MODELING THE BRAZILIAN ETHANOL MARKET:
How flex-fuel vehicles are shaping the long run equilibrium
Hugo Pedro Boff (IE-UFRJ)
(*)
ABSTRACT
The paper models the Brazilian market of hydrated alcohol fuel (ethanol) and details the role of price rates
ethanol/sugar and ethanol/gasoline in the long run equilibrium. In the market balance, the transmission elasticities of
the ethanol price w.r.t. sugar and gasoline prices are positive and add 1. This condition favors the competitiveness of
ethanol vis à vis sugar (supply side) and gasoline (demand side). A cointegration analysis is then carried out to check
the adequacy of the model to describe the price behavior in the retail market of metropolitan areas of São Paulo and
Rio de Janeiro (2001:07 – 2010:03). The results obtained suggest the robustness of the price rate relationship.
Following the entry of flex-fuel vehicles into the Brazilian car market (2003 on), fuel demand switching between
ethanol and gasoline gave rise to a consistent movement of their price rate towards the fuel efficiency rate. As a
consequence, the estimated price transmission elasticity of ethanol with respect to gasoline (sugar), increases over
time towards 1 (decreases towards zero). So, the consolidation of an ethanol retail market independent of the sugar
market is now on the way, which is an important step towards the sugarcane industry restructuring. Finally, the
current ethanol price adjusts to meet its long run equilibrium level within a cycle period of about one year.
JEL codes: L11, L81, Q41, Q42.
Keywords: ethanol, gasoline, sugar, retail prices, market equilibrium, price-transmission elasticity, sugarcane.
I – INTRODUCTION
The depletion of natural resources inaugurated by the industrial revolution has progressively
increased the common perception that mineral sources of energy (mainly oil and gas) should be
replaced by other renewable sources such as hydropower, ethanol, biodiesel and biogas. In the
past two decades, that challenge appears even more appealing within the environmental context,
once having recourse to “clean” energy is view as the main action to fight the global warming
and to reduce the levels of air pollution.
In this scenario, the ethanol (= alcohol fuel) emerges as one of the most important economic
weapons because of the diversity of vegetables from which it can be obtained and, especially,
the high degree of substitution it has with respect to gasoline. There is even a prevailing view
that sooner or later, ethanol will convert into a commodity, and the more recent investment
plans to expand its production in Brazil, have been drawn under such perspective.
An historical overview
The Brazilian official experience of producing alcohol fuel from sugarcane starts in July 1931,
with the creation of the Commission for the Study of Alcohol Engine by the Government
Vargas. At that time, the government authorized fuel distributors to add 5% of anhydrous
alcohol per volume of gasoline. Besides, since the late of 1970s, a domestic market for hydrated
alcohol fuel has been developed to feed cars specially adapted for that use. That market enlarges
significantly in the 1980s, thanks to the high level of oil prices prevailing at that moment and to
the subsidies and tax credits granted by the government to improve alcohol production.
However, the ethanol market growth hampered progressively in the second half of 1980, as the
(*) Instituto de Economia.-Universidade Federal Rio de Janeiro (Brazil) Av.Pasteur 250 – Praia Vermelha.
[email protected] . The author is indebted to Eduardo Pontual Ribeiro (UFRJ/CADE) whose suggestions helped to
improve an early version of this paper, as well as to Maria da Graça Fonseca (IE-UFRJ), Getulio da Silveira (IEUFRJ) and the seminar participants at IPEA-Rio and IPEA-Brasilia. My thanks also go to Iraci Matos Vasconcellos
(IE-UFRJ), Edmar Almeida (IE-UFRJ), Raquel de Souza (COPPE-UFRJ), and to Heloisa Borges and Bruno Caselli
(ANP) who make available to me the ANP data.
gasoline price begin to fall and the government incentives are progressively eliminated.
Finally, the market growth stops completely when sugar prices start to rise in the world market,
once this product competes with alcohol in processing sugarcane. Frequent supply shortages in
the ethanol domestic market culminate in 1990 with the import of the product from abroad to
meet the domestic demand. A crisis of confidence is then installed among ethanol fuel
consumers’ and the internal market shrinks dramatically later on.
A decade later, in March 2003, Volkswagen pioneers the launch of a flex-fuel car model (Gol
Total Flex) capable to operate simultaneously with any mix of gasoline and alcohol fuel, which
makes hydrated alcohol and gasoline perfect substitute fuels one each other.
The superiority of the innovation which allows consumers to use benefit-cost calculus to guide
their fuel choice and the easy access to it (in the case of the Honda Civic, +2.5% of the vehicle
price in March 2007) rapidly stimulate the demand for mixed fuel cars.1 At the same time, the
innovation spreads quickly among carmakers, so that, by the end of 2009, 92% of cars supplied
in the domestic market were of flex-fuel type.
The main motivation
The resulting enlargement of the domestic trade and the world commodity prospect, stirred up
the interest of economists and academicians on the ethanol market. One important issue on
which the quantitative literature is still lacking, however, regards the price setting mechanism in
the long run equilibrium of the market.
At the moment, there is a growing perception of market players that price fluctuations and
predictability concerns are delaying many investment decisions in the Brazilian alcohol
industry, and thus, delaying also the market stabilization and the world trade prospect.
Among the suggestions aiming the stabilization goal, there is to set long-term contracts directly
between producers and distributors of ethanol. Widening the industry storage capacity is also a
perceived need. Downstream, the operation with ethanol forward contracts negotiated at the
BM&F, the Brazilian Mercantile and Futures Stock Exchange could also contribute to increase
their liquidity and hence to reduce the price volatility in the long run.
In the prospect, it would be useful to know how ethanol prices react to fluctuations of sugar and
gasoline prices in the short term and, more importantly, how the current price is linked to its
long run equilibrium path. Besides, it is instigating to see how the massive adoption of flex-fuel
cars by Brazilian consumers is actually shaping the ethanol market balances.
On the demand side, it is expected that the maximizing behavior of a growing number of new
consumers is driving the demand price rate alcohol/gasoline to the corresponding technical
efficiency rate of fuels. Given the present market distribution of car models in Brazil, it is
believed that ethanol fuel bring in about 60% to 70% of the motor power of gasoline.2 Thus, a
representative consumer which, in other respects, is indifferent between both fuels, chooses
ethanol if its price is below 0.6 to 0.7 times the price of gasoline. 3
1
According to the ANFAVEA-National Association of Automobile Manufacturers and Automotive Vehicles, the
aggregate stock of vehicles operating with ethanol fuel, once discounted by the annual scrapping rate, restart to grow
from early 2004.
2
According to MARJOTTA-MAISTRO(2008), the fuel efficiency rate ethanol/gasoline is 0.67 for the model
Volkswagen Gol 1.0 Total Flex.
3
It is believed that CO2 emissions caused by ethanol fuel are about 73% lower than those caused by gasoline.
Altruistic consumers that value a clean atmosphere may be willing to pay an overprice to consume ethanol.
2
On the supply side, ethanol competes with sugar in processing sugarcane. In Brazil, most
alcohol distilleries integrate with sugar factories in the same production plant. Thus, the
producers’ benchmark to setting the supply price of ethanol is the sugar price. If suppliers
equate markup over costs of both products, they would be willing to set prices in such a way
that the price rate alcohol/sugar equals the corresponding rate of mean costs of production.
In the equilibrium, demand and supply prices must be equal. The scale effects resulting from the
enlargement of the domestic market owing to the new flex-fuel cars suggest that the demand
forces are now invigorating and that the dynamics of ethanol prices is little by little determined
by gasoline prices. If this is true, then we should find that the supply of ethanol adjusts over
time to meet the demand and that the optimal price rate ethanol/gasoline is shaping the
equilibrium price of ethanol in the long run.
In order to address these and other related issues, the present paper builds a mathematical model
describing the market for hydrated alcohol fuel (ethanol). The structure of the model was taken
as simple as possible, in order to ease its economic interpretation and empirical verification.
