Demand for light fuels in Brazil: an approach using spatial panel data models

The need for changes in the current energy matrix is a reality due to the possibility of a shortage of fossil fuels and the environmental damage caused by emissions related to fossil fuel use. The correct prescription of public policies for energy markets depends on the knowledge of demand elasticities. Hence, the aim of this work was to estimate the main determinants of light fuel demands in Brazil. Dynamic and non-dynamic estimators were used


Introduction
The need for changes in the current energy matrix is a reality due to both the shortage of oil and the emissions caused by fossil fuel use.Although the news has indicated otherwise, more than 85% of the world's primary energy consumption still comes from fossil fuels and only 10% of primary energy is provided by renewable sources (BP, 2018).Even though the reserves-to-production ratio (R/P) has increased in the last years,1 in the medium and long terms, matrix diversity is still necessary.
This fi rst paragraph could have been written ten or twenty years ago with little adjustment to the percentages, so why did the new technologies take so long to attain larger shares of the energy market?Economic viability is the main problem of most energy alternatives.Some may present technology viability; however, their production is not economically viable due to high costs.At this point, Brazilian ethanol is already economically viable and used extensively in some states in Brazil.This is possible due to institutional arrangements including mandates and subsidies (CARDOSO et al., 2019) and a long tradition in research and private and public investments.Other reasons to consider Brazilian ethanol from sugarcane in the medium term are its advantages over other crops used for ethanol production: a better fossil energy balance, reduced CO2 emissions in comparison with gasoline and lower land intensity (GOLDEMBERG and GUARDABASSI, 2009;NARDY and GURGEL, 2013).Despite all these advantages, in many Brazilian states, the ethanol demand is constrained.This is due to large differences in relative prices across states (see Figure -1).In some of them, for example Roraima (RO), Amapá (AP) and Pará (PA), the relative price indicates that ethanol should be bought in less than 15% of months.
These differences, shown in Figure 1, indicate that the price ratio between ethanol and gasoline is not aleatory: space plays a role -and the use of a spatial econometrics framework to estimate the ethanol and gasoline demands in Brazil can be a solution.This choice will also allow the cross-section dependence (CD) in panel data to be controlled, which is a problem that the literature regarding fuels in Brazil has usually neglected.In addition to the common variables used to estimate light fuel demands (price and income), in the Brazilian market, 2 it is necessary to include the prices of the main alternative fuels (the ethanol price for the gasoline demand and the gasoline price for the ethanol demand).An extra variable named "fl eet" will therefore be added to consider the possible effects that an increase in the number of vehicles might have on the demand.Spatial non-dynamic and dynamic models will be estimated.For light fuel demands, dynamic models present some advantages: they add information for computing long-and short-run responses.
After this introduction, the paper presents a literature review about light fuels, followed by a section on the Brazilian market.Then, a methodology-related section explains the spatial models and the data set.Finally, the last two sections are dedicated to the results, discussion and conclusions.
2 In 2003, fl ex-fuel cars were introduced into the Brazilian market, which explains the need to include own prices and their main substitutes in the estimates of the demand for light fuels in Brazil.

