Gasoline demand in Brazil: an empirical analysis

Thaís Machado de Matos Vilela

Leonardo Bandeira Rezende

Marcelo Cunha Medeiros

Pontical Catholic University of Rio de Janeiro, Departament of Economics

Rua Marquês de São Vicente, 225, Gávea, Rio de Janeiro, RJ - Brazil - 22451-900

Phone: 55 21 3527-1078/ Email: thais.vilela@econ.puc-rio.br

Abstract

I estimate the elasticity of demand for gasoline in Brazil taking into account that gasoline and ethanol

prices are endogenous variables in the aggregate demand curve. Combining dierent identication strategies, I nd that consumers are more elastic to price than earlier studies suggest. An increase, ceteris

paribus, of 1 percent in gasoline and ethanol prices reduces gasoline demand by 1.67 percent and raises

gasoline demand by 0.73 percent respectively. To analyze the behavior of gasoline demand in the face

of exogenous shocks, I also calculate impulse response analysis. The results suggest that a 1 percent

temporary increase in gasoline and ethanol prices reduces gasoline demand by 0.4 percent and raises

gasoline demand by 0.2 percent respectively. Both of these eects are permanent.

In this study I also look for evidences that the introduction of ex-fuel automobiles in Brazil led to

consumers more elastic to price change. I divide my sample in three periods and analyze the rst and

the last subsample. The elasticities estimated using the rst subsample are closer to the ones found for

other countries and in meta-analysis studies, being consistent with the idea that both fuels are not close

substitutes at the initial period of my sample. The results found using the last subsample suggest a

completely dierent scenario. Although we cannot interpret such results as a causal relationship between

the introduction of ex-fuel automobiles and more elastic consumers, we can interpret these results as

evidence that this new technology may have had an impact over consumers' behavior.

1 Introduction

Most papers in the demand for fuel literature, especially those which use Brazilian data, assume that fuel

prices are exogenous with respect to aggregate gasoline demand shocks.1 Not taking into account price

endogeneity might lead to biased estimates if there is simultaneity between the supply and demand equations.

While an increase in the price of gasoline reduces consumption, it is also plausible that rms respond to

negative changes in demand by lowering prices. If this is true, the estimated impact of gasoline price over

demand will be mitigated by the second channel. The same is true for ethanol price. An increase of ethanol

price raises gasoline consumption, which in turn reduces ethanol price by reducing its demand. The estimated

eect of ethanol price over gasoline demand will be once more attenuated by the reverse causation.

In this paper, I follow Engle and Granger two stage estimation to calculate the price elasticity of demand

for gasoline in Brazil. I use panel data and allow for price endogeneity. The use of panel data is important

to control for unobserved time-invariant heterogeneity among the Brazilian states.2 To control for price

endogeneity, I combine dierent identication strategies. Consistent with the negative bias in demand

estimation, mine estimates are consistently larger in magnitude than the ones found earlier.

1See Alves, Denisard. C. O. and Bueno, Rodrigo de Losso S. (2003) and Santos, Gervásio F (2012). Both papers estimate

price elasticity of gasoline demand in Brazil assuming price exogeneity. Alves and Bueno (2003) is the most cited article in the

Brazilian literature and Santos (2012) is the article that comes closest to mine as it uses a panel cointegration approach.

2See Phillips, Peter C.B. and Moon, Hyungsik R. (2000) for an overview about nonstationary panel data and some empirical

applications.

1
Figure 1: A comparison between the international oil price and gasoline price in Brazil (in real terms)

Note: To compare easily with the price of gasoline in Brazil, the international crude oil price, originally in

Dollars per barrel, was converted to Real per liter.

There is a growing literature, especially for the United States, that allow for endogenous price in the

aggregate demand curve.3 Usually, the identication approach used in these articles is Instrumental Variable

(IV), with most instruments associated with the international oil market.4 However, the Brazilian fuel market

is dierent from other fuel markets in the world. Due to government intervention in the renery section,

gasoline price to consumers do not follow the international oil price as can be seen in Figure 1. Thus, it seems

that using petroleum market variables as instruments will not solve the endogeneity problem in Brazil's case.

In this study, I use as instruments for gasoline and ethanol prices the federal tax rate over gasoline and

the total recoverable sugar price respectively. The federal tax over gasoline, known as CIDE - Contribution

for Intervention in the Economic Domain - was introduced in Brazil in 20015 with the aim of raising funds

to nance infrastructure projects. In practice, however, this tax has been used by the Federal Government

as a means to control price. The tax rate is often reduced following a gasoline price hike at the renery

level to avoid increases in prices at gas stations. Over the past eleven years, the tax rate has been reduced

from 0.50 R$/liter of gasoline to 0 R$/liter, conrming that the initial aim of this tax was replaced by its

practical goal and that changes in this rate are not motivated by changes in the demand for gasoline, as can

be seen in Figure 2.