Characterizing the Brazilian market and review of the literature
The model takes into account four characteristics of the Brazilian ethanol industry:
1. Alcohol and sugar compete among themselves in the use of the sugarcane juice, which is
the more productive input used in both manufactures.
2. The alcohol industry produces two main differentiated products: the hydrous alcohol fuel
for vehicles mono fuel or flex fuel, and the anhydrous alcohol, which is mixed to gasoline.
3. A risk-free internal market for anhydrous alcohol is created through a mandatory product
mixture to gasoline fuel, imposed by the National Energy Agency (ANP). From July 2007 on, a
mix of ¼ anhydrous per volume of gasoline is adopted.
4. A continuous demand for hydrate alcohol was created in late 1970s for ethanol fuelled
vehicles and, after 2003, for new flex-fuel vehicles. Nowadays, ethanol and gasoline became
perfect substitute fuels for a growing number of consumers.
The Brazilian alcohol distilleries are mostly integrated with sugar mills,4 so that a large number
of producers can switch the supply of alcohol to sugar and vice-versa, according to the expected
changes in their relative prices.5
The first of these characteristics suggests that the supply of ethanol can be expressed as an
increasing function of the ethanol/sugar price ratio. In Appendix (I) it is shown that such
relationship can emerge when producers choose the mix of production that maximizes profits in
the alcohol and sugar production separately, given the technology and the input and product
prices. Alternatively, a supply of alcohol as a function of relative prices can also be obtained
when suppliers choose the production mix that equate the markup ratios profit/costs of both
products.6
4
According to the Department of Agriculture of the Brazilian Government, there was 408 plants operating in the
country until August 2008. Out of them, 254 (62%) were integrated plants, 139 (34%) only alcohol distilleries and 15
(4%) only sugar factories.
5
ELOBEID and TOKGOZ (2006) refer that, switches are limited to 60% of the production level in the two
directions.
6
The importance of the relative prices in determining the supply level of ethanol is recognized in the literature. See
DIAS et al. (2002) and, for econometric estimations, MARJOTTA-MAISTRO and BARROS (2002), OLIVEIRA et
alii (2008), KOIZUMI (2003) and ELOBEID and TOKGOZ (2006). In the latter reference, the authors model the
3
The second and the third characteristics make the demand for anhydrous alcohol proportional to
the consumption of gasoline. Indeed, if A and G stand for the consumption of anhydrous and
gasoline, respectively, and c is the mandatory mixture rate, we have: A = cG/(1-c). 7
The present model only deals with the hydrated alcohol fuel market. By excluding from the
analysis the supply and demand of anhydrous alcohol, we avoid to model gasoline. In the last
two years, hydrate alcohol represents more than 50% of total production. 8
The fourth characteristic of the Brazilian market suggests that the demand for hydrate fuel may
be written as a decreasing function of the alcohol/gasoline price ratio. Such relation is obtained
by assuming a representative consumer getting a continuous, strictly increasing and strictly
quasi concave utility in the consumption of ethanol and gasoline. Given the prices and income,
he chooses the mix of fuels that maximizes utility. The implied Marshallian demand functions
are homogeneous of degree zero in prices and nominal income. So, the demand for ethanol
becomes a function of the alcohol/gasoline price ratio and the nominal income deflated by the
price of gasoline.
OLIVEIRA et al. (2008) regressed supply and demand quantities of alcohol and gasoline on
their price levels and other control variables for the period 1995-2005. However, their structural
system does not account for the market equilibrium. Moreover, the statistical evidence found for
the demand elasticity parameters is very poor.9
The model describes the ethanol supply and demand at retail. However, supply and demand
equations are not estimated themselves, only the price equation resulting from the market
clearing do. Since ethanol storages are not significant at retail, it is assumed that, in the long
run, instantaneous price adjustments occur at the market equilibrium.
Overview of the article and main results
In Section II, we present the general model and the price equation in the long run market
equilibrium. A remarkable property of the model ensures that the transmission elasticities of the
ethanol price with respect to sugar and gasoline prices, are positive and sum up l. Thus, the long
run equilibrium does not require that exogenous increases in these prices must be fully
transmitted to the ethanol price. Smaller increases in the ethanol price should be sufficient to
restore the market equilibrium. Once the production of ethanol is economically viable10, the
free market forces tend to guarantee the competitiveness of ethanol against sugar and gasoline.
A comparative static analysis of the price adjustments is carried out in Section 2.2 .
Section III describes the sample characteristics of prices collected by ANP from petrol stations
in the metropolitan areas of São Paulo-North and Rio de Janeiro (2001:07 to 2010:03) and
analyses the price series used in the estimation. Tests ADF, KPSS and UR-SB (Unit Root with
international ethanol market (Brazil+USA) to assess the potential impacts on both markets of an US liberalization of
imports with and without removing tax credits and internal subsidies to the domestic ethanol industry.
7
Available studies estimating the demand for gasoline in Brazil (ASSIS and LOPES, 1980; BURNQUIST and
BACCHI, 2002, OLIVEIRA et al. 2008), all indicate that the demand is relatively inelastic with respect to prices and
income.
8
The price of anhydrous alcohol is equal to the price of the hydrated alcohol plus the cost of dehydration. This cost
is almost constant. So, the correlation between the two prices is very high, in the order of 0.98 in our sample.
Moreover, the seasonal component of both prices are almost identical. See also BACCHI (2006).
9
The shortcoming may be explained by the sample period, within which, most prices were administered.
In the sense that it can be produced at an equivalent mean cost lower than sugar and gasoline (taxes included).
10
4
Structural Break) for level and trend stationary are performed for the individual series. All
information criteria used (Akaike, Schwarz and Hannan and Quinn) applied to the inverse of all
price series, ethanol, gasoline and sugar, allow to identify them as AR(1) processes. The test
results indicate that all series are I(1).
In Section IV a VECM analysis is carried out in order to obtain estimates for the price
equilibrium equation. Preliminary Granger causality and Johansen cointegration tests are
performed. We found statistical evidence of Granger causality from sugar and gasoline prices to
the ethanol price. Further, LR test indicates one cointegrating equation at 5% significance level.
The transmission elasticities of the price of ethanol are estimated with high precision. With
respect to the price of gasoline its value increases throughout the sample period from a mean
0.876 before 2004 in São Paulo to a mean 0.930 after 2006 (0.944 to 0.970 in Rio). With
respect to the price of sugar, its value declines from a mean 0.114 before 2004 to 0.070 mean
afterwards (0.050 to 0.030 in Rio). Upstream, on the ethanol distribution chain, the estimated
transmission elasticities of the gasoline are higher than at retail and show a similar time path.
Thus, the expected convergence of the price rate ethanol/gasoline to the fuel efficiency rate
emerges in the model as the result of market balances through which the demand side forces
overtake supply forces and the price-sensitivity of ethanol with respect to sugar declines
progressively.
For the São Paulo fuel market, it is found that the deviations of current prices of ethanol from
their estimated long run equilibrium, is a stationary AR(2) process without drift, that is, with
zero mean. This finding is consistent with the main assumption regarding relative prices for the
market of ethanol in the long run. Further, the finding also holds upstream at the distribution
level, which adds to the robustness of the assumed model.
The main results of the paper are commented and their economic implications for the Brazilian
sugarcane industry are derived in the last Section V.
II – EQUILIBRIUM IN THE LONG RUN
2.1 The model
Two additional assumptions are adopted for the ethanol market: First, in some
S
D
neighborhood of the equilibrium, the quantities supplied q and demanded q are additive
functions separating relative prices of sugar and gasoline from other short run shifters and
stochastic shocks.
q S = S ( Pe / Ps ) + φ S ( x ; u s )
(1)
q D = D( Pe / Pg ) + φ D ( y ; u d )
Here
Pe , Pg
and
Ps
( 2)
are the current prices (R$) per liter of ethanol, gasoline and per kilo of
sugar, respectively. The functions
their argument, with
S ′(.) > 0
S
and
and
D
are supposed to be differentiable with respect
D′(.) < 0.
Expressions
φS
and
φD
are unspecified
5
functions of shifters x , y
respectively.
and of stochastic shocks
us , ud
for supply and demand,
Note that in specification (1) and (2), supply and demand are degree zero
homogeneous functions of their respective prices.
