how to estimate gasoline price elasticities of automobile travel demand julian dieler a), frank...

How to Estimate Gasoline Price Elasticities of Automobile Travel Demand

Julian Dieler a), Frank Goetzke b) and Colin Vance c)

a) Ifo Institute for Economic Research at the University of Munichb) University of Louisville

c) RWI Institute for Economic Research Essen

33rd USAEE/IAEE North America Conference October 27, 2015 / Pittsburgh

Motivation

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• The magnitude of price elasticities of travel demand/fuel demand is broadly discussed in the literature

• Implications for the policy debate: CAFE standards vs. fuel taxes

• Discussion is mainly about the specification and identification:

- Endogeneity of the price- Differentiation between tax and price elasticity

BUT: There is only little to no discussion about the econometric methodology

• The methodology mostly applied in this literature: Estimating the log-linearized demand function with least squares estimators

Dieler How to Estimate Gasoline Price Elasticities of Automobile Travel Demand

3

The Log of GravitySilva and Tenreyro, The Review of Economics and Statistics (2006)

• Challenge the simple log-linearization of multiplicative models

• Log-linearization causes two problems:

- Jensen’s inequality: Most probably leads to endogeneity of the covariates

- Problems at dealing with zero observations of the dependent variable


Motivation

4

1. Theoretical background on problems of log-linearization

2. Alternative estimation methods

3. Case study: German Mobility Panel

4. Model comparison tests

5. Results

6. Conclusion


Outline

5

Demand for kilometers traveled:

Problem of pseudo endogeneity:

is a function of the second order moments of its distribution

• When the depends on any of the explanatory variables the OLS exogeneity assumption is violated

• This feature is the case with many datasets

The OLS estimator for is biased



: kilometers traveled : constant : gasoline price : error term : elasticity

Assumption OLS.1:

6

Log-transformed demand function:

Problem of zero-observations for the dependent variable:

Methods to deal with zero-Observations

• Drop zero observations information loss

• Add an infinitesimal small constant to all observations:

Biased estimate of



7

1) OLS with Inverse Hyperbolic Sine Transformation

Solves zero problem, but not pseudo-endogeneity problem of log linearization

2) Pseudo Poisson Maximum Likelihood (PPML) regression• Estimates demand in its multiplicative form• Allows for zero observations as dependent variable as it is

numerically identical to Poisson regression• Is a non weighted version of the NLS regression• Assumes: with

3) Negative Binomial regression• A poisson mixture model for overdispersed data ()• More efficient for than Poisson but inconsistent otherwise



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4) Two-Part models• Accommodate the idea of modeling travel demand as a two-step

process (buying a car/driving it)• Binary first step consists of a Probit modela) Hurdle models

Second step is modeled as a truncated-at-zero regression model (OLS/Poisson)

b) Zero-inflated models- Also allow for zero-observations on the second stage- Second step consists of count-data model like Poisson or NB

5) Heckit model• Equal to the Hurdle model with the difference that Heckit controls

for a potential correlation of the errors from the two steps



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German Mobility Panel


3. Case study

050

010

0015

00Fr

eque

ncy

0 50 100 150 200daily kilometers

• 1997 – 2013• Rotating panel of

1500 households• Each household stays

in the panel for 3 years

• Variables of interest:- daily kilometers

driven- local gasoline price- monthly income

• N = 4891Summary statistics

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Model Confidence Set (Hansen et al. 2011)• Determines the best performing model given a certain dataset

• The MCS procedure:1. Definition of a set of models to be compared2. Test of the null hypothesis of equal predictive ability (EPA) of the

models3. If the null hypothesis is rejected, the worst performing models are

eliminated from the comparison set and the null hypothesis is tested again. This process is repeated until the null hypothesis is accepted und thereby the MCS is determined.

