# 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 ethanolprices 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.

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

1Figure 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 2001 5 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.

3 See 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). 4 For 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). 5 Law 10.336/01.

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

3Price 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

4would 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

6 The 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. 7 The 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.

5Variable 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 = f g (price gasoline , price ethanol , 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, X j ) , j = gasoline, ethanol (2)

Where X

j 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.

6For 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 rice sugar = gsugar (price ethanol , 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 (price gasoline , price ethanol income ) (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 = α i + γm + β 12 · lpgit + β 13 · lpah it + β 14 · lyit + β 15 · lfleet it + u it (5)

Where α i 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 ; lpah it is the log of ethanol price in state i and month t ; and lyit and lfleet it are, respectively, the log of income and the log of automobile eet in state i and month t

. My interest lies in β 12 and β 13 and in obtaining the log-run deviation so I can use it in the second stage. The coecients β 12 and β 13 , 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 = α i + γm + β 13 · lpah it + Xit · β + u it (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 ) = Σ K k =
− K δk · L k

. Substituting the linear projection into Equation 6, we get:

lcgit = α i + γm + β 13 · lpah it + Xit · β + Σ K k =
− K δk · 4 Xit

− 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.

7From 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: Y t = ( Y 0

1 t , Y 0 2 t , . . . , 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:

4 Y t = c · Dt + α · ˆ

ut

− 1 + Σp

− 1

j =1 Γj · 4 Y

t

− j + ξt (9)

Where Y

t is a K × 1 vector with all variables used in this model 8
, Dt refers to the deterministic terms and ˆ ut

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

Y t = ( 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

· Y t = c · Dt + A · Y t

− 1 + A · Y

t

− 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 a 12 a 13 a 14 a 15 a 16 a 17
a 21 1 a 23 0 0 a 26 a 27 0 a 32 1 a 34 a 35 a 36 0 0 0 0 1 0 0 0 0 a 52 a 53 a 54 1 0 0 0 0 a 63 0 0 1 0 0 0 0 0 0 0 1 

         · 

         lcgt lpgt lpah t lyt lfleet t lsugart cide t 

         (11)

For example, the restrictions impose in the rst line represent the exclusion restrictions. This rst lineindicates 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 K 2 × 1 2 · K

· ( K + 1)

. If not, the model is not identied.   − 2

· D +

k · Σ u · A

− 1  D + k · A

− 1 ⊗ A

− 1 

· D + k C A 0 0 C σ 

 (12)

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

8Dependent 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, Σ u is the covariance matrix of the reduced form, D k is a ( K 2 × 1 2 · K

· ( K + 1)) duplication matrix, D + k ≡ D 0

k · D k  − 1

· D 0

k , C A is a ( 1

2 · K

· ( K + 1) × K 2 ) selection matrix which selects
the elements of vec ( A) , C σ is a ( 1

2 · K

· ( K

− 1) × 1 2 · K

· ( K + 1)) selection matrix which selects the elements of vech (Σ w ) 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

9Dependent 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 accordancewith 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

10Figure 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).

11Figure 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

12Dependent 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.



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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.

14Dependent 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