Second, it is assumed a priori that in the equilibrium, that is
and random shocks on the demand of ethanol that is,
qS = qD ,
the net effect of shifters
ε ≡ φ D ( y ;ud ) − φ S ( x ;us ) ,
is a zero
mean stationary random process independent of fuel prices. So, from (1) and (2) we obtain the
following equilibrium price equation:
S ( Pe / Ps ) = D ( Pe / Pg ) + ε
(3)
The equation (3) says that the market imbalances in the long run are the result of short run
random shocks and the action of supply and demand shifters. If the demand factors are strong in
such a way that
long run
ε = φ D − φ S > 0 , the supply of ethanol tends to overtake the demand in the
( S > D) ,
as the result for example, of overinvestment in production and/or the
overvaluation of ethanol with respect to sugar. The opposite would occur if supply factors
dominate in the short run.
The equilibrium assumed in equation (3), requires the existence of a cointegration relation
between the prices of ethanol, sugar and gasoline. Also, the stability of the equilibrium requires
that the process
ε
must be stationary with zero mean. Such relation will be empirically
evaluated in Section IV, along with the implied stationary assumption of the error process ε .
Price transmission elasticities
By differentiating (3) with respect to all prices, after isolating
dPe
on the l.h.s. we obtain:
dPe / Pe = − [ D′Ps (dPg / Pg ) − S ′Pg (dPs / Ps )] [ S ′Pg − D′Ps ]
(4)
By noting the transmission elasticity of the ethanol price with respect to the sugar price by
ηs ≡
dPe Ps
.
Pe dPs
dPg = 0
and with respect to the gasoline price by
ηg ≡
dPe Pg
.
Pe dPg
dPs = 0
we
obtain from the equation (4);
ηs =
S ′Pg
[ S ′Pg − D′Ps ]
(5a)
and
ηg =
− D′Ps
[ S ′Pg − D′Ps ]
(5b)
6
Notice that the elasticities are positive and sum up to 1:
η s + η g = 1.
This is the adequate
property enabling us to check in the model whether or not the supply of ethanol adjusts over
time to demand in order to set the price rate ethanol/gasoline equal to the fuel efficiency rate.
Indeed, a constant price rate in the long run implies that the gasoline transmission elasticity
becomes close to 1, so that the sugar elasticity tends to zero. This means that, in the long run,
the retail price of ethanol becomes independent of the price of sugar.
Particular cases:
Straightforward particularizations of
1. Linear case, assume
S
and
D
functions are the linear and the logarithm form.
S = α S + β S ( Pe / Ps )
and
D = α D − β D ( Pe / Pg ) , where the
α ' s and β ' s are nonnegative parameters, with α D > α S . From equation (3), after isolating
Pe on the left-hand-side, we obtain a linear equilibrium equation in the inverse of prices levels:
1
1
1
=θ S +θ D
+v
Pe
Ps
Pg
where θ
S
( 6)
= β S /(α D − α S ) > 0 ; θ D = β D /(α D − α S ) > 0 ; v = −ε / Pe (α D − α S ) .
From equations (5a) and (5b), the implied transmission elasticities are:
ηs =
1
[1 + θ Ps / θ S Pg ]
(7 a )
ηg =
1
[1 + θ Pg / θ D Ps ]
( 7b )
D
S
When ν > 0 , we have ε = φ − φ < 0 meaning that shifters or stochastic shocks on the
supply side are stronger than those on the demand side. In other words, the supply of ethanol
tends to overtake the demand in the short run. Otherwise, if ν < 0 the market forces tend to
create an excess of demand.
D
S
Once the equation (6) is estimated and
1 ˆS 1 ˆD 1
=θ
+θ
+ νˆ
Pe
Ps
Pg
^
enables us to write:
νˆ ≅ 1/ Pe − 1 / Pˆe
rewriting the l.h.s. and simplifying with the r.h.s. we obtain:
1 / Pe ≅ 1 / Pˆe
εˆ /(α D − α S ) ≅ ( Pe − Pˆe ) / Pˆe
, the approximation
≅ −εˆ / Pe (α D − α S ) .
After
(8)
The later statistics will be used in Section 4.1. to test the stationary assumption on the
unobserved process ε .
7
2.
Logarithm case, assume
S = a S + b S ln( Pe / Ps )
and
D = a D − b D ln( Pe / Pg ) ,
where a' s and b' s are positive parameters. By using (3), the price equilibrium equation
obtained is double log with intercept:
ln Pe = γ o + η s ln Ps + η g ln Pg + u
where
(9)
γ o = (a D − a S ) /(b D + b S ) ; u = ε /(b D + b S ) .
In this case, the transmission elasticities of the ethanol price are constant:
η s = b S /(b D + b S )
for sugar ; η g
= b D /(b D + b S )
for gasoline.
Misconduct
Let us consider that imbalances in the ethanol market makes room of misconduct from the part
of distributors or retailers in compliance with the official regulations. According to a monthly
survey of ANP aiming to assess the quality of the fuel traded, two "non-conformities" were
frequently observed from 2004 on:
a) 7% of water is added to a volume of anhydrous alcohol after which the mix is sold as
hydrated fuel. This is called the "anhydrous wetting" fraud;
b) The addition of anhydrous to gasoline in quantities above the official rate (25%).
The occurrence of these frauds is obviously favored in case of oversupply of anhydrous alcohol
fuel. In this case, the dealers can earn additional profits by re-hydrating anhydrous alcohol
when the price of gasoline and / or the hydrated price increases (↑ Pg , and / or Pe↑) or by
adding an extra amount of anhydrous to gasoline (which is more expensive).
The rebalancing of the ethanol market occurs with a reduction in the demand for anhydrous
alcohol fuel and the corresponding increase of its supply. In the re-hydration fraud case, the
ethanol supply curve shifts downward. See Fig.1 below. The anhydrous alcool market will not
be considered here. So, only the "anhydrous wetting" fraud can possibly be accounted for by
the present model.
2.2 Effects of price changes
The Figure 1 below shows the increasing line of the ethanol supply as a function of the price
S
S
ratio ethanol / sugar q = S ( Pe / Ps ) + φ ( x ; u s ) , and the decreasing line of the ethanol
demand
q D = D( Pe / Pg ) + φ D ( y ; u d )
as a function of the price ratio ethanol/gasoline. The
initial equilibrium is at q , and the price ratios are
gasoline.
o
so
for ethanol/ sugar and
do
for ethanol /
8
Figure 1 : The Brazilian market of ethanol
P relativo
Fig.1
MERCAD O DO ÁLCO OL HID RATADO
qs
s2
so
s1
d1
do
d2
qd
f
q1
c1
qo
q2
c2
q
1. Suppose there is an increase in the price of sugar. The relative price of ethanol
decreases for producers and the ethanol supply reduces to point c1, creating a supply shortage
o
1
o
equal to q − c , since the demand still unchanged at q . The excess of demand causes an
ethanol price increase so that the new market equilibrium sets at
s
1
for suppliers and
than before ( q
1
<q
d
o
1
q1
with the new price ratios
for consumers. Notice that, the new equilibrium quantities are lower
) Now, ethanol is cheaper relatively to sugar ( s
expensive relatively to gasoline ( d
1
>d
o
1
< so )
and more
).
2. Suppose now an increase in the price of gasoline. The relative price of ethanol
2
decreases for consumers, so that the ethanol demand expands to c . The increase in the price of
gasoline reduces the demand for the product and, consequently, the demand for anhydrous
mixture. The induced oversupply of anhydrous may or not generate the "anhydrous wetting"
misconduct described above.
In the absence of fraud, the supply curve of hydrated remain unchanged after the gasoline price
2
o
increase, so that the have an excess of demand for ethanol equal to c − q . Such imbalance
forces the ethanol price to rise and the new equilibrium will be set at
relative prices are
s
2
and
d
2
q2 ,
where the new
.
