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The share of diesel-fueled passenger cars in the total car stock has continuously increased during the last decade especially in Europe. Previous studies on gasoline demand have not accounted for this fact by relating gasoline consumption to the total number of cars. This paper argues that estimates based on such a misspecified demand equation are biased owing to the related omitted variable problem. We thus expect estimates of income, price and car ownership elasticities reported in recent studies covering gasoline demand to be overstated. In particular, the elasticity of gasoline consumption with respect to car ownership is overestimated when no distinction is made between gasoline and diesel-powered cars.

To our small 14x15 panel data set we applied 9 common dynamic panel estimators. Three of the four IV/GMM estimators considered conveyed unreliable estimates. The quite good performance of the Andersen-Hsiao (1982) estimator in small samples32could not be affirmed by our study. The Blundell-Bond (1998) estimator suffers from a too large set of instruments relative to the sample size. Only the one-step Arellano-Bond (1991) estimator seems to perform well in our small sample setting. Our results show that good candidates for estimating small dynamic panel data sets with a dynamic coefficient close to one are the standard Within estimator, its bias-corrected version LSDVc, GLS with heteroscedastic, cross-sectional correlation and/or AR(1) error structure, and the Arellano-Bond estimator FD-GMM.

The qualitative results of the estimation of the gasoline demand equation correspond to those obtained by previous studies like Baltagi and Griffin (1983, 1997) and Baltagi et al. (2003). The income elasticity is positive, the price effect is negative, and the effect of increased car ownership on gasoline consumption is negative. Comparing the Within estimates of these studies, however, the coefficient estimates in this paper are found to be somewhat lower in absolut terms, depending on the specified model and the included countries, as well as on time period. This is accredited to the omitted variable bias 32

See for instance Kiviet (1995) and Judson and Owen (1999).

effect, from which the estimate of the gasoline-fueled cars per driver variable especially suffers. We interpret its low value together with an inelastic short-run gasoline price response as such that car owners react to increasing fuel prices by gradually replacing their gasoline-powered cars with diesel-powered ones. In most European countries such a shift towards diesel cars can be observed since the 1990s. When fuel supply tightens, the income and price elasticities of diesel consumption should therefore display relatively more elastic responses than in the gasoline case. Exactly this can be observed in the estimation results.

Acknowledgement:

I would like to thank the following institutions for kindly supplying me with data: ARB ¨O - Auto-, Motor- und Radfahrerbund ¨Osterreichs (AT); ¨OAMTC - ¨Osterreichische Automobil-, Motorrad- und Touring Club (AT); FVMI-Fachverband der Mineral¨olin- dustrie ¨Osterreichs (AT); DESTATIS - Statistisches Bundesamt Deutschland (DE); DBI - De Danske Bilimportører (Danish Car Importers Association); DGT - Direcci´on Gen- eral de Tr´afico, Servicio de Estad´ıstica (ES); Tilastokeskus - Statistics Finland; CCFA - Comit´e des Constructeurs Fran¸cais d’Automobiles (FR); ACI - Automobile Club d’Italia; ANFIA - Associazione Nazionale fra Industria Automobilistiche (IT); CBS - Centraal Bureau voor de Statistiek (NL); SSB - Statistik Sentralbyr˚a (NO); SCB - Statistiska Centralbyr˚an (SE); DfT - Department for Transport (UK).

A

Appendix

A.1 Data description

The data framework originates from EUROSTAT. We completed or substituted individ- ual items of data whenever necessary and available from national statistics agencies and ministries as well as local automobile associations. Due to data limitations, Greece and Portugal were excluded from the panel set. The final balanced panel comprises data for the period 1990 till 2004 from 14 European countries: Austria (AT), Belgium (BE), Switzerland (CH), Germany (DE), Denmark (DK), Spain (ES), Finland (FI), France (FR), Ireland (IE), Italy (IT), the Netherlands (NL), Norway (NO), Sweden (SE) and the United Kingdom (UK).

The stock of passenger cars is given as an annual average or for a certain point during the year, mainly per end of December. The official data of the car series for Germany suffer from breaks due to the German reunification in 1991 and a switch in the reference date in 2001. We reconstructed our time series out of data from DESTATIS and EUROSTAT, smoothing out the switch and updating the series backwards from 1991 using the growth rates of the original series.

As a proxy for the average annual number of drivers within a country we used end- of-year numbers from EUROSTAT population data for the 18 to 69 age group. The use of the number of drivers instead of the country’s total population avoids demographic effects.

Annual data series for purchasing power parity (P P P ) in US dollars and real GDP adjusted by P P P , basis 2000, for each investigated country in US dollars were taken from the OECD Economic Outlook No. 76 and Annual National Accounts.