An equivalent tax for ethanol exists in Brazil, but since April 2004 the tax rate is set to zero. Therefore,

since the data set used in this study begins in December 2002, there is not enough variation to use this tax as

an instrument. Instead, I use the total recoverable sugar price. This is the reference price of sugarcane, the

main component of Brazilian-produced ethanol. It is an important factor in the cost of ethanol but should

be otherwise unrelated to the gasoline market.

3See Ramsey, J.; Raasche, R. and Allen, B. (1975), Dahl, Carol A. (1979), Davis, Lucas W. and Killian, Lutz (2011), Liu,

Weiwei (2011) and Scott, K. Rebecca (2012).

4For papers that use variables associate to the oil international market as instrument for gasoline price see Ramsey et al

(1975), Dahl (1979), Hughes, Jonathan E.; Knittel, Christopher R. and Sperling, Daniel (2008), Coyle, David; DeBacker, J.

and Prisinzano, R (2012) , Scott (2012) and Burke, Paul J. and Nishitateno, Shuhei (2013).

5Law 10.336/01.

2
0

200

400

600

800

1000

1200

1400

1600

1800

0

5

10

15

20

25

30

35

40

Nov2002

Mar2003

Jul2003

Nov2003

Mar2004

Jul2004

Nov2004

Mar2005

Jul2005

Nov2005

Mar2006

Jul2006

Nov2006

Mar2007

Jul2007

Nov2007

Mar2008

Jul2008

Nov2008

Mar2009

Jul2009

Nov2009

Mar2010

Jul2010

Nov2010

Mar2011

Jul2011

Nov2011

Mar2012

Jul2012

Nov2012

CIDE rates (R$/ m3)

Gasoline consumption (m3) x 100000

Gasoline consumption

CIDE (jan 2013 = 100)

Figure 2: Gasoline consumption in Brazil and the federal tax over gasoline, CIDE.

3
Price elasticity of gasoline demand in Brazil

Period covered Own price elasticity Cross price elasticity

Alves and Bueno (2003) 1973-1998 -0.46 0.48

Pinto Jr et al (2006) 07.2001 - 06.2006 -0.14 0.18

Nappo (2007) 08.1994 - 07.2006 -0.19 -

Santos (2013) 07.2001 - 12.2010 -1.18 0.29

My estimates 12.2002 - 01.2013 -1.68 0.73

Table 1: Price elasticity of gasoline demand for Brazil in the long run.

Along with IV, I use some cointegration techniques as identication strategy. As most series of my

database is non-stationary, I follow Stock, James H. and Watson, Mark W (1993) and use Dynamic Ordinary

Least Square (DOLS). Following this strategy, I found that consumers are more elastic to price than earlier

studies suggest. Table 1 shows some long-run price elasticities estimated in previously articles for Brazil and

in the last row I show the estimates obtained in this study.

Naturally, the Brazilian fuel market changed over the years, so comparisons should be done with care. One

of the most important changes occurred in March 2003. The introduction of the ex-fuel automobiles changed

the relationship between gasoline and ethanol and the proximity of both fuels probably changed consumers'

perception over price variation. It is reasonable to think that, if both fuels become more substitutable by one

another, the cross-price elasticity should increase. I explicitly test this hypothesis and nd some evidence

that the introduction of this technology has indeed changed consumers' behavior. When I divide my sample

and compare the results for the rst years of the 2000's with those for the most recent period, it seems

that gasoline demand became more elastic to price variation. For sure, I cannot rule out the existence

of confounding factors, but I believe that the results found should be interpreted as a suggestion that

something has changed and that a possible explanation for this is the large presence of ex-fuel automobiles

in the Brazilian market in the last few years.

The remainder of the paper is organized as follows. In Section 2, I present a brief discussion about the

choice of instrumental variables. In Section 3 the estimation and identication strategies are described in

detail. Section 4 presents the price elasticities and the gasoline demand impulse responses. In Section 5,

I look for evidences that ex-fuel automobiles changed consumers' elasticities and, nally, in Section 6, I

present a brief synopsis of the results found in this study.

2 Fuel price endogeneity and the choice of instrumental variables

Most papers that allow for price endogeneity use IV for controlling for simultaneity bias. Ramsey, Raasche

and Allen (1975) and Dahl (1979), for example, use as instruments for gasoline price the price of other

products derived from petroleum, such as kerosene and heavy fuel oil. However, it is possible that those

prices are correlated with gasoline demand shocks through shocks in the petroleum market. If this is true,

than the orthogonality restriction is violated and those instruments are no longer valid.

Yatchew, Adonis and No, Joungyeo A. (2001) and Manzan, Sebastiano and Zerom, Dawit (2008) use

regional dummies as instrument for gasoline price. However, it is possible that the exclusion restriction be

once more violated because of the possible correlation between the dummies and the gasoline consumption

of that region through, for example, the state size and the level of development.

Burke and Nishitateno (2013), Coyle et al. (2012) and Scott (2012) use as instrument proven oil reserves,

oil supply shocks and international oil price respectively. Once more the validity of these instruments depends

on the non-correlation among the gasoline demand shocks.