In case of misconduct, re-hydrated anhydrous is added to the current ethanol so that the supply
o
o
curve moves to the right, as shown in the figure. At the relative price s , f − q units of
counterfeited ethanol are supplied, so that the excess of demand reduces to c
2
− f
.
Notice also that, whether the fraud occurs or not, the amount traded will be higher after the price
2
o
change than before, q > q . By the way, the ethanol becomes relatively cheaper to
consumers ( d
2
< d o ) and relatively more profitable to producers ( s 2 > s o ).
9
However, the persistence of fraudulent behavior over time may not take away the stationary
property required to the error term ε . However, it may generate persistent market imbalances
that can take the form of a nonzero drift in the estimated error term εˆ .
III – EMPIRICAL FINDINGS
The estimation of the more general linear specification (8) was chosen because it allows for
variable transmission elasticities as shown in equations (7a) and (7b). Moreover, the linear
model can be obtained, in a neighborhood of the equilibrium, as a first approximation from any
other relationship assumed between quantities and price ratios.
It was found a strong evidence of cointegration between these variables, specially for the
ethanol equation. The cointegration vectors are qualitatively equivalent in both specifications.
Only the estimates obtained in the linear specification are shown in the paper, for both markets
São Paulo and Rio de Janeiro separately.
3.1 Data sample and Structure of the ethanol market
The ethanol and gasoline prices used in the estimations were obtained from the ANP National
Petroleum Agency web page (www.anp.gov.br). Monthly retail prices were collected from gas
stations of the metropolitan areas of São Paulo-North and Rio de Janeiro, amounting to 105
observations in the period 2001:07 to 2010:03.
Prices of packed crystal sugar traded in the domestic market (taxes + transport costs included)
were obtained from the the website of CEPEA-ESALQ (www.cepea.esalq.usp.br).
For the retail price of ethanol, negative seasonal variations are observed during the harvest of
sugar cane in São Paulo State, May-August, when the supply of ethanol increases. In both
markets, retail prices of ethanol show a positive trend until mid-2006. The price variations
smooth at lower price levels later on to mid 2009, when it starts increasing sharply again, until
recently (2010:01). In the sample average, ethanol is 29 cents more expensive in Rio de Janeiro
(R$ 1.48 per liter against R$ 1.19 in São Paulo).
In both markets, retail prices of gasoline show a positive trend until the first half of 2006. The
series stabilizes at a higher level until mid 2009, when it starts showing a moderate increase
until recently (2010:01). In the sample gasoline is 32 cents per liter more expensive in Rio de
Janeiro than in São Paulo, R$ 2.48 against R$ 2.16.
The series of sugar prices shows two important increasing-decreasing waves: the first from the
mid-2002 until beginning of 2004 with a peak of R$1.03 in 2003:03; the second, from early
2004 until late 2007 with a peak of R$1.18 in 2006:03. From 2008 on domestic sugar prices
start escalating from R$0.6 per kg in 2008:01 to reach R$1.68 in 2010:02.
Looking at the coefficient of variation measure, prices are more volatile in Rio than in São
Paulo. Further, sugar prices are more volatile than ethanol prices which are more volatile than
gasoline. The greater variation of sugar internal prices is possibly explained by the higher
volatility of world prices, since the country is the main world trader of the commodity.
Recently, the price ratio ethanol/sugar decreases consistently from the rate 2.15 in 2008:01 to
the rate 0.98 in 2010:03. At the same time, the price ratio ethanol/gasoline shows a sustainable
increase. For São Paulo, the rate increases from 0.50 in 2009:06 to 0.73 in 2010:02. For Rio it
10
goes from 0.64 in 2009:09 to 0.79 in 2010:02. See the Figure 6 ahead. The sample means are
0.55 and 0.65 respectively. The coefficient of variation of the price rate is 23% lower in Rio .11
At the retail level, the ethanol fuel market is almost perfectly competitive. It is composed by a
large number of small local fuel stations. The same cannot be said upstream, about the
distribution segment, which is dominated by a few number of large firms, with a competitive
fringe of small local distributors. BR-Distribuidora, Cosan-Esso and Shell are the main
nationwide distributors. After a period when important acquisitions and mergers among alcohol
distilleries occurred, the industry consolidation now in process points to the vertical integration
of the production and distribution activities and the merge of ethanol distribution services into
the petrol distribution network. The ethanol price at the distribution level reflects directly the
price set by the main alcohol distilleries.
3.2 Estimations
Information criteria of Akaike, Schwarz and Hannan and Quinn applied to price levels and to
their inverses for São Paulo and Rio, all indicate that the implied series may be adequately
described as AR(1) processes.
Tests ADF, KPSS and UR-SB (Unit Root with Structural Break, LANNE et.al., 2000) for
integrated processes with time trend and without time trend, show that all series are non
stationary at 1% significant level. The only exception is to series of the inverse of ethanol price
1 / Pe for Rio with time trend, for which the unit root assumption is rejected in the UR-SB test.
However, if we remove the time trend and allow for nonzero mean the test does not reject the
null hypothesis in this case.
The break dates suggested in the UR-SB test are all coincident, whether or not a time trend is
allowed with the shift dummy. However, the structural break date suggested for the ethanol
prices series in Rio (2002:11) is different from that of São Paulo (2004:03). For the sugar prices
series the structural break suggested occurs in 2004:04. For the series of gasoline prices the date
break suggested is 2002:11 for São Paulo and Rio.
The parameters estimated are those of the linear model. Since the reduced form equation (6)
gives the set of prices in the long run equilibrium of the ethanol market, the appropriate
econometric model that provides an estimation method allowing for both the interdependence of
prices and short and long run effects is the VECM (Vector Error Correction Model).
The equilibrium relationship described in the general equation (3) presumes that the price rates
of ethanol with respect to sugar and gasoline are simultaneously determined. In the estimated
equation (6) the price of ethanol is set as the dependent variable while sugar and gasoline prices
appear as independent variables.
In order to get a first insight on the existence of a precedence ordering among the variables,
Granger Causality tests to the six pairs of the inverse of prices for São Paulo and Rio de Janeiro
were run. The results are shown in Table 1 of the Appendix. As we can see, with a time lag of
2 periods for both samples, at significance levels lower than 0.4%, the precedence relations that
we cannot reject are only those going from sugar and gasoline to ethanol. This result favors the
specification (6).
Previous Johansen cointegration tests were carried out. The intercept is not significant in the
cointegration equation for São Paulo. On the other side, the dummy SAFRA was introduced as
11
All over the sample period, the price ratio alcohol/sugar is higher than the price ratio alcohol/gasoline. This shows
that the quantities traded in equilibrium are located to the right side of the intersection of supply and demand curves
as illustrated in Figure 1.
11
an exogenous variable because it was highly significant, and São Paulo state is the main ethanol
producer of the country. The variable values 1 in the main sugarcane harvest period (MaiAugust). For Rio the Janeiro such variable is not significant, but the intercept is significant in
the cointegration equation. The results appear on Table 2 of the Appendix. Not surprisingly,
the assumption of only one cointegrating vector cannot be rejected in both markets.
The estimations of the VECM are presented in Table 3 of the Appendix. For both markets São
Paulo and Rio de Janeiro, the estimates of the cointegrating vector differ from those appearing
in Table 2 for the cointegration test because in the VECM estimation, the coefficient of the
cointegration relation for the equation of the price of gasoline was non significant so that it was
set to zero. From the estimates of the cointegrating relations appearing in Table 3, the implied
estimated equation (6) is presented below, for both markets (t values are given in parenthesis):
São Paulo (2001:07-2010:03):
1
1
1
= 0.1935 + 1.2468
+ vˆ
( 3.322 ) P
( 6.855 ) P
Pe
s
g
(6 sp )
Rio de Janeiro (2001:07-2010:03):
1
1
1
= 0.1071 + 1.6360 − 0.2017 + uˆ
( 3.973 ) P
(13.803 ) P
( 4.957 )
Pe
s
g
(6rj )
To give an illustration, the Figure 2 below plots the estimated equilibrium price equation for
São Paulo:
Figure 2 : SÃO PAULO – The surface of ethanol equilibrium prices
1.6
1.4
Price Ethanol 1.2
1.0
2.5
2.0
1.5
Price Gasoline
0.8
1.00.0
0.2
0.4
0.6
0.8
1.0
Price Sugar
Pˆe = [(0.1935 / Ps ) + (1.2468 / Pg )]−1
The parameters of the long run equation are estimated with high precision in both markets, as
we can see in the equation (6sp) and (6rj) above. The same can be said for the coefficients of the
integrating relation in the equation of the ethanol and the sugar prices, as we can see on Table 3
of the Appendix.