For annual gasoline and diesel consumption we used EUROSTAT-data on final energy consumption of road traffic in thousand tonnes per year.

EUROSTAT also provided data on gasoline and diesel retail prices per 100 liters inclusive of taxes, averaged per year. In order to account for the gradual displacement of leaded gasoline fuel by unleaded (the first showing a price mark-up) in most European countries during the early 1990s, we constructed the gasoline price series by means of a stepwise changing weighted average of the two fuel sorts from 1990 to 1994. By the end of 1999, leaded fuel had been withdrawn in most European countries.

The relative fuel prices were calculated with the help of national consumer price indices (CPI), basis 1995, retrieved from AMECO, the annual macro-economic database of the European Commission’s Directorate General for Economic and Financial Affairs (DG ECFIN). Note that we do not adjust relative fuel prices for PPP, as we presume

that consumer decisions are affected by local prices rather than by those that prevail in a reference country.

Out of this we constructed the series for estimation: gasoline consumption per total number of cars in logarithm ln(GAS), gasoline consumption per gasoline-powered car in logarithm ln(GASG), diesel consumption per diesel-powered car in logarithm ln(GASD), PPP-adjusted real output per capita in US$ in logarithm ln(Y ), number of total cars per capita in logarithm ln(CAR), number of gasoline-powered cars per capita in loga- rithm ln(CARG), number of diesel-powered cars per capita in logarithm ln(CARD), the relative price of gasoline to other goods ln(P G), and the relative price of diesel to other goods ln(P D).

A.2 Omitted variable bias

Here, we illustrate the omitted variable bias effect of the Within estimator due to the incorrect use of the number of total passenger cars C instead of gasoline-powered cars CG in the variables gasoline consumption per gasoline-powered car GASG and gasoline cars per adult CARG in the gasoline demand specification given in equation (7).

First, we define Dt= Ct/CGt capturing the growth in the numbers of diesel-fueled

passenger cars over time as the ratio between total number of cars and number of gaso- line passenger cars. In other words, D is the inverse of the share of gasoline-powered cars. Substituting CG for C/D in the variables GASG and CARG in equation (7) and rearranging the terms, one gets:

ln GASi,t = α ln GASi,t−1+ β ln Yi,t+ γ ln P Gi,t+ δ ln CARi,t+ µi+ i,t+

φ ln CARDi,t+ α ln Di,t−1− (1 + δ) ln Di,t (9)

where the variable GAS is gasoline consumption per total cars. Comparing equation (5) with (7) one notes that the term in the second line of equation (9) captures the effect of the omitted variables CARDt and D, hidden in the dependent variable as well as in

the two regressors GASt−1 and CAR, total cars per driver. Note that (9) differs from

(7) by a slight change in the coefficient notation.

Further, applying within transformation in order to eliminate the individual fixed effects, stacking the observations over time and across countries, and collating the loga- rithmized exogenous variables into the N T xK matrix ˜X = [ eY...gP G... gCAR] yields:

˜

with the coefficient vector κ = (α, β, γ, δ)0, the lag-operator L, the N T x1 matrices ˜

y = (INN(IT − iTi

0

T/T ) ln GAS, ˜ and ˜D, and the N T x(K + 1) matrix ˜W = [˜y−1... ˜X],

respectively.

Applying OLS to the above equation without the last term yields the Within or least-square-dummy-variable estimator LSDV: ˆ κLSDV = ( ˜W0W )˜ −1W˜0y˜ = κ + ( ˜W0W )˜ −1W˜0˜ + ( ˜W0W )˜ −1W˜0 h φ gCARD + (αL − δ − 1) ˜D i (11) with the true parameters κ. Equation (11) implies that the LSDV estimator is biased due to the so-called Nickell bias given by the second term on the RHS, and in addition through the correlation of the omitted variablesCARD and ˜g D with the regressor matrix

˜

W represented by the third term.

Nickell (1981) examines the bias of the LSDV estimator with exogenous regressors for N → ∞ and finite T :

plim_{N →∞}( ˆα − α) = (plim_{N →∞}1 Ny˜ 0 −1M_X˜y˜−1)−1plimN →∞ 1 Ny˜ 0 −1˜ (12) and

plim_{N →∞}( ˆβ − β) = −plim_{N →∞}[( ˜X0X)˜ −1X˜0y˜−1]plimN →∞( ˆα − α) (13)

with the projection matrix M_X˜ = I − ˜X( ˜X0X˜0)−1X˜0 and β = (β, γ, δ)0. The bias of α

given in equation (12) is of order O(T−1) and negative for positive values of α. For the AR(1) panel model the simplest bias approximation is given by33