Besides international oil price shock, Scott (2012) uses gasoline federal and state taxes as instruments.

Davis and Killian (2011) also use gasoline taxes rate, but they consider its nominal variation over time as

instrument. Assuming that gasoline taxes rates are not directly correlated with gasoline demand, they seem

more appropriate to the Brazilian context than oil market variables.

Liu (2011) uses an average of the gasoline regional prices excluding neighboring regions as instrument.

The validity of this strategy depends on the non-correlation among the gasoline demand shocks in the states.

Even though taking into account price endogeneity, Liu (2011) argues that the endogenous part of price

4
would represent only a small part of its variation, being therefore insignicant to the price total variation.

This argument is used to justify the similar results obtained by the author when using Ordinary Least Square

(OLS) and Two Stage Least Square (2SLS).

A similar argument could be developed for Brazil since the gasoline sold by producers, mainly Petrobras,

to distributors is controlled by the government. So, indeed, we also have a signicant exogenous component

in the nal gasoline price. However, the results obtained in this study show important dierences between

OLS and the methodology used taking into account endogeneity.

All in all, nding a good identication strategy has been a challenge in this literature. Instrumental

Variables is the most common approach, but nding a valid instrument has been a hard task. To contribute

to this literature, I combine two identication strategies. Taking into account the non-stationarity of most

series allows me to use DOLS for controlling for gasoline price endogeneity. However, as ethanol price is

stationary and in the absence of natural experiments, I still use an instrumental variable to identify its

parameter. I also use the panel structure of the data to control for time-invariant heterogeneity among

Brazilian states.

3 Methodology

3.1 Data

In this study, I use data from dierent sources. From the National Petroleum, Natural Gas and Biofuel

Agency (ANP), I get data on gasoline consumption and gasoline and ethanol prices. Both gasoline and

ethanol refers to the fuels sold in gas stations. ANP collects data over consumption and price in gas stations

over dierent states of Brazil and provide state-level averages. The fuel prices are converted to constant

January 2013 Reais using the ocial consumer price index, IPCA, obtained from the Brazilian Institute of

Geography and Statistics (IBGE).

The automobile eet is collected from the National Trac Department (Denatran). As I do not have

an income measure for each state, I follow the literature and use as proxy electric power consumption. The

data is available from Eletrobras.

Regarding my instruments, the federal tax rates over gasoline, CIDE is obtained from the Brazilian

legislation and the total recoverable sugar price is obtained from the Producers Council of Sugarcane, Sugar

and Ethanol of the state of São Paulo (Consecana/SP). From now on, to simplify the notation, I am going

to refer to the total recoverable sugar price as sugar price. Both instruments are deated by IPCA.

Due to the availability of data on automobile eet, the data set used in this study covers the period from

December 2002 to January 2013. To control for unobserved time-invariant heterogeneity across the 27 states

of Brazil, I use state xed eects in all regressions. In total, I have 3,294 observations.

The data set just described is far from ideal. As mentioned earlier, I do not have an income measure for

each state so, following the literature, I use electric power consumption as a proxy. However, the data is

available only at the regional level, not the state level (there are ve regions in Brazil). In all specications

and also when estimating the condence intervals of the impulse response functions, we report cluster-robust

standard errors to account for this dependence within regions for part of the data.

To try to overcome this limitation and as a robustness check, I use banking and trade information as

income proxy. These data are available for each Brazilian state and are provided by the Central Bank of

Brazil and the Ministry of Development, Industry and Foreign Trade respectively. In the Appendix , I show

that the results are robust to the specic income proxy.

Regarding my instruments, the limitation is that they only vary at the national level. However, as long

as the endogenous component in price is common to all states, the time-series variation in the instruments

is sucient to eliminate the endogeneity bias.

Another aspect of my database refers to the process of each series. Except for ethanol and sugar prices,

all series are non-stationary.6 Even not having all series integrated of order one, it is still possible, according

to Lutkepohl, Helmut (2007), to have cointegrated series. In fact, statistics tests corroborate this.7

6The unit root tests were done in Eviews 7, considering a model with constant. The tests that were done were: Levin, Lin

and Chu; Im, Pesaran and Shin; ADF-Fisher and PP-Fisher.

7The panel cointegration tests were also done in Eviews 7. The tests done were: Kao and Pedroni. For Kao and Pedroni,

the null hypothesis of no cointegration was rejected.

5
Variable Cross-section Source Process level

Gasoline consumption (million liters) State ANP Non-stationary

Gasoline price (R$/liter) State ANP Non-stationary

Ethanol price (R$/liter) State ANP Stationary

Electric power consumption (GWh) Region Eletrobras Non-stationary

Automobile eet (unity) State Denatran Non-stationary

CIDE over gasoline (R$/liter) Federal Brazilian legislation Non-stationary

Sugar price (R$/liter) São Paulo Consecana/SP Stationary

Table 2: Database description

By assumption, the cointegration relationship among the variables in this study is unique and given

by economic theory. I assume that the equilibrium relationship represents the long-run demand curve for

gasoline and that deviations from this equilibrium are accompanied by responses in the supply side. Without

this hypothesis, the model would not be identied and we could not interpret the cointegration relationship

as a structural relationship.