12
IV – ANALYSIS OF RESULTS
A first point to be assessed is the stationary assumption on the error term ε . A second one is the
sensitivity of the ethanol price with respect to the gasoline and sugar prices in the long run
equilibrium of the market.
4.1 Checking the long run equilibrium relationship
The checking of the equilibrium relation (6) for São Paulo can be done, after relation (8),
by using the rate of change of the current price of ethanol from its long run level. The Figure 3
below plots the level of deviations
Pe − Pˆe
and the deviation rate
( Pe − Pˆe ) / Pˆe .
Figure 3 – SÃO PAULO: Deviations of the observed price of ethanol from the estimated
equilibrium price (deviation level: thin line; deviation rate: thick line)
0.3
0.2
0.1
0.0
-0. 1
-0. 2
-0. 3
02
03
04
05
LEVEL
06
07
RATE
08
09
10
0
The level and the rate of deviations are almost the same. Both series have mean close to zero (.0078 against -.0097) and very similar stochastic trends. Then we can focus the analysis only on
ˆe . This series has no unit root, as we can see by the ADF
the deviations of price levels Pe − P
test shown in Table 4 of the Appendix. By using information criteria tests, the series can be
identified as a stationary AR(2) process with zero mean.
Notice on Figure 3 that the values of “level” above (below) the zero line correspond to current
ethanol prices above (below) their long run levels. This is equivalent to say that the effect of
shifters and shocks on the demand side overtake (are subdue by) their supply side counterparts,
that is,
φˆ D − φˆ S > 0 (< 0).
The equation of the ADF unit root test for
Pe − Pˆe
(level) generates the following
homogeneous difference equation: level t  1. 1723level t1  0. 4805level t2  0 .
The solution have complex conjugate roots 0.58616 ± 0.37003i so that the real part of the
levelt = co (0.65861) t cos(0.56311t + c1 )
c1 are determined from the initial conditions at t = 0 and t = 1 .
deterministic process can be written as:
where constants
co
and
Following an initial deviation from its equilibrium level, the current price return to its long run
level after a cycle of almost one year; more precisely, 2π / 0.56311 = 11.2 months.
The Figure 4 below plots levelt (thin line) with initial conditions at t = 0,
− 0.089 (2009 : 10) and at t = 1, 0.039 (2009 : 11) which
level . For illustration purposes, the corresponding solution
are two recent values of
of the deviation rate
13
( Pe − Pˆe ) / Pˆe is also plotted on Figure 4 (thick line), with
− 0.0058 (2009 : 10) and at t = 1, 0.025 (2009 : 11) .
the initial values at t = 0,
Figure 4 - SÃO PAULO: Cycle convergence of the ethanol price to its estimated
long run equilibrium level
Level, Rate
0.08
0.06
0.04
0.02
0.00
-0.02
1
2
3
4
5
6
7
8
9
10
11
12
13
Months
-0.04
-0.06
-0.08
levelt = −0.026704(0.65861) t cos(0.56311t + 1.2313)
ratet = −0.18159(0.68528) t cos(0.53875t + 1.2407)
The convergence period of one year can also be inferred from the Figure 4a in the Appendix
that plots the response of 1 / Pe from Cholesky innovations on that variable and on 1 / Ps
and 1 / Pg . In each case, the value of the dependent variable stabilizes after 12 months.
For Rio de Janeiro, stationary deviations
Pe − Pˆe
with zero mean, similar to São Paulo, can
only be obtained if an intercept θ o (say) is added to the equilibrium equation (6), as shows the
estimated
equation
(6rj).
This
means
that
if
we
define
(1 /̂ Pe ) ≅ 1 / Pˆe = 0.10715
(3.972)
1
1
+ 1.6360 − 0.20171
( 4.957)
Ps (13.802) Pg
the deviations
Pe − Pˆe
( Pe − Pˆe ) / Pˆe (rate) are stationary with zero mean like São Paulo, but not the
D
S
estimated error εˆ /(α − α ) as it is required by the model assumption. Indeed, if a constant
θ is added to (6) one can check that εˆ /(α D − α S ) ≅ rate − θˆ P . The r.h.s. of this
(level) and
o
o
e
rate* ≡ ( Pe − Pˆe ) / Pˆe + 0.20171Pe
equality, say
can be identified as a stationary AR(2)
process, but not with zero mean. The sample mean is 0.284. This can be also deduced from the
equation of the ADF unit root test shown in Table 4 of the Appendix.
Therefore, a systematic (positive) error is present in the long run equilibrium assumed in
equation (3) for Rio de Janeiro. One is not willing to believe that such systematic error could be
accounted for the action of demand shifters or stochastic shocks φ − φ , since these net
effects are supposed to be of short term nature while the intercept is a parameter in the long run
equation. Rather, the source of the systematic error should be found in the core functions S and
D
D,
because the error appears as a systematic oversupply in the estimations:
S
Sˆ − Dˆ > 0 .
14
One possible cause of such imbalance may be linked with the persistence of the re-hydrating
anhydrous fraud in the Rio market, as indicated at the end of Section 2.2. This and other
possible explanations will be further discussed ahead in Section V.
4.2 Checking the price sensitivities
In order to evaluate the long run sensitivity of the price of ethanol with respect to sugar and
gasoline prices, we obtain the estimators η̂ s andη̂ g of the elasticities by replacing the θ ′s in
equations (7a) and (7b) by their estimates given in equations (6sp) for São Paulo and (6rj) for
Rio de Janeiro. For sugar we use the identityηˆ s = 1 − ηˆ g . The Figure 5 below plots the value
of the elasticity w.r.t. the price of gasoline for São Paulo (“elgsp”) and Rio de Janeiro (“elgrj”).
Figure 5 : Gasoline Price Transmission Elasticity of the Ethanol
São Paulo (blue thick) - Rio de Janeiro (red thin)
1.00
0.96
0.92
0.88
0.84
0.80
02
03
04
05
ELGSP
06
07
08
09
10
ELGRJ
As we see from the figure, in both markets, the price of ethanol is more sensitive to changes of
gasoline price than of sugar price. In the mean of the sample, the gasoline price transmission
elasticity is 0.91 in São Paulo and 0.96 in Rio. As a consequence, the mean sugar price
transmission elasticity is 0.09 for São Paulo and 0.04 for Rio.
Thus, facing an exogenous increase of 20% in the price of gasoline (sugar), a rise of 18.2%
(1.8%) of the ethanol price is sufficient to restore the long run market equilibrium in São Paulo.
Under the same circumstances, a rise of 19.2% (0.8%) would be necessary in Rio.
The lower sugar-sensitivity of the ethanol price in Rio may be linked to the fact that the city is a
net major importer of both, sugar and ethanol, mainly from São Paulo. So, the supply of ethanol
in Rio is derived from that of São Paulo. The existence of transportation costs and regulatory
sugar stocks possibly weaken the sugar-elasticity of the ethanol supply in the local market.
More importantly, there is a clear tendency of the gasoline elasticity to increase towards one, in
both markets. As a consequence, the sugar elasticity decreases towards zero in the sample
period. Comparing the mean value of the gasoline elasticity in the period after 2006 when flexfuel technology begin to spread in the car market, with the period before 2004 when it was
absent, we can see that its value increases by 6.0% in São Paulo (0.877 to 0.930) and by 2.1%
in Rio (0.95 to 0.97).
So, in both markets, the supply of ethanol adjusts to meet the demand requirement for setting
the price rate ethanol/gasoline close to the constant fuel efficiency rate (between 0.6 to 0.7).