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v.30 n.1 2020 Nova Economia� 2 Demand for light fuels A large number of studies worldwide dealing with the demand for light fuels have indicated gasoline as an inelastic good in the short and long runs, with long-run elasticity being higher than short-run elasticity.Fuels are considered to be "essential goods" in the short run, but the probability of substitution increases in the long run.The light fuel demand has invariably been modelled using price and income as explanatory variables (possible proxies for income are electricity consumption, industrial production and the GDP, as in RODRIGUES and BACCHI, 2016;RODRIGUES et al., 2018).Some studies, such as those by BURNQUIST and BACCHI (2002), CHEUNG and THOMSON (2004) and RAMANATHAN (1999), did not use other variables and estimated the demand using price and income only.Other common controls are the vehicles' characteristics, such as effi ciency, the price of new vehicles, credit availability (RODRIGUES and BACCHI, 2016) and the stock of vehicles (RODRIGUES et al., 2018).Table A (Appendix) presents many studies regarding the demand for light fuels in Brazil and other countries.The high variation among the estimated elasticities could be due to the models employed by the studies (BASSO and OUM, 2007), including the choice between static and dynamic models (BRONS et al., 2008;ESPEY, 1998), the data types used for the estimation (time series, cross-sectional or panel data) and the interval of data (monthly, quarterly or annual) (GOODWIN et al., 2004).
A large range of econometric techniques are used to estimate light fuels' demand.A survey by DAHL and STERNER (1991) 3 presented estimations using time series, two-and three-stage least squares, instrumental variables, panel data and other approaches.The range of results for price elasticity was (-0.12; -0.44) in the short run and (-0.23; -1.05) in the long run.The range of income elasticity was (0.14; 0.58) in the short run and (0.68; 1.31) in the long run.Another comprehensive survey is that by HUNTINGTON et al. (2019), which emphasized studies published after 2000, paying attention to the long-run responses to changes in income and prices.Most of the surveyed studies have shown that the price and income elasticities for liquid fuels are generally less than unity for many countries and sectors.Long-run income elasticity, however, can range widely by country between 0.24 and 1.75 while averaging 0.94 for all countries.
In the Brazilian market, BURNQUIST and BACCHI (2002) estimated the demand from 1973 to 1998 using time series (Table A).More recently, NAPPO (2007) used a co-integrated time series to model the gasoline demand.The gasoline price, income (per capita GDP), ethanol price and a dummy associated with the gasoline price starting in 2003 were used as explanatory variables.The results indicated that fl ex-fuel cars contributed to making the gasoline demand more elastic after 2003.The short-run elasticities estimated were -0.20 (before 2003) and -0.33 (after 2003).
SERIGATI et al. (2010) estimated the Brazilian ethanol demand and the sugar and ethanol supply, simultaneously, using 3SLS.The addition of sugar demand was justifi ed due to the possibility of shifting production from sugar to ethanol and vice versa.The results indicated that the demand for ethanol is price elastic, with elasticity around -1.2 (before 2003) and -2.0 (after 2003).The cross-price elasticity increased from 1.3 to 2.2 (all results for the short run).
RANDOW et al. (2010) estimated the long-run ethanol demand using co-integrated time series models.The variables used to estimate ethanol consumption were the ethanol price, gasoline price and GDP (income proxy).The results indicated very elastic long-run demands related to prices, with elasticities of -11.26 (price elasticity) and 12.79 (cross-price elasticity).The estimated income elasticity was 0.46.
Also making use of co-integrated time series models for the Brazilian ethanol market, FARINA et al. (2010) analysed the period from July 2001 to August 2009.Their results showed a price elasticity of -1.23 and a cross elasticity of 1.45, both for the short run.CARDOSO and BITTENCOURT (2012) and SANTOS (2013) estimated the Brazilian ethanol demand in the long and short runs using co-integrated panel data models.CARDOSO and BITTENCOURT's (2012) study resulted in ethanol price elasticities of -1.42 (short run) and -3.30 (long run), while SANTOS's (2013) elasticity estimates with respect to the ethanol price were around -1.52 (short run) and -8.45 (long run).Regarding the long-run elasticities, SANTOS (2013) indicated that the reported results were likely to be overestimated.
Although intensive research has been carried out, only one conference paper has reported the use of spatial econometrics to assess the Brazilian market.It was co-authored by SANTOS and FARIA (2012), and the ethanol and gasoline demands were estimated on a quarterly basis.The explanatory variables were the ethanol price, gasoline price and service trade tax as an income proxy.Here the dynamic estimators were used to aggregate short-run information for further analysis.ALMEIDA et al. (2016) used a linear approximation almost ideal demand system (LA-AIDS) with quarterly data from 2001 to 2015 to estimate the Marshallian and Hicksian demands for the state of Pernambuco (PE), Brazil, for ethanol, gasoline and diesel.Using seemingly unrelated regressions (SURs), the results were similar to the elasticities reported in the literature, with an inelastic price demand for gasoline and diesel, and close to unitary elasticity for the Marshallian ethanol price elasticity.
Using a vector autoregression (VAR) model, RODRIGUES and BAC-CHI (2016) identifi ed the main determinants of the demand for fuels used by the light-vehicle fl eet in Brazil between 2003 and 2013.The results showed that the income and price elasticities are not different from the estimates reported by the literature.The novelty was the importance of credit and car prices to the demand for transportation in Brazil.
In a recent study about the demand for vehicle fuels in Brazil, RO-DRIGUES et al. (2018) analysed the role of the asymmetric price response (APR) and underlying energy demand trend (UEDT) in the demand for automotive fuels in Brazil for the period 2001-2016.The authors determined that consumer responses to changes in prices are not linear, with high substitutability between gasoline and ethanol, and the demand for ethanol is more price elastic than the demand for gasoline in the short and long runs.
Finally, CARDOSO et al. (2019) estimated the own-price, cross-price and income elasticities of the demand for ethanol and gasoline for Brazil between 2001 and 2014.They used a novel instrumental variable approach to control for endogeneity between the supply and the demand, which is based on wholesale prices for gasoline, ethanol and diesel from non-adjacent states, to construct the instrumental variables.This study took into account regional and spatial features of the fuel market along with the role of fl ex-fuel cars.The results showed that, after the introduction of fl ex-fuel cars, the own-price elasticities for gasoline and ethanol increased.
Other recent studies have investigated other dimensions of the fuel market in Brazil.SALVINI et al. (2017), for instance, investigated price asymmetry in the state of Sao Paulo (SP) for ethanol and gasoline.The results favoured the existence of price asymmetry for both fuels from the wholesale to the retail market in the short run.Increases in the wholesale prices imply larger increases for the consumers.