As most series are non-stationary, the estimation strategy is based on Engle and Granger (1987) two

stage estimation. In both stages, the interest of this study lies on the gasoline aggregate demand curve.

3.2 Description of the model and the identication strategy

The estimation of the causal eect of gasoline and ethanol prices over gasoline demand is done in two

stages. For each stage an identication strategy is need. In the rst stage, I estimate the cointegration

relationship by combining two identication strategies: IV and DOLS. In the second stage, to estimate the

short run dynamics I use a non-recursive identication method, known as A-Model. To better understand

the identication approach used in this paper, I rst describe some theoretical points that are important to

the empirical analysis in both stages.

First, following the economic theory, I assume that the gasoline aggregate demand curve in Brazil is a

function of price, income and automobile eet. I also allow for state and seasonal variation.

Demandgasoline = fg (pricegasoline, priceethanol, income, fleet, state, month) (1)

Dierently from other countries, we do not expect that the automobile eet elasticity of gasoline demand

equals one since most automobiles sold in Brazil is ex-fuel. Since gasoline market share equals 60-70 percent,

we should expect an elasticity close to these numbers. Therefore, I do not consider as dependent variable

the ratio between gasoline demand and automobile eet as some papers do (Baltagi, Badi H. and Grin,

James M., 1983).

If I followed the early papers which use Brazilian data, I could estimate Equation 1 by OLS since the

series are cointegrated. However, allowing endogeneity of both prices implies that the OLS estimates will be

confounded by the reverse causality between the quantity demanded and the fuel prices. So, to obtain the

causal eect of a price change over gasoline demand, we need to identify the gasoline demand curve.

Although I combine dierent identication strategies, I still need one instrument for each endogenous

variable. In the rst stage, I use the IV approach to control for ethanol price endogeneity and in the second

stage I need two instruments to control for both gasoline and ethanol prices endogeneity.

So, as an attempt to obtain an instrument for both fuel prices, I look at the equation of price formation.

P ricej = gj (production costsj , taxes, Xj ), j = gasoline, ethanol (2)

Where Xj refers to other variables such as shipping and margins.

From Equation 2, I chose to use the federal tax, CIDE, as an instrument for gasoline price. The only

channel through which this tax aects gasoline demand is through gasoline price, satisfying thereby the

exclusion restriction.

6
For the ethanol price, as mentioned earlier, the federal tax CIDE over ethanol has hardly changed during

the study period. So, as an attempt to nd a good instrument for the ethanol price, I turn my attention to

the production costs.

I chose to use the Total Recoverable Sugar price which refers to the quantity of sugar present in the

sugar cane. This is a reference price for the payment to sugar cane producers by mills. It is available for the

state of São Paulo which responds for, approximately, 60% of total sugar cane production in Brazil. As with

the CIDE, the only channel through which the sugar price aects gasoline demand is through fuel prices,

satisfying thereby the exclusion restriction.

At this point, it is important to mention that, among other things, sugar price might be a function of

ethanol price. This reverse causality, however, does not impose a problem since our interest lies on the

correlation between ethanol and sugar prices.

P ricesugar = gsugar (priceethanol, Xsugar) (3)

To complete the description of the model, I assume that income is exogenous to the gasoline market and

that the automobile eet is a function of fuel prices and income.

Fleet = gf leet (pricegasoline, priceethanolincome) (4)

Having described the theoretical basis, I now detail the empirical procedures.

In the rst stage, I estimate an equilibrium relationship. I follow the literature and assume that the

aggregate demand curve can be described by a log-log model:

lcgit = αi + γm + β12 · lpgit + β13 · lpahit + β14 · lyit + β15 · lfleetit + uit (5)

Where αi and γm are the state and month xed eects respectively; lcgit is the log of gasoline consumption

in state i and month t; lpgit is the log of gasoline price in state i and month t; lpahit is the log of ethanol price

in state i and month t; and lyit and lfleetit are, respectively, the log of income and the log of automobile

eet in state i and month t.

My interest lies in β12 and β13 and in obtaining the log-run deviation so I can use it in the second stage.

The coecients β12 and β13, once identied, can be interpreted as price elasticities. So, ceteris paribus, those

parameters give the percentage gasoline demand variation in response to a 1 percent increase in fuel prices.

The identication strategy in this rst stage combines IV with DOLS. As gasoline price is non-stationary,

I use DOLS to control for its endogeneity and for a possible autocorrelation. This strategy can be thought

as a control function. To gain some intuition, we can rewrite Equation 5 as:

lcgit = αi + γm + β13 · lpahit + Xit · β + uit (6)

Where Xit is a vector with all non-stationary and integrated of order one variables. We can write Xit as:

Xit = Xit−1 + vt (7)

Because I do not assume that the error terms of Equations 6 and 7 are independent and identically

distributed, the linear projection of u on v, dierently from the standard control function, must take into

account not onlyvit, but δ(L) · vit, where δ(L) = ΣK

k=−Kδk · L

k

. Substituting the linear projection into

Equation 6, we get:

lcgit = αi + γm + β13 · lpahit + Xit · β + ΣK

k=−Kδk · 4Xit−k + it (8)

Equation 8, however, is not completely identied. We need yet to control for ethanol price endogeneity.