To give an illustration of this, the Figure 6 below shows the observed price rate
Pe / Pg
for the
Rio market and its sample mean (= 0.656). The figure for São Paulo is similar.
15
Figure 6 : RIO DE JANEIRO – Observed price rate ethanol/gasoline
0.9
0.8
0.7
0.6
0.5
02
03
04
05
PREG
06
07
08
09
10
MEAN
By the use of information criteria tests and the ADF unit root test we can identify the series of
price rates as a stationary AR(2) process. The series tends to stabilize to the long run mean 0.66.
The volatility, measured by the coefficient of variation of the price rate (standard
deviation/mean) reduces by 2.1% after 2006 when compared with its value before 2004 (0.081
against 0.079).
V – FINAL COMMENTS ON THE MAIN RESULTS
The main results obtained here for the retail segment of the ethanol market in São Paulo and
Rio, are also achieved by using price data upstream, on the ethanol distribution channel. These
results are not reproduced here for obvious reasons. Only a significant, though expected
difference worth to be noted: In both markets, the sugar (gasoline) transmission elasticities are
higher (lower) than at the retail segment: 0.142 (0.858) for São Paulo and 0.072 (0.928) for Rio,
at the mean of the sample. However, the increase of the gasoline elasticity over time is steeper.
Comparing periods after 2006 and before 2004, the variations of the gasoline elasticity are:
+8.0% in São Paulo and +5.0% in Rio de Janeiro. These values are to be compared with
corresponding values +6.2% and +2.7% reported previously for the retail segment.
In the sequel we will comment the main results of this paper.
(i) The model is found to be adequate to explain the long run behavior of the ethanol market in
São Paulo, as it was shown in Section 4.1. A long run equilibrium price is estimated for the
ethanol. Deviations of the current price from that equilibrium do not generate permanent effects,
the market equilibrium is restored after a cycle of period about one year.
The exercise enables us to identify periods of supply or demand pressure in the short run,
according to current price is lower or higher the estimated equilibrium price. In the model, such
pressures result from the action of shifters and exogenous shocks on supply and on demand.
The following dates identify the periods when supply pressures dominate: 2001:07-12 ;
2002:04-10 ; 2003:07-09 ; 2004:02-09 ; 2005:04-11 ; 2006:05-12 ; 2007: 08-10 ; 2008:09-10 ;
2009:01-09. In the other periods, demand pressures dominate, in particular, from 2009:10 to
now (April 2010).
(ii) The observed tendency of the price rate ethanol/gasoline to set to the constant fuel efficiency
rate is featured in the model as a long run market result. The ethanol supply progressively
adjusts to meet the demand of a growing number of rational consumers driving flex-fuel cars
who can switch to ethanol whenever the price rate is lower than the fuel efficiency rate.
In both markets, São Paulo and Rio de Janeiro, we have found that the transmission elasticity of
the ethanol price with respect to the price of gasoline increases over time towards one. By a
property of the model, the elasticity with respect to the sugar price decreases towards zero. So,
in the long run, the price of ethanol will no longer depend significantly on the price of sugar.
16
This fact indicates that the consolidation of an ethanol retail market independent of the
traditional sugar market is now on the way, which is an important step towards the long run
sugarcane industry restructuring. If at the market equilibrium the sugar price volatility has no
significant effect on the ethanol price, one of the most important sources of the ethanol price
volatility will be removed in the long run. By this way, individual ethanol producers will no
longer need to integrate the ethanol production with sugar factoring, in order to be protected
against revenue risk. The recently observed trend to creating new isolated alcohol distilleries
everywhere in the country can be better understood in the light of this path. 12
(iii) The linear model used to describe the long-run equilibrium in the ethanol market for Rio de
Janeiro is only partially adequate. The error term in the equilibrium price of ethanol is stationary
but not with zero mean. So, there is a systematic (positive) error in the long run equilibrium
price equation, which appears in the sample to have a permanent nature, since it is
parameterized by a significant intercept in the long run equation.
Several hypothesis could be raised in order to explain the systematic oversupply estimated in
the ethanol market of Rio. We list below two of them, the first linked to the demand, the second
to the supply.
The first one may be the omission of an important variable in the demand equation. One
possible candidate is the price of fuel gas, which consumption in Rio, differently from São
Paulo, was heavily subsidized by the regional government since early 2000, particularly to feed
the taxi fleet of the metropolitan area.13 Since natural gas is a substitute to ethanol and to
gasoline fuel for consumers, the omission of the price rate ethanol/gas in the demand of ethanol
cause a shift downward of the long run price surface. See Figure 2. As a consequence, the mean
difference between the observed ethanol price and its estimated equilibrium level is larger than
it would be if the positive effect of gas fuel price on the ethanol price was taken into account.
The second hypothesis is linked to the persistence over the sample period, of the re-hydrating
anhydrous fraud suggested at the end of Section 4.1.
First of all, a systematic overproduction of anhydrous alcohol,14 together with distortions in the
tax system for the ethanol industry, both do make selling re-hydrated anhydrous alcohol as
ethanol fuel a very profitable (and illegal) activity. The profitability of the fraud could be even
larger in Rio, because the sales tax (TVA) on the ethanol trade is higher than in São Paulo. 15
In order to help rationalizing why the fraud phenomena could happen more significantly in Rio
than in São Paulo, consider that the profitability margin in trading ethanol (true hydrated fuel) is
lower in Rio than in São Paulo, 18% against 22% in the mean of the sample. Further, when
comparing the period after 2006 with the period before 2004, the margins fell down more
steeply in Rio: -40% (23.9 to 14.4) against -18.8% (25.6 to 20.8) in São Paulo. So, retailers
from Rio may be more willing to get their profit margins widen by falsifying ethanol than their
colleagues of São Paulo do.
12
For example, 20 new isolated ethanol distilleries are planned to be installed in 2012 with minor stake of Petrobras,
the Brazilian Petroleum Company.
13
However, data on the price of gas fuel which is compatible with the present sample period still lacking.
14
From data reported by RAMOS (2008, Table 09) the national accumulated stocks of anhydrous alcohol (internal
surplus minus exports) amounted 2.4 millions m3 in the period 2001:01 to 2005:06. To mitigate the anhydrous
market imbalance, the government increases the mandatory mixture of anhydrous in gasoline from 20% to 25% after
2007:07.
15
The value added tax (VAT) of trading alcohol applies only to hydrated, not to anhydrous alcohol. This makes the
former more expensive than the later. The tax is higher in Rio (around 20%) than in São Paulo (12%). For São Paulo
(2005), BRAGATO and MAISTRO(2006) estimate a net mean profit of the fraud by around $30.5 per m3 of rehydrated anhydrous traded.
17
Last but not least, there is sample evidence that ethanol falsifications are much more frequent in
Rio than in São Paulo. According to a quarterly sampling survey from fuel stations of the
metropolitan area by ANP, the relative frequency of “non-conformities” detected in the ethanol
trading, in yearly means, are 1.76 times higher in Rio than in São Paulo (16.2% against 9.2%)
in 2004; 2.41 times higher in 2005 (17.4% against 7.2%) ; 2.25 times higher in 2006 (7.2%
against 3.2%); 5.47 times higher in 2007 (11.0% against 1.7%); 1.7 times higher in 2008 (2.2%
against 1.3%) and 5.37 times higher in the last quarter of 2009 (4.3% against 0.8%).
The present article is a pioneering initiative to model the Brazilian ethanol fuel market. The
main objective pursued was to see how the price of ethanol interacts with sugar and gasoline
prices in the long run equilibrium. Moreover, we would want to see how new flex-fuel vehicles
are going to affect such equilibrium. The merit of the paper, if any, is precisely to build such a
theoretical framework within which important stylized facts currently observed or predicted for
the Brazilian ethanol fuel market, are enhanced from the estimations, as the result of the
maximizing behavior of producers and consumers.
Rio de Janeiro, February 2010
REFERENCES
ASSIS,A.N. e L.B.R.LOPES(1980) A Ineficiência da Política de Preços para conter o
Consumo de Derivados de Petróleo, Revista Brasileira de Economia, 34, n.3, 417-428.