Brazilian market of fuels
The recent history of light fuels in Brazil presents two relevant events: a) the Petroleum Law (Law 9.478/97), which broke the state monopoly in the oil production; b) the introduction of fl ex-fuel cars in 2003, allowing consumers to choose between ethanol and gasoline on every visit to the gas station to fi ll up the vehicle.
Ethanol and gasoline are not evenly consumed throughout the country.The total consumption of ethanol in relation to the total consumption of gasoline in Brazil 4 (Figure 2, dashed line) during our sample period is 0.23 on average.However, the same variable by state ranges from values around 0.5 in São Paulo to less than 0.05 in Acre and Tocantins.If we look at the more recent values in São Paulo (dark light), ethanol has achieved the same market share as gasoline (relative consumption = 1).3 (a) shows the mean of the relative consumption of ethanol by gasoline plotted by state -the relative shade indicates the intensity of the variable, with the darkest shades representing the states where the relative consumption of ethanol is lower.These differences in relative consumption are basically the effect of the relative price between ethanol and gasoline 4 Which from now on we will call only relative consumption.This measure uses consumption in barrels of oil equivalent, so the differences in energy content are already controlled. .In this fi gure, we plot the proportion of time for which ethanol is more price competitive than gasoline during the entire sample period by state.This dummy variable is 1 if the ratio of the ethanol price to the gasoline price is lower than 0.7, which is the reference to control for energy content differences between ethanol and gasoline in Brazil, and 0 otherwise.oline-C (Qgas), which are sold at gas stations. 5Gasoline prices (Pg) and ethanol prices (Pe) are the monthly weighted averages of consumer prices.The income proxy is the amount of state tax on the circulation of goods and services (ICMS, acronym in Portuguese) from the Ministry of Finance.
The correlation between the gross domestic product and the ICMS in Brazil for our sample is larger than 0.99, indicating the quality of this proxy.
The variable Fleet-e corresponds to the total number of vehicles that used ethanol along with fl ex-fuel vehicles.It will be used for the ethanol demand estimation.Fleet-g is the total number of vehicles that used gasoline plus the fl ex-fuel vehicles, and it will be used for the gasoline demand estimation.The fl eet variables are constructed from the database of the National Department of Transportation (Denatran, acronym in Portuguese).
Income and prices are the real variables adjusted using the monthly growth of the consumer price index from the Brazilian Institute of Geography and Statistics (IPCA, acronym in Portuguese), based on 1 in 2001m7.Table 2 summarizes the data set statistics.Note: Data are in logarithmic form.