Here, I follow the literature and use an IV approach. The instrument for the ethanol price is the sugar price

as already discussed.

7
From the estimation of Equation 8, we obtain the long-run elasticities and the equilibrium deviation

which will be used in the second stage. In this stage, I estimate a Vector Error Correction (VEC) model to

obtain the short run dynamics and calculate the impulse response functions.

To deal with the panel structure of my database, I follow Holz-Eakin, Douglas; Newey, Whitney and

Rosen, Harvey S (1988) and rewrite the series as: Yt = (Y

0

1t

, Y 0

2t

, . . . , Y 0

27t

)

0

. Then, by reorganizing the

regressor matrix, it is possible to identify all parameters of the gasoline demand equation. The model can

be described as:

4Yt = c · Dt + α · uˆt−1 + Σp−1

j=1Γj · 4Yt−j + ξt (9)

Where Yt is a K × 1 vector with all variables used in this model8, Dt refers to the deterministic terms

and uˆt−1 is the long-run deviation estimated in the rst stage.

Yt = (lcg, lpg, lpah, ly, lfleet, cide, lpsugar)

0

Following, I use the VEC estimates to construct a structural VAR model, enabling me to calculate impulse

response functions. I use the Schwarz Information Criterion to select the order of the VAR, which is set to

two. Finally, to obtain meaningful impulse response functions, it is necessary to obtain a structural model,

as presented in Equation 6.

A · Yt = c · Dt + A · Yt−1 + A · Yt−2 + wt (10)

The identication strategy used in this stage corresponds to the non-recursive identication, known as

A-Model. The idea is to restrict the contemporaneous relationship among variables by restricting some

elements of the matrix A. The restrictions follow the model structure presented at the beginning of this

section and both instruments are needed here.





















1 a12 a13 a14 a15 a16 a17

a21 1 a23 0 0 a26 a27

0 a32 1 a34 a35 a36 0

0 0 0 1 0 0 0

0 a52 a53 a54 1 0 0

0 0 a63 0 0 1 0

0 0 0 0 0 0 1





















·





















lcgt

lpgt

lpaht

lyt

lfleett

lsugart

cidet





















(11)

For example, the restrictions impose in the rst line represent the exclusion restrictions. This rst line

indicates that contemporaneous shocks in all variables, except the instruments, can aect gasoline consumption. On the second line, we impose that the price of gasoline can respond to all variables contemporaneously,

except eet and income. Such constraints imposed over A satisfy both the order and rank conditions.

Regarding the order condition, to solve uniquely for A we need a total of (K · (K + 1))/2 restrictions.

Because I choose the diagonal elements of A to be unity, we are left to a total of (K ·(K −1))/2 restrictions.

As it happens, based on the model described above, I have 26 restrictions on A, more than enough to identify

the remaining parameters.

The order condition, however, is not a sucient condition for identication. To verify the rank condition,

I follow Lutkepohl (2007) and calculate the rank of the matrix below and test if it equals K2 ×

1

2

·K ·(K + 1).

If not, the model is not identied.





−2 · D

+

k

·



Σu · A−1



D

+

k

·



A−1 ⊗ A−1



· D

+

k

CA 0

0 Cσ



 (12)

8As, since 2012, the federal tax rate over gasoline is zero, I do not use the log of this variable.

8
Dependent variable Ethanol price

Sugar price 0.312***

(0.049)

Gasoline price 0.630***

(0.164)

Income -0.055

(0.463)

Automobile eet -0.038

(0.130)

Controls: leads and lags? Yes

State and month dummies included? Yes

F statistic [p-value] 70.85 [0.001]

R2 0.805

No.of obs. 3,213

Table 3: 2SLS First-stage result: cointegration relationship.

Notes: Cluster-robust standard errors are in parentheses. Due to income aggregation, I am clustering on

Brazilian's regions. Following, Cameron, A. Colin; Gelbach, Jonah B. and Miller, Douglas L (2008), I

use wild cluster bootstrapped standard errors. Controls refer to the leads and lags of the rst-dierences

introduced in the regression for controlling gasoline price endogeneity.

In the matrix above, Σu is the covariance matrix of the reduced form, Dk is a (K2 ×

1

2

· K · (K + 1))

duplication matrix, D

+

k ≡



D

0

k

· Dk

−1

· D

0

k

, CA is a (

1

2

· K · (K + 1) × K2) selection matrix which selects

the elements of vec (A), Cσ is a (

1

2

· K ·(K − 1) ×

1

2

· K ·(K + 1)) selection matrix which selects the elements

of vech(Σw) below the main diagonal.