BACCHI,M.R.P. (2006) Estoques Reguladores de Álcool, CEPEA/ESALQ.
BRAGATO,I.R. and M.C. MARJOTTA-MAISTRO (2006) Corante no Anidro Combustível:
Aumento da Credibilidade do Produto, CEPEA/ESALQ
BURNQUIST, H.L. and BACCHI, M.R.P.(2002) A Demanda por Gasolina no Brasil: Uma
Análise Utilizando Técnicas de Co-Integração, CEPEA/ESALQ.
DIAS, G.L.S., J.R.M. BARROS and A.L.M.BARROS(2002), Modelo de Intervenção
Mínima para o Setor Canavieiro, in Moraes, M.A.F.D. e P.F.A.Shikida (Org.) Agroindústria
Canavieira no Brasil, Ed. Atlas.
ELOBEID,A. and S.TOKGOZ (2006) Removal of U.S. Ethanol Domestic and Trade
Distortions: Impact on U.S. and Brazilian Ethanol Markets, Center for Agricultural and Rural
Development, 06-WP 427, Iowa State University.
JEHLE,G.A. and P.J.RENY(2001) Advanced Microeconomic Theory, 2nd.ed., Addison
Wesley.
KOIZUMI,T.(2003) The Brazilian Ethanol Programme: Impacts on World Ethanol and
Sugar Markets, FAO Commodity and Trade Policy Research Working Paper nº 1.
LANNE, M., H.LUTKEPOHL and P.SAIKKONEN (2002) Comparison of Unit Root Time
Series with Level Shifts, Journal of Time Series Analysis, 23, N.6, 667-685;
LUTKEPOHL, H. and M.KATZIG (2004) Applied Time Series Econometrics, Cambridge
Univ.Press;
MARJOTTA-MAISTRO(2008) Biocombustíveis: Novos Desafios para o Setor SucroAlcooleiro Nacional. www.cepea.esalq.usp.br
MARJOTTA-MAISTRO,M.C. and G.S.C.BARROS(2002) Relações Comerciais e de
Preços no Mercado Nacional de Combustíveis, ESALQ/USP, XL Congresso da Sociedade
Brasileira de Economia, Administração e Sociologia Rural -SOBER.
OLIVEIRA,M.P., J.R.ALENCAR e G.S.SOUZA(2008) Energia Renovável: Uma Análise
sobre Oferta e Demanda de Etanol no Brasil, EMBRAPA, XLVI Congresso da Sociedade
Brasileira de Economia, Administração e Sociologia Rural -SOBER.
RAMOS,P. (2008) A Evolução da Agroindústria Canavieira e os Mercados de Açúcar e de
Álcool Carburante no Brasil: A Necessidade de Planejamento e Controle, IE-UNICAMP,
XLVI Congresso da Sociedade Brasileira de Economia, Administração e Sociologia Rural SOBER.
18
APPENDIX
I - Let qe , q s be quantities supplied of ethanol and sugar, Pe , Ps their unit prices, we ,ws the
prices of inputs used in the manufacture of both products, and
functions that minimize the production cost of
π e (qe , we ) = Pe qe − Ce (qe , we )
π s (q s , ws ) = Ps q s − C s (q s , ws )
The
choice
of
quantities
qe
and
maximizing
Pe / Ps = Ce′ (qe , we ) / C s′ (q s , ws ) .
qs
Ce (qe , we ) , C s (q s , ws )
the cost
, respectively. Then, the profit functions are:
profits
separately,
given
prices,
requires:
But as the sugar and alcohol can be measured by a single
common measure, the TSR-Total Sugar Recovered, there is a positive constant
≡ Ce′ (qe , we ) / C s′ (kqe , ws )
−1
will be a function of the relative prices: qe S ( Pe / Ps ) .
so that if the function S ( qe )
k
such that
q s = kqe ,
can be inverted, the supply of ethanol
The values of conversion suggested by CONSECANA are: 1kg sugar = 1.0495 kg TSR and 1 liter
ethanol = 1.78 kg TSR.
By measuring sugar in kg and ethanol in liters we have:
k = 1.0495 / 1.78 , or q s = 0.59qe .
On the other hand, if the producers equal the mark-up of both products, we have:
π e / Ce = π s / C s ⇒ Pe / Ps = kCe (qe , we ) / C s (kqe , ws ) ≡ M (qe ) .
Then, if the function M is invertible, we will have:
qe = M −1 ( Pe / Ps ) .
TABLE 1 – Granger Causality Tests
SÃO PAULO
Pairwise Granger Causality Tests
Date: 04/23/10 Time: 12:41
Sample: 2001:07 2010:03
Lags: 2
Null Hypothesis:
Obs
F-Statistic
Probability
1/PS does not Granger Cause 1/PESP
1/PESP does not Granger Cause 1/PS
103
6.07367
0.20009
0.00326
0.81899
1/PGSP does not Granger Cause 1/PESP
1/PESP does not Granger Cause 1/PGSP
103
4.86729
2.31213
0.00965
0.10443
1/PGSP does not Granger Cause 1/PS
1/PS does not Granger Cause 1/PGSP
103
0.99288
1.18515
0.37420
0.31004
Null Hypothesis:
Obs
F-Statistic
Probability
1/PS does not Granger Cause 1/PERJ
1/PERJ does not Granger Cause 1/PS
103
5.80895
0.11154
0.00413
0.89457
1/PGRJ does not Granger Cause 1/PERJ
1/PERJ does not Granger Cause 1/PGRJ
103
6.79646
1.76459
0.00172
0.17666
1/PGRJ does not Granger Cause 1/PS
1/PS does not Granger Cause 1/PGRJ
103
1.02184
1.96410
0.36374
0.14577
RIO DE JANEIRO
Pairwise Granger Causality Tests
Date: 04/23/10 Time: 12:43
Sample: 2001:07 2010:03
Lags: 2
19
TABLE 2 : Johansen Cointegration Tests
SÃO PAULO
Date: 04/23/10 Time: 12:56
Sample: 2001:07 2010:03
Included observations: 96
Test assumption: No deterministic trend in the data
Series: 1/PESP 1/PS 1/PGSP
Exogenous series: SAFRA
Warning: Critical values were derived assuming no exogenous series
Lags interval: 1 to 1
Likelihood
Eigenvalue
Ratio
0.236811
0.070496
0.025709
5 Percent
Critical Value
35.46217
9.518274
2.500298
24.31
12.53
3.84
1 Percent
Critical Value
29.75
16.31
6.51
Hypothesized
No. of CE(s)
None **
At most 1
At most 2
*(**) denotes rejection of the hypothesis at 5%(1%) significance level
L.R. test indicates 1 cointegrating equation(s) at 5% significance level
Unnormalized Cointegrating Coefficients:
1/PESP 1/PS
-1.395020
0.276585
0.198119
1/PGSP
0.284635
-0.456907
0.101620
1.676115
0.795202
-0.924343
Normalized Cointegrating Coefficients: 1 Cointegrating Equation(s)
1/PESP 1/PS
1/PGSP
1.000000
-0.204037
-1.201499
(0.05581)
(0.17337)
Log likelihood
518.7164
Normalized Cointegrating Coefficients: 2 Cointegrating Equation(s)
1/PESP 1/PS
1.000000
0.000000
Log likelihood
1/PGSP
0.000000
(0.06903)
1.000000
(0.26629)
-1.775958
-2.815467
522.2254
20
RIO DE JANEIRO
Date: 04/23/10 Time: 13:11
Sample: 2001:07 2010:03
Included observations: 103
Test assumption: No deterministic trend in the data
Series: 1/PERJ 1/PS 1/PGRJ
Lags interval: 1 to 1
Likelihood
Eigenvalue
Ratio
0.276095
0.059666
0.037514
5 Percent
Critical Value
43.55369
10.27493
3.938315
34.91
19.96
9.24
1 Percent
Critical Value
41.07
24.60
12.97
Hypothesized
No. of CE(s)
None **
At most 1
At most 2
*(**) denotes rejection of the hypothesis at 5%(1%) significance level
L.R. test indicates 1 cointegrating equation(s) at 5% significance level
Unnormalized Cointegrating Coefficients:
1/PERJ 1/PS
2.464580
-0.177895
-0.341693
1/PGRJ C
-0.228420
0.375669
0.179121
-4.093366
-1.431052
1.074124
0.449777
0.243075
-0.444327
Normalized Cointegrating Coefficients: 1 Cointegrating Equation(s)
1/PERJPERJ(1) 1/PS
1/PGRJ C
1.000000
-0.092681
-1.660878
0.182496
(0.02540)
(0.12100)
(0.03969)
Log likelihood
629.6150
Normalized Cointegrating Coefficients: 2 Cointegrating Equation(s)
1/PERJ 1/PS
1.000000
0.000000
Log likelihood
1/PGRJ C
0.000000
(0.17524)
1.000000
(1.57088)
-2.106378
(0.08014)
-4.806805
(0.71837)
0.253595
0.767135
632.7833
21
TABLE 3: Vector Error Correction Model (VECM)
SÃO PAULO
Vector Error Correction Estimates
Date: 04/14/10 Time: 20:49
Sample (adjusted): 2001M09 2009M08
Included observations: 96 after adjustments
Standard errors in ( ) & t-statistics in [ ]
Cointegration Restrictions:
B(1,1)=1 , A(3,1)=0
Convergence achieved after 4 iterations.