Methodology: spatial models and empirical strategy
Estimating a model using panel data is indicated when there is heterogeneity among individuals (states in this case) -individual effects play an important role in the estimations.However, panel estimators also assume that cross-sections are independent from each other.
According to ALMEIDA (2012, p. 109), it is possible to test spatial effects using a scatter diagram of Moran from spatial lagged residuals.Unfortunately, it works with the alternative hypothesis that there is no spatial dependence on the way in which W (the neighbourhood matrix) is specifi ed.In addition, it does not mean that there is no spatial dependence at all, but accepting the alternative does not guarantee the absence of spatial effects.Hence, while working with panel data, it is more appropriate to use some group-wise tests, so the BREUSCH-PAGAN (1980) test will be used here. 6 The literature presents a possible solution whenever CD is confi rmed.A way of handling the problem is to use estimators consistent with CD, GLS with correction to CD and AR(1) residuals or the PRAIS-WINSTEN (1954) estimator, for example. 7Another possibility is to use the spatial econometric approach, adding spatial matrices to the model to capture these spatial effects (ALMEIDA, 2012;ANSELIN et al., 2008;SANTOS and FARIA, 2012).The spatial effects can be included in the spatial lags of the dependent variable (Y), in the explanatory variables (X) and/or in the error term (ε).Using a basic econometric model: Adding the spatial lags to the model (1), we have: where: Adding all the spatial lags, the complete model is given by: 6 It is referred to below as BP (1980).7 Both estimators are theoretically consistent in the presence of cross-sectional dependence. (1) 240 Nova Economia� v.30 n.1 2020 In equation ( 4), W1, W2 and W3 are different spatial matrices, but it is possible to consider them to be equal.Depending on which parameters are equal to zero (τ, λ and/or ρ), 8 in equation ( 4) we can have different spatial models.Table 2 presents some of these models.
The spatial lags of the dependent variable indicate that the consumption in state (i) is affected by the consumption in state (j).The spatial lags of the explanatory variables indicate that the determinants of consumption in state (i) can be affected by the explanatory variables of state (j).In addition, the spatial lags are used when the error terms across spatial units are correlated, usually indicating an omitted variable problem.
Using our variables and including spatial matrices, the equations for the ethanol and gasoline demand are: Equations ( 5) and ( 6) are used in the SAR and SDM models, and in both 8 It is also possible to have a range of models if spatial effects are considered, associated with an average spatial moving error.For more information, see ALMEIDA (2012) and FINGLE-TON (2008).
(5) of them the marginal effects represent long-run effects,9 as they do not provide short-run parameters.However, there is economic relevance to knowing both long-and short-run elasticities.Hence, in addition to the SAR and SDM models, a dynamic panel estimation is proposed here through the use of the HAN and PHILLIPS (2010) estimator.In a dynamic specifi cation, the model is represented by: Rearranging the equation, we obtain: This specifi cation allows us to divide the effects between the short and the long run and between direct and indirect effects.10Marginal effects are calculated from a matrix with partial derivatives of Y with respect to the explanatory variable of interest,11 which is called Matrix A here.
The total marginal effects are the sum of the indirect and direct effects, and they are calculated using the average of non-zero elements of Matrix A (Equation 9).The mean of the matrix trace gives the direct short-run effects, while the sum of the remaining non-zero elements gives the average indirect effects.If the specifi ed model is an SAR, the parameter τ is zero and Matrix A is simplifi ed, being represented only by its fi rst term Differentiation between short-and long-run parameters is made through the ϕ parameter (Equations 7 and 8), 12 which represents the adjustment speed.A low ϕ represents a high adjustment speed, and the short-and long-run parameters will be close.Equation (10) below shows 242 Nova Economia� v.30 n.1 2020 the long-run impact matrix: As in the short run, the long-run effects can be differentiated between direct and indirect effects, and they are calculated using the same process.
It is clear that SAR models have parameter τ equal to zero, which means that the ratio between direct and indirect effects is the same for all the explanatory variables.SDM models, however, do not present this limitation, which is the reason why, for each explanatory variable, these ratios might be different (DEBARSY et al., 2012;ELHORST, 2012;LESAGE and PACE, 2011).
Concerning the introduction of a spatial weights matrix W, many economists are "skeptical, puzzled, or both" and argue that it is applied in a "mechanical fashion" without theoretical justifi cation (CORRADO and FINGLETON, 2012, pp. 210 and 211).Secondly, critics of spatial econometrics have claimed that spatial lagged variables are inputted into models just because of the signifi cance level, without a hard decision criterion.Other usual comments have concerned sensitivity to the choice of weight matrix (W).ARBIA and FINGLETON and ARBIA (2008) highlighted the relevance of this arbitrary decision with respect to the model structure and its consequences for the model results.Hence, we will run the regressions and change W to determine whether our particular study presents substantial sensitivity to the W choice.