4 Empirical results

The results presented in Table 3 suggest that the price of sugar is a good instrument for the price of ethanol.

Both variables are strongly correlated and the F-statistic of the rst stage equals 70.85.

As can be seen in Table 6, controlling for endogeneity results in larger estimates when compared with

the parameters obtained via OLS. Column 1 does not take into account price endogeneity and indicates that

the eect of gasoline and ethanol price over gasoline consumption is, respectively, -1.35 percent and 0.39

percent. When controlling for price endogeneity, the coecient increases by, approximately, 0.3 percentage

points in magnitude. An increase of 1 percent of gasoline price, ceteris paribus, reduces gasoline demand by

1.67 percent and an increase of 1 percent of ethanol price, raises gasoline consumption by 0.74 percent. The

price estimates in Table 6 are therefore consistent with the hypothesis that the OLS estimates are downward

biased.

Still in Table 4, income and automobile eet estimates are not statistically dierent from zero. One

possible explanation for that result is the high correlation between income and automobile eet which do

not allow estimating both precisely. As a robustness exercise, I omit one of those variables and re-estimate

the equilibrium relationship. The results are presented in Columns 3 and 4. When omitting either income or

automobile eet, the other variable becomes statistically signicant meaning that highly correlation variables

may be a good explanation. Nonetheless, omitting one of those variables introduces an omitted variable bias,

since automobile eet is a function of income and fuel prices. So, although I cannot estimate precisely income

and automobile eet elasticity, my preferred regression is the one presented in Column 2.

The results presented so far consider a long-run equilibrium relationship among the variables. So, when

we change one variable, all other controls remain constant. Another way to study the dynamics of the fuel

market is to analyze impulse response. In this context, we allow all variables to react after the occurrence

of an exogenous shock in one of them.

I rst discuss impulse responses in the VAR model, meaning that the shocks are temporary and displaying

the demand response in level. Following, I use the SVEC model to obtain the impulse responses. In that

9
Dependent variable Gasoline demand

OLS DOLS/2SLS

(1) (2) (3) (4)

Gasoline price -1.346*** -1.668*** -1.937*** -2.214***

(0.164) (0.234) (0.353) (0.227)

Ethanol price 0.393*** 0.737*** 0.911*** 1.028***

(0.108) (0.179) (0.143) (0.096)

Income 0.829 0.726* 0.713***

(0.360) (0.502) (0.168)

Automobile eet 0.159 0.190 0.460***

(0.119) (0.151) (0.110)

Controls: lead ans lags? No Yes Yes Yes

State and month dummies included? Yes Yes Yes Yes

R2 0.805

No. of obs. 3,294 3,213 3,051 3,213

Table 4: Gasoline demand in Brazil: equilibrium relationship.

Notes: Cluster-robust standard errors are in parentheses. To calculate the standard errors for the IV

regressions, I use wild cluster (unrestricted) bootstrap following Davidson, Russell and MacKinnon, James

G. (2010). Except for Column 3, I am clustering on Brazilian's regions due to income aggregation. In Column

3, I am clustering on Brazilian's states. Controls refer to the leads and lags of the rst-dierences introduced

in the regression for controlling gasoline price endogeneity. According to the Information Criterion AIC, HQ

and BIC, the optimal number of leads and lags in Column 2 and 4 is one and in Column 3, four.

case, a shock in the rst dierence is equivalent to a permanent shock in level and I display the response of

the rst dierence of gasoline demand.

The responses to temporary exogenous shocks are presented in Figure 3. The results are in accordance

with economic theory. In Panel A, a negative gasoline supply shock immediately reduces gasoline consumption in, approximately, 0.3 percent. Because of the non-stationary nature of gasoline demand, temporary

shocks have a permanent eect. So, the results suggest that a 1 percent temporary increase in gasoline price

will reduce gasoline consumption permanently in 0.4 percent. In Panel B, we study the response of gasoline

consumption to an exogenous increase in ethanol prices. As we do not study ethanol demand, this can be

interpreted either as a supply or demand shock, as long as it has no direct eects over the gasoline market

except via ethanol prices. Although not statistically signicant at the beginning, it seems that a temporary

shock in the ethanol market raises gasoline demand permanently by 0.2 percent approximately.

To estimate the impulse responses of the rst dierence of gasoline demand I rearrange the structural

VAR in order to obtain the structural VEC. The responses to an exogenous shocks based on the variable in

rst dierence are presented in Figure 4. The result suggests that the magnitude of the short-run responses

is, approximately, 0.17 percent in both cases. The impact of an exogenous shock in ethanol market seems

to be quicker than a negative gasoline supply shock. In both situations, the eects of the shocks after four

months are negligible.

Note that the impulse response analysis show a smaller eect than the elasticity we obtained in the rst

stage. This is because, in the rst stage, we study a long-run demand response while holding all other

variables xed. The impulse response analysis allows all other variables to adjust to the initial shock. For

instance, ethanol suppliers can respond to negative shocks in gasoline supply by raising prices as well, thus

dampening the reduction in gasoline demand caused by substitution to ethanol. Each result provides a

dierent perspective regarding public policies.

