Estimating confidence intervals for willingness to pay measures: comparisons and extensions

1. Estimating confidence intervals for willingness to pay measures: comparisons and extensions GattaV.a, MarcucciE.a, ScacciaL.b a DIPES/CREI, University of Roma Tre b DIEF, University of Macerata "Transport, Spatial Organization and Sustainable Economic Development” - Venice - September 18-20, 2013 XV Conference of the Italian Association of Transport Economics and Logistics

2. Outline • Motivation and research goals • Methods • Contributions to literature • Data • Test settings • Performance indicators • Results and discussion • Conclusions and future research

3. Motivation and research goals (I) • Motivation • WTP calculation is a core issue in transportation economics • WTP measures are estimates with a given (not known) probability distribution βx/βc► point estimate is not enough ► confidence interval (CI) need to be calculated • Different methods to construct CI can be adopted • Research goals • Compare alternative CI estimation methods (already used in the literature and newly proposed) in the case of MNL specification • Provide motivated suggestions concerning which method to use given different context scenarios.

4. Motivation and research goals (II) The derivation of reliable WTP measures is relevant for: • project evaluation • regulatory policies • price and income elasticities in demand systems • travel demand • time reliability • mode/path choice • service quality evaluation • etc…

5. Methods (I) • Delta method • The most frequently used, WTP est is asympt. ~ N(~ distributed • Assumptions • Pros:… • Cons:… • Not only Delta method but also…

6. Methods (II) • Approach • Approximation versus Simulation • The distinction rests on the use of either the analytic or simulated distribution of the parameter estimator. • Family • Pivotal (in which CI is constructed in the usual way, using a pivotal function, except that the quantiles of known distributions, e.g. Normal, Student's-t, are replaced by their bootstrap estimates). • Non-pivotal (which all originate from the percentile method as successively more complex analytical corrections for this). • Test-inversion (which exploits the duality between confidence intervals and tests).

7. Methods (III) • Scheme (lo faccioio)

8. Contributions to the literature (I) • The paper contributes in three different ways to the extant literature: • provides a comprehensive illustration and systematic comparison for the methods used in choice modeling literature; • proposes, borrowing from different research contexts, additional methods; • introduces new performance indicators for evaluating the methods considered.

9. Contributions to the literature (II) • Scheme (lo faccioio)

10. Data • Simulated data • … • Real data • TPL… • Airport…

11. Test settings • … • …

12. Performance indicators • … • …

13. Results and discussion (I) • Output

14. Results and discussion (II) • General considerations: • …

15. Conclusion • Final remarks • Different methods to compute CI for WTP measures were compared • All the scenarios considered revealed a certain degree of skewness in the distribution of WTP estimates. • Delta method and bootstrap normal-theory method produce, by construction • Future research • …

16. Thanks for your attention! • Questions? • Questions? • Questions? • Questions? • Questions?

17. WTP in a MNL framework • Diciamoqualcosasulrapporto di due coefficientistimati con la massimaverosimiglianza??? • …