBI)
in the first differencing specifications. In Chen and Rogoff (2002) this
approach is considered not appropriate if a long term relation between
variables is observed, but there are no further explanations on the subject.
Also, there is no third (not cointegrating) variable in their models, which
makes things substantially different. Theoretical proof of this affirmation
could not be found by this author, nor could similar analysis could be found in
the literature review. However, perhaps it is wiser to consider the
specifications that included the risk premium variable very carefully,
especially when gauging forecasting performance on Section 5.
5. Forecasting properties
Following the results presented in
the last section, we advance to a simple comparison of outofsample
forecasting performance of main specifications. As in Meese and Rogoff (1983),
the idea is to measure the root mean square forecast errors of fundamental
models (in this case with commodity prices) and compare to a random walk (in
this case with a trend) error. They were calculated according to the authors
cited formulation:
Where
k are the forecast horizons, s the modelling choice, F(t) the forecast value,
A(t) the actual value already known and _{} the total number of forecasts in the
projection period. Basic real exchange rate versus real commodity prices
regression and the one including the risk premium variable were chosen, and
four different forecasting horizons (1 month, 6 months, 12 months and 5 years)
were selected to measure how models behave in the long run. Results in Table 7
show a good performance of the pure commodity prices specification in the short
run, which fades away over time. Random walk predictions are better only in the
longer horizon, contradicting Meese and Rogoff findings of predominance of the
random walk for every term. Modelling with the risk premium variable give us
low and balanced root mean square errors. Note that all outofsample forecasts
use actual values of explanatory variables.
Table 7. Root
mean square forescat errors*
Horizon 
Random Walk (with a Trend) 
Basic 1^{st}
differencing 
Augmented 1^{st }differencing
with lags 
1 month 
3.69 
2.98 
3.06 
6 month 
2.98 
2.93 
2.16 
12 months 
10.64 
16.92 
6.02 
5 years 
9.27 
13.71 
13.02 
Note: *Approximately in percentage terms
These
interest findings show how the Brazilian exchange rate cannot be easily
modelled, and all results undoubtfully suffer from omitted variables problems.
This could have been corrected with an extended research and perhaps the use of
monthly data only (not every possible variable is available in weekly terms).
6. Conclusion
It is clear from the diversity of
exchange rate determination models developed through the years that
establishing what variables or fundamentals influence currencies valuations is
not an easy task. This is especially true when dealing with developing
economies such as Brazil. In this paper we were able to at least determine some
important features for the Real/US dollar exchange rate, which kept us away
from extremely misleading econometric results.
As described in other papers for
different currencies and other related variables, the Brazilian real exchange
rate and real commodity prices were found to be nonstationary. Also, no strong
signs of cointegration between these variables could be seen after many tests
specifications. A long term relationship with a risk premium variable, however,
was easily spotted. These mixed results led us to different modelling
approaches, which produced interesting yet not quite as expected results.
An array of basic first difference
models was best considered, trying to avoid any severe misspecification. Their
consistent results allow us to say that, in the case of Brazil, during the last
eleven years the real exchange rate elasticity to risk premium was more than
twice as large as the one to real commodity prices, although both variables had
reasonably large influences. Compared with a traditional random walk model,
forecasting performances of these models are strikingly good. Contrary to
classic findings, structural first difference models outperformed random walk
when considering root mean square forecast errors in some different horizons.
Random walk proved to be a better forecaster only in the longer period.
Many improvements can be made to all
specifications defined in this paper. There are clearly omitted variables that
could have produced better results, but due to either lack of time or
availability of data could not be used. Also, the question regarding the
validity of using a cointegrating variable on first differences models is left
open.
More research is necessary if one is
to accomplish the difficult task of defining the most efficient exchange rate
determination model for Brazil. From this work, however, it is possible to say
that commodity prices have a moderate influence on the country’s currency,
although characterizing the Real as a commodity currency might be extreme.
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