5 Price-elasticity and the ex-fuel automobiles

To study how the presence of ex-fuel automobiles in Brazilian market can change the price elasticities of

gasoline demand, I divide my sample in three periods. My goal is to compare the estimates for the rst

period, from 12.2002 to 12.2006, to the last one, from 12.2008 to 12.2012. In Figure 5, I show that the

10
Figure 3: Gasoline demand impulse responses to exogenous shocks.

Note: Wild cluster bootstrap condence interval with Rademacher weight and 100 simulations (Cameron,

Gelbach and Miller, 2008).

Figure 4: Gasoline demand impulse responses to exogenous shocks  SVECM.

Note: Wild cluster bootstrap condence interval with Rademacher weight and 100 simulations. (Cameron,

Gelbach and Miller, 2008).

11
Figure 5: Licensing of new automobiles by fuel type in Brazil (Anfavea, 2013).

choice of both periods is not arbitrary. The initial subsample can be interpreted as a transition period,

while the nal subsample represents the consolidation of ex-fuel automobiles in Brazilian's market. For

each subsample, I re-estimate the rst stage of my procedure, where I combine IV with DOLS. The results

are presented in Table 5.

The price elasticity of gasoline demand has increased over time, suggesting that the introduction of exfuel automobiles allowed consumers' demand to be more elastic to price change. Column 1 presents the

estimates for the initial period. An increase of 1 percent of gasoline price, ceteris paribus, reduces gasoline

consumption by 0.51 percent. It is interesting to note that such elasticity is near elasticities calculated for

other countries and found in meta-analysis studies. Also in the initial period, it seems that ethanol price

is not important for explaining gasoline demand variation, which is consistent with the idea that both fuels

are not close substitutes in this subsample. Regarding the nal period, Column 2 shows that consumers are

more elastic to gasoline price variation and that ethanol price become statistically signicant. Although we

cannot interpret such results as a causal relationship between the introduction of ex-fuel automobiles and

more elastic consumers, we can interpret these results as evidence that this new technology may have had an

impact over consumers' behavior. To get more precise results we would need to control for other potential

confounding factors not captured by income or automobile eet that might have changed the aggregate

gasoline consumption function from one period to another.

6 Conclusion

Dierently from most papers that use Brazilian data, I estimate price elasticity of demand for gasoline taking

price endogeneity into account. Combining dierent identication strategies, I nd that consumers are more

elastic to price variation than earlier studies suggest.

In this study, I also analyze the behavior of gasoline demand in the face of exogenous shocks through

impulse responses analysis. The results found suggest that the eects of temporary shocks on gasoline

demand are permanent and statistically signicant.

To better understand price elasticity of gasoline demand, I divide my sample to search for evidences

that ex-fuel automobiles changed consumes' behavior. Although we cannot interpret the results found as a

12
Dependent variable Gasoline demand

12.2002 - 12.2006 12.2008 - 12.2012

Gasoline price -0.509*** -0.994***

(0.228) (0.152)

Ethanol price -0.019 0.577***

(0.141) (0.133)

Income 0.921*** 0.351***

(0.159) (0.102)

Automobile eet -0.002 1.004***

(0.016) (0.168)

Controls: leads and lags? Yes Yes

State and month dummies included? Yes Yes

No. of obs. 1,206 1,206

Table 5: Additional exercise - Gasoline demand in Brazil: equilibrium relationship.

Notes: Cluster-robust standard errors are in parentheses. To calculate the standard errors for the IV

regressions, I use wild cluster (unrestricted) bootstrap following Davidson, Russell and MacKinnon, James

G. (2010). I am clustering on Brazilian's regions due to income aggregation. Controls refer to the leads and

lags of the rst-dierences introduced in the regression for controlling gasoline price endogeneity.

causal relationship between the introduction of ex-fuel automobiles and more elastic consumers, the results

suggest that ex-fuel automobiles had indeed an impact over price elasticity.

All in all, this study suggests that Brazilian consumers react to gasoline and ethanol price shocks more

than initially thought which can be of paramount importance for the development of public policies in Brazil.

References

[1] Alves, Denisard. C. O. and Bueno, Rodrigo de Losso S. Short-run, long-run and cross elasticities of

gasoline demand in Brazil. Energy Economics, March 2003, 25, pp. 191-99.

[2] Baltagi, Badi H. and Grin, James M. Gasoline demand in the OECD: an application of poolling and

testing procedures. European Economic Review, 1983, 22, pp. 117-37.

[3] Burke, Paul J. and Nishitateno, Shuhei. Gasoline prices, gasoline consumption, and new-vehicle fuel

economy: Evidence for a large sample of countries. Energy Economics, March 2013, 36, pp. 363-70.

[4] Cameron, A. Colin; Gelbach, Jonah B. and Miller, Douglas L. Bootstrap-Based Improvements for

Inference with Clustered Errors. Review of Economics and Statistics, August 2008, 90 (3), pp. 414-27.