− 1 + α

T − 1, (14)

Hence, the absolute value of the bias in estimating α increases with α and gets quite large as α → 1. The presence of exogenous regressors influences the bias given by equation (12) and (13). Phillips and Sul (2004) proved that the inconsistency of the parameter estimates is decreased in absolute values when exogenous variables are present. This result is in contrast to Nickell (1981). Also, the bias on ˆβ depends on the relationship between the transformed exogenous variables and ˜y−1. If there is positive (negative) cor-

relation between the projected variables, then equation (13) indicates that its coefficient will be upward (downward) biased. For our data set, this means that the Nickell-bias 33

See Nickell (1981), formula (19). With α = 0.9 and T = 15 this amounts to -0.136.

induces the estimated income, price and car ownership elasticities in the demand models of equations (7) and (8) to be over-, under- and over-estimated, respectively, in absolute terms.

Kiviet (1995) derived approximation formula for the bias of the LSDV estimator with strictly exogenous regressors but when both N and T are small. Subtracting the approximated bias from the LSDV estimate one arrives at the corrected LSDV estimator which performed well in simulation studies34. This estimator has also been applied to our data set (see section 5).

The following discusses the effects of neglecting the diesel car series on the parameter estimates, as it is stated in the text. Extending the third term on the right hand side of equation (11), the omitted variable bias of the estimates in the specific gasoline demand equation (9) is given by:

φ( ˜W0W )˜ −1W˜0CARD + α( ˜g W0W )˜ −1W˜0D˜₋₁− (1 + δ)( ˜W0W )˜ −1W˜0D˜ (15) To size up the direction of the expected bias of the estimated coefficients in our specific data set we have to evaluate the covariances between the omitted variables and the corresponding transformed regressor. For instance, in equation (15) the first element of the last term is equivalent to cov(M_X˜y˜−1, M_X˜D)/var(M˜ _X˜y˜−1) = −0.54, with the

projection matrix M_X˜ defined above. Because the true value of δ probably lies around

-0.2, the bias of the estimated coefficient α, which is due to the omission of ˜D in the demand equation, is positive. Calculating the empirical counterparts of all expressions in (15) along the same lines and assuming true values for α = 0.8 and φ = −0.05, we are able to evaluate the direction of the omitted variabel bias for each estimated coefficient. Depending on the resulting sign this bias augments or reduces the Nickell bias given by equation (12) and (13).

The omitted variable bias of the lagged dependent variable coefficient ˆα is small and positive, and thus moderately mitigates the negative Nickell bias given in equation (14). The omitted variable effect by itself results in an overestimation of ˆα. In the case of the coefficient estimate of the gasoline price variable, the low and negative omitted variable bias only marginally reduces the Nickell bias and hence can be ignored. In contrast, the omitted variable bias causes a considerable overestimation in absolute terms of the negative coefficient of the variable cars per driver gCAR and to a lesser extent that of the positive coefficient of the income variable ˜Y . Consequently, this augments the negative and positive Nickell bias of ˆδ and ˆβ, respectively.

Alternatively, the extent and direction of the omitted variable bias and the small sample bias in dynamic panels can be read off from the Within and corrected LSDV co- efficient estimates of the gasoline demand equations (5) and (7). Given that the LSDVc estimator fully corrects for the Nickell bias, the latter can be extracted from the differ- ence between the Within and LSDVc estimates of the correct specified gasoline demand equation (7). For instance, the difference in the estimates of the lagged dependent vari- able yields -0.075 (see Table 3), which is nearly half of the Nickell bias calculated by the approximation formula in equation (14). The pure omitted variable bias is obtained by taking the differences between the LSDVc estimates of the equation (5) and (7). For the coefficients α, β, γ and δ one obtains 0.042, 0.166, -0.007 and -0.412, respectively (see Table 2 and 3). Thus, by not taking into account the recent strong development of the diesel-fueled cars in the common dynamic gasoline demand equation, the resulting omitted variable bias causes an overestimation in absolute terms of all coefficient esti- mates. The elasticity of the car fleet per driver is in particular affected, whereas that of the gasoline price is negligible. Further, the omitted variable bias mitigates the Nickell bias in the case of the lagged dependent variable. In contrast, the overall bias of the car fleet elasticity is considerably aggravated by its omitted variable bias.

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Author: Markus Pock

Title: Gasoline and Diesel Demand in Europe: New Insights Reihe Ökonomie / Economics Series 202

Editor: Robert M. Kunst (Econometrics)

Associate Editors: Walter Fisher (Macroeconomics), Klaus Ritzberger (Microeconomics) ISSN: 1605-7996

© 2007 by the Department of Economics and Finance, Institute for Advanced Studies (IHS),