• Criteria for the predictive ability are loss functions:1. Absolute deviance of the predictions from the observations2. Squared error



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Leave-One-Out Cross Validation (LOOCV)• Resampling method:

1. Take a subsample of

2. Fit the model to the subsample and use the fitted model to predict the response for the left-out observation

3. Repeat 1. and 2. for all observations

4. Calculation of MSE of the predictions

• LOOCV results in another indicator for the goodness of fit of the models



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Model Selection Test

Marginal Effects


5. Results

Variables OLS OLS IHS PPML Hurdle OLS

Hurdle Poisson

Heckit NB ZIP ZINB

Fuel price -0.340* -0.718** -0.457** -0.588* -0.343* -0.342* -0.477** -0.343* -0.408**Income (real) 0.164** 1.156** 0.514** 1.065** 0.456** 0.169** 0.533** 0.456** 0.446**

* p<0.05; ** p<0.01

Model Confidence Set Robustness checkLoss function: LOOCV MSE

Model squared error absolute valueOLS 7 7 6OLS IHS 9 9 9PPML 4 4 4Hurdle OLS 8 8 8Hurdle Poisson 1* 1* 1Heckit 6 6 7NB 5 5 5ZIP 2* 2* 2ZINB 3 3* 3

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• Theory predicts the log-linear model estimated by OLS to be biased when the variance of the error depends on the covariates.

• We present alternative models which do not suffer from this problem and model selection tests to compare the goodness of fit of the different models.

• Applying the models to a German driving survey we find that the log-linear model’s performance is among the worst. Best performing model in our application is the Hurdle Poisson model.

• It is worth to compare the goodness of fit of different econometric models to the data at hand, as the elasticity estimates differ quite substantially (-0.340 -0.718 price elasticity)


6. Conclusion

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A.1 Summary statistics

MOP (Germany)


Appendix

Variable Variable definition Mean Std.Dev. Min MaxDaily kilometers Daily kilometers driven in km on

average in the observation period28.43 24.57 0 202.6

Fuel price Real fuel price in € per liter 1.389 0.134 1.085 1.687

Income (real) Real net monthly household income in €

2122 961.2 236.5 4376

Household size Number of people living in the household

1.863 0.967 1 7

Employed 1 if person is employed in full- or half-time job

0.487 0.500 0 1

N = 4891

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A.2 Regression results


Appendix

Variables OLS OLS IHS PPML Hurdle OLS

Hurdle Poisson

Heckit NB ZIP ZINB

Fuel price

-0.340* -0.718** -0.457** -0.339* -0.256* -0.342* -0.477** -0.256* -0.322*(0.134) (0.267) (0.146) (0.133) (0.126) (0.134) (0.163) (0.126) (0.128)

Income (real)

0.164** 1.156** 0.514** 0.164** 0.186** 0.169** 0.533** 0.186** 0.176**(0.034) (0.071) (0.039) (0.034) (0.034) (0.037) (0.050) (0.034) (0.032)

Household size

0.158** 0.622** 0.185** 0.157** 0.064* 0.161** 0.267** 0.064* 0.087**(0.032) (0.065) (0.037) (0.032) (0.032) (0.033) (0.038) (0.032) (0.031)

Employed

0.327** 0.170** 0.256** 0.326** 0.287** 0.326** 0.272** 0.287** 0.289**(0.029) (0.059) (0.033) (0.029) (0.028) (0.029) (0.033) (0.028) (0.027)

Constant

1.940** -5.617** -0.665* 2.634** 2.015** 1.897** -0.861* 2.015** 2.095**(0.250) (0.519) (0.285) (0.249) (0.247) (0.278) (0.370) (0.247) (0.237)

N 3968 4891 4891 4891 4891 4891 4891 4891 4891 AIC 7991.1 17946.1 114805.5 11859.5 72284.2 11894.7 41884.9 72284.2 38221.8BIC 8022.5 17978.6 114837.9 11924.5 72349.2 11972.7 41923.9 72349.2 38293.3

* p<0.05; ** p<0.01

how to estimate gasoline price elasticities of automobile travel demand julian dieler a), frank...

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