[5] Coyle, David; DeBacker, J. and Prisinzano, R. Estimating the supply and demand of gasoline using

tax data. Energy Economics, January 2012, 34, pp. 195200.

[6] Dahl, Carol A. Consumer adjustment to a gasoline tax. Review of Economics and Statistics, August

1979, 63 (3), pp. 427-32.

[7] Davidson, Russell and MacKinnon, James G. Wild bootstrap tests for IV regression. Journal of Business and Economic Statistics, 2010, 28(1), pp. 128-44.

[8] Davis, Lucas W. and Killian, Lutz. Estimating the eect of gasoline tax on carbon emissions. Journal

of Applied Econometrics, November/December 2011, 26, pp. 1187-214.

[9] Engle, Robert F. and Granger, C. W. J. Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica, March 1987, 55 (2), pp. 251-76.

[10] Holz-Eakin, Douglas; Newey, Whitney and Rosen, Harvey S. Estimating Vector Autoregressions with

Panel Data. Econometrica, November 1988, 56 (6), pp. 1371-95.

13
[11] Hughes, Jonathan E.; Knittel, Christopher R. and Sperling, Daniel. Evidence of a shift in the short-run

price elasticity of gasoline demand. The Energy Journal, 2008, 29 (1), pp. 93-114.

[12] Liu, Weiwei. Modelling gasoline demand in the United States: a exible semiparametric approach.

Job market paper, State University of New York at Binghamton, 2011.

[13] Lutkepohl, Helmut. New introduction to multiple time series analysis. Springer, 2007.

[14] Manzan, Sebastiano and Zerom, Dawit. A semiparametric analysis of gasoline demand in the United

States reexamining the impact of price. Econometric Reviews, 2010, 29 (4), pp. 439-68.

[15] Nappo, Márcio. Demanda por gasolina no Brasil: uma avaliação de suas elasticidades após a introdução

dos carros bicombustíveis. Master's thesis, Fundação Getúlio Vargas - EESP, 2007.

[16] Pinto Jr, Helder Q (Org). Matriz brasileira de combustíveis. Instituto de Economia da UFRJ e Núcleo de Assuntos Estratégicos da Presidência da República, 2006.

<http://www.biblioteca.presidencia.gov.br> cited 22 November 2013.

[17] Santos, Gervásio F. Fuel demand in Brazil in a dynamic panel data approach. Energy Economics,

March 2013, 36, pp. 229-40.

[18] Scott, K. Rebecca. Rational habits in gasoline demand. Energy Economics, September 2012, 34, pp.

1713-23.

[19] Stock, James H. and Watson, Mark W. A simple estimator of cointegrating vectors in higher order

integrated systems. Econometric, July 1993, vol 61, pp. 783-820.

[20] Ramsey, J.; Raasche, R. and Allen, B. An analysis of the private and commercial demand for gasoline.

Review of Economics and Statistics, November 1975, 57 (4), pp. 502-7.

[21] Yatchew, Adonis and No, Joungyeo A. Household gasoline demand in Canada. Econometrica, November 2011, 69, pp. 1679-1709.

Appendix - Robustness check

Dierent income proxies

To obtain state level variation, I use banking and trade information as income proxy. The data are obtained

from the Central Bank of Brazil and the Ministry of Development, Industry and Foreign Trade respectively.

The results are shown in Table 6. In the rst Column, I show the results from the benchmark model. The

coecients estimated for the price of gasoline and ethanol and the automobile eet - shown in Columns 2

to 5 - do not diverge abruptly of the benchmark results, suggesting that the results are robust to dierent

income variables.

14
Dependent variable: Gasoline demand

(1) (2) (3) (4) (5)

Gasoline price -1.668*** -1.545*** -2.247*** -0.956*** -2.001***

(0.234) (0.223) (0.340) (0.219) (0.220)

Ethanol price 0.737*** 0.693*** 0.957*** 0.494*** 1.009***

(0.179) (0.101) (0.117) (0.087) (0.105)

Electric power 0.726*

(0.502)

No. bank agencies 0.702***

(0.129)

Bank deposits -0.022

(0.010)

Bank Loans 0.114***

(0.020)

Export 0.049

(0.015)

Import 0.064

(0.018)

Automobile eet 0.190 0.267* 0.300*** 0.182 0.225

(0.151) (0.116) (0.139) (0.106) (0.111)

Controls: leads and lags? No Yes Yes Yes Yes

State and month dummies? Yes Yes Yes Yes Yes

No. of obs. 3,213 3,051 3,161 2,889 2,378

Table 6: Gasoline demand function with dierent income proxies.

Note: Cluster-robust standard errors are in parentheses. To calculate the standard errors for the IV regressions, I use wild cluster (unrestricted) bootstrap following Davidson and MacKinnon (2010). Except for the

rst column, I am clustering on Brazilian's states. Controls refer to the leads and lags of the rst-dierences

introduced in the regression for controlling gasoline price endogeneity. Indeed, the number of observation

diers due to the number of leads and lags introduced in each model.

15