Results and discussion
Pesaran's CD test for each variable (ethanol and gasoline prices, income and fl eet-g and fl eet-e) indicates cross-sectional dependence (CD) for all the variables and for the OLS residuals.The Breusch-Pagan test (BP) is carried out; however, the results remain the same.To correct the CD, a row standardized queen matrix (W) is adopted for the spatial models and a GLS with AR(1) and CD corrections is estimated.For comparison purposes, an OLS is estimated.All the spatial models estimated initially use the same queen standardized matrix, but, at the end of this section, we relax it, performing the same estimator using different W matrices.
Table 3 reports the estimated parameters for the ethanol demand.The short-run parameters are estimated using OLS, GLS and HP, while the long-run parameters are estimated using the SAR, SDM and HP estimators.The sample size differences between HP and the other models are due to the lagged variable used in HP.It is worth mentioning that τ parameters are found only in Durbin models (SDM models) and that, in column 7 (Table 3), ρ is very close to zero, indicating that the indirect effects in HP-SAR will also be very close to zero.Hence, we drop these results in Table 4.
The direct effects of HP-SDM, since there is no ρ, are -2.583(ethanol price) and 3.426 (gasoline price).The indirect effects in this case are in the second part of Table 3, -0.271 (ethanol) and 0.109 (gasoline).The total effects are the sum of the indirect and direct effects, so, for gasoline, we have a direct effect of 3.426, an indirect effect of 0.109 and a total effect of 3.426+0.109.The Φ parameters estimated in HP-SAR and HP-SDM are around 0.5 (Table 3), suggesting that the long-run effects are double the short-run effects.
Both HP estimators used for the ethanol demand seem to overestimate the price and cross-price elasticities, even considering that other studies have indicated an increase in these.Some attempts are made in the direction of determining whether the unit roots play a role in these results, using Hodrick-Prescott fi lter prices, but the estimates of own-price elasticity in the ethanol demand are consistently between 3 and 4.
As previously mentioned, only the parameters found in OLS and GLS are immediately interpreted as marginal effects.Hence, the marginal effects for estimators 3-6 are presented in Table 4.The cross-price elasticity indicates that the ethanol demand is as sensitive to gasoline prices as to its own prices.This suggests that policies that aim to change the ethanol demand could effi ciently target either of the two fuels.
The marginal effect of the number of vehicles, or "fl eet elasticity", represents the demand sensitivity to changes in the number of vehicles.This total effect is between 0.8 and 1.4, considering specifi cations 3-6 from Table 4.The income elasticities are around 0.3 in the long run, considering only the SAR and HP estimators.Among the three most researched elasticities in this market (own-price, cross-price and income), the last one has the largest range of results in the literature, varying from 0.14 in the study by SANTOS and FARIA (2012) to 12.76 in the one by RANDOW et al. (2010).This large variation can be justifi ed by the different proxies used for income (per capita GDP in cross-sectional studies and electricity and taxes in panel data studies).It seems that part of the income effect is naturally captured by the fl eet increases.If we drop the fl eet from the regressions, the ethanol demand becomes income elastic, with elasticities around 1.3.The parameters for the gasoline demand are in Table 5.The explanatory variables used to estimate the gasoline demand are the same as those for the ethanol demand, with the exception of the variable "fl eet-g", which is used instead of "fl eet-e".For the gasoline demand, it is also necessary to calculate the marginal effects.However, it is important to state that parameters ρ and Φ in HP-SAR are very close to zero, indicating that the differences between direct and indirect effects and between short-run and long-run effects will both be very small.Hence, we can interpret column 7 in Table 5 as the long-run total effects of HP-SAR.The same logic can be applied to HP-SDM: all the indirect effects (measured with the interaction between τ and elasticities) are significant but very close to zero.Therefore, we report in Table 6 only the marginal effects of estimators 3-6 from Table 5, excluding HP-SAR and HP-SDM.
The price elasticity of the gasoline demand is between -1.0 and -1.3, indicating that a change of 1% in the price will be followed by a reduction in consumption from 1.0% to 1.3%.The cross-price elasticities also have the expected signal (positive), with values that are approximately one-third of the gasoline price.Hence, changes in gasoline prices will have three times greater impact than changes in ethanol prices, in line with MORIZONO et al. (2018).
The marginal effect of the number of vehicles is lower than one in the long run.This result could be caused by the fuel economy of the new cars or by different consumption profi les of the owners of the marginal cars.With respect to the income elasticity, the results indicate that gasoline is a normal good with income elasticity around 0.2.The results are lower than the previous estimates of income elasticity, but, again, there is a large range of estimates due to the use of different proxies.
The results also indicate that both demands have higher sensitivity to the gasoline price than to the ethanol price.If a policy goal is to change the demanded quantity, this result suggests that the gasoline price is the factor on which the policy should focus.On the other hand, if the government's objective is to increase the tax revenue, the focus should be on the ethanol price.
When looking at future increases in the demand for light fuels, the results indicate that, ceteris paribus, increases in the number of vehicles or in income have a greater effect on the ethanol demand than the gasoline demand.These results come from the comparison between ethanol and gasoline long-run "fl eet" elasticities and income elasticities.
The last part of the study comprehended tests to check whether the results are sensitive to a prior specifi cation of the W matrix.The W matrix defi ned here needs to be symmetric, 13 containing 729 elements (27 × 27).The fi rst kind of matrix used is a Queen-1 (Q1).In Q1, Wij = 1 if states share a common edge with each other and 0 otherwise.With Queen-2, Wij = 1 for the neighbours and for the regions that border the neighbours.There are also Queen-3 and Queen-4 matrices, but, since there are only 27 states in Brazil, it does not make sense to use matrices of orders higher than 2. The inverse distance matrix (ID) and some K-nearest neighbour matrices (K = 5, 4 and 3) are also used.For each given K, the K-nearest neighbour will have a value equal to 1, while the more distant units will equal 0. 14Using the same estimator (SAR-FE), we change only the matrices and report the marginal total effects in Table 7.As Table 7 shows, the results obtained using different spatial matrices are close.Only the SAR model is applied to the gasoline demand, and the lack of sensitivity to the W choice, as LESAGE and PACE (2011) argued, is confi rmed.