Restrictions identify all cointegrating vectors
LR test for binding restrictions (rank = 1):
Chi-square(1)
1.770840
Probability
0.183278
Cointegrating Eq:
CointEq1
1/PESP(-1)
1.000000
1/PS(-1)
-0.193572
(0.05827)
[-3.32216]
1/PGSP(-1)
-1.246867
(0.18189)
[-6.85487]
Error Correction:
D(1/PESP)
D(1/PS)
D(1/PGSP)
CointEq1
-0.328096
(0.06375)
[-5.14625]
-0.393206
(0.17844)
[-2.20352]
0.000000
(0.00000)
[ NA]
D(1/PESP(-1))
0.445311
(0.10781)
[ 4.13054]
-0.166394
(0.27953)
[-0.59525]
0.050738
(0.02852)
[ 1.77888]
D(1/PS(-1))
0.021992
(0.04706)
[ 0.46727]
0.104661
(0.12203)
[ 0.85766]
-0.001074
(0.01245)
[-0.08623]
D(1/PGSP(-1))
-0.118103
(0.42470)
[-0.27809]
1.320275
(1.10117)
[ 1.19897]
0.164880
(0.11236)
[ 1.46745]
SAFRA
0.021616
(0.00942)
[ 2.29515]
0.037234
(0.02442)
[ 1.52470]
0.000824
(0.00249)
[ 0.33051]
0.410560
0.384651
0.223715
0.049582
15.84598
154.7450
-3.119687
-2.986127
-0.003315
0.063207
0.111782
0.072739
1.504018
0.128560
2.863067
63.27987
-1.214164
-1.080604
-0.009454
0.133507
0.108510
0.069324
0.015658
0.013118
2.769076
282.3942
-5.779046
-5.645486
-0.001869
0.013597
R-squared
Adj. R-squared
Sum sq. resids
S.E. equation
F-statistic
Log likelihood
Akaike AIC
Schwarz SC
Mean dependent
S.D. dependent
Determinant resid covariance (dof adj.)
Determinant resid covariance
Log likelihood
Akaike information criterion
Schwarz criterion
4.78E-09
4.07E-09
517.8310
-10.41315
-9.932331
22
RIO DE JANEIRO
Vector Error Correction Estimates
Date: 04/17/10 Time: 13:51
Sample (adjusted): 2001M09 2009M08
Included observations: 96 after adjustments
Standard errors in ( ) & t-statistics in [ ]
Cointegration Restrictions:
B(1,1)=1 , A(3,1)=0
Convergence achieved after 3 iterations.
Restrictions identify all cointegrating vectors
LR test for binding restrictions (rank = 1):
Chi-square(1)
0.032866
Probability
0.856141
Cointegrating Eq:
CointEq1
1/PERJ(-1)
1.000000
1/PS(-1)
-0.107150
(0.02697)
[-3.97287]
1/PGRJ(-1)
-1.633996
(0.11838)
[-13.8026]
C
0.201716
(0.04069)
[ 4.95751]
Error Correction:
D(1/PERJ)
D(1/PS)
D(1/PGRJ)
CointEq1
-0.392120
(0.06386)
[-6.14012]
-0.815982
(0.32491)
[-2.51141]
0.000000
(0.00000)
[ NA]
D(1/PERJ(-1))
0.532957
(0.10817)
[ 4.92691]
0.115147
(0.45926)
[ 0.25072]
0.054570
(0.04131)
[ 1.32098]
D(1/PS(-1))
0.017393
(0.02831)
[ 0.61430]
0.039568
(0.12021)
[ 0.32916]
0.009977
(0.01081)
[ 0.92269]
D(1/PGRJ(-1))
-0.240264
(0.30570)
[-0.78594]
0.842968
(1.29788)
[ 0.64950]
0.307586
(0.11675)
[ 2.63466]
SAFRA
0.011280
(0.00573)
[ 1.96753]
0.031498
(0.02434)
[ 1.29410]
-0.000108
(0.00219)
[-0.04918]
0.457338
0.433484
0.084000
0.030382
19.17294
201.7635
-4.099240
-3.965680
-0.004067
0.040366
0.105827
0.066522
1.514102
0.128990
2.692494
62.95914
-1.207482
-1.073922
-0.009454
0.133507
0.204826
0.169873
0.012251
0.011603
5.860074
294.1741
-6.024460
-5.890901
-0.002057
0.012735
R-squared
Adj. R-squared
Sum sq. resids
S.E. equation
F-statistic
Log likelihood
Akaike AIC
Schwarz SC
Mean dependent
S.D. dependent
Determinant resid covariance (dof adj.)
Determinant resid covariance
Log likelihood
Akaike information criterion
Schwarz criterion
1.27E-09
1.09E-09
582.1071
-11.73140
-11.22387
23
TABLE 4. ADF Testes for Price Deviations
São Paulo
ADF Test Statistic
-5.377139
1% Critical Value*
5% Critical Value
10% Critical Value
-2.5858
-1.9432
-1.6174
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LEVEL)
Method: Least Squares
Date: 04/24/10 Time: 11:51
Sample(adjusted): 2001:09 2010:03
Included observations: 103 after adjusting endpoints
Variable
Coefficient Std. Error
LEVEL(-1)
D(LEVEL(-1))
-0.308182
0.480504
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.292497
0.285492
0.058056
0.340422
148.0327
1.891257
0.057313
0.092615
t-Statistic
Prob.
-5.377139
5.188174
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
0.000202
0.068682
-2.835587
-2.784427
41.75557
0.000000
Rio de Janeiro
ADF Test Statistic
-4.505218
1% Critical Value*
5% Critical Value
10% Critical Value
-3.4946
-2.8895
-2.5815
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(RATESTAR)
Method: Least Squares
Date: 04/24/10 Time: 11:58
Sample(adjusted): 2001:09 2010:03
Included observations: 103 after adjusting endpoints
Variable
Coefficient Std. Error
RATESTAR(-1)
D(RATESTAR(-1))
C
-0.222032
0.435292
0.064189
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.253415
0.238483
0.045309
0.205288
174.0799
1.920117
0.049283
0.090535
0.014652
t-Statistic
Prob.
-4.505218
4.808020
4.381028
0.0000
0.0000
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
0.002143
0.051921
-3.321940
-3.245201
16.97157
0.000000
24
FIGURE 4a: SÃO PAULO – Inverse Ethanol Price Response to Innovations
Response of 1/PESP to Cholesky
One S.D. Innovations
.07
.06
.05
.04
.03
.02
.01
.00
2
4
6
1/PESP
8
1/PS
10
12
14
1/PGSP
25