Conclusions
For both demands (gasoline and ethanol), the tests using OLS residuals indicated cross-sectional dependence (CD).To solve this problem, two dif-ferent procedures were carried out: GLS with AR(1) and estimators for CD correction, which is effi cient whenever there is CD, and a spatial queen matrix (W), which makes it possible to capture non-observed effects that are responsible for such dependence.Although these strategies achieved better results than the standard OLS, both failed to reject the null hypothesis of the Breusch-Pagan (BP) test.15There were no surprises with the parameters: the own-price elasticity was negative, and the cross-price, income and "fl eet" elasticities were positive.The results also indicated higher long-run parameters than shortrun ones for the ethanol demand, while, for the gasoline demand, the differences between short-and long-run parameters were insignifi cant.
The results also indicated that the ethanol demand is price and crossprice inelastic in the short and long runs, in line with the Brazilian empirical literature (Table A -Appendix).The gasoline demand is less sensitive to prices than the ethanol demand, which might suggest that higher volatility can be expected in the ethanol market.
The ethanol parameters were more elastic than the gasoline parameters, considering the fl eet and income parameters.Hence, increases in fl eet or income have a greater impact on the ethanol demand than on the gasoline demand.Even though LESAGE and PACE (2012) claimed that the sensitivity of marginal effects to the neighbourhood matrix (W) is a myth in spatial econometrics, other specifi cations of W were tested and the results indicated that our estimates did not present high sensitivity to this choice.
The literature regarding spatial econometrics is still expanding, and it is expected that more accurate tests will be available to identify individual effects in panels with CD.It is important to highlight our novelty of including dynamic spatial estimators for the light fuel market in Brazil.However, the dynamics among variables here were still limited, and the ratio between short-and long-run effects was the same for all the explanatory variables.If Φ was 0.5, for example, the values of the long-run parameters would be double those of the short-run parameters for all the variables, but there is no theoretical or empirical guarantee for that.
The use of ethanol as an alternative fuel in the medium run is reasonable in producing states, but distance (and logistics) could be a problem.

Figure 1
Figure 1 Ratio between ethanol and gasoline prices

Figure 2
Figure 2 Relative consumption, ethanol by gasoline

Figure
Figure3(a) shows the mean of the relative consumption of ethanol by gasoline plotted by state -the relative shade indicates the intensity of the variable, with the darkest shades representing the states where the relative consumption of ethanol is lower.These differences in relative consumption are basically the effect of the relative price between ethanol and gasoline

Figure 3
Figure 3 The relative consumption of ethanol by state (a) and The proportion of time or which it is worthwhile for fl ex-fuel car owners to buy ethanol rather than gasoline (b) , ** and *** indicate the signifi cance levels of 10%, 5% and 1%, respectively.245 v.30 n.1 2020 Nova Economia�

Table 1
Summary statistics

Table 2
Selected types of spatial models

Table 3
Estimates for the ethanol demand

Table 4
Marginal effects for the ethanol demand (long run)

Table 5
Estimates for the gasoline demand

Table 6
Marginal effects for the gasoline